RESOURCE MANUAL

BO213 REVISION DATE : 06/16/04 1

RESOURCE MANUAL

ACCURACY

When making measurements or collecting data one hopes to obtain estimates which approach the true value of the unknown. An accurate measurement is one that does this. It is important to note, however, that accuracy is not the same thing as precision (see PRECISION). An accurate measurement is not necessarily precise.

ASSUMPTION

Basic concepts which are generally accepted are a common type of assumption made by people in everyday life. This is also true in science. However, frequently when designing an experiment you must decide that some factors in your experiment must be accepted on faith in order to test other factors. In other words, you believe that some factors will not influence the experiment.

Frequently, advances in science have occurred when basic assumptions have been tested and found not to be valid. For instance, for years it was thought that the only way to speed up flowering of plants was to give them extra fertilizer, cold temperatures, and more light. In the

1920's two scientists decided to test the role of light in flowering. They found that many plants actually require shorter light periods to promote flowering.

BUFFER The purpose of a buffer is to resist pH change in a solution and thus maintain the pH under a wide range of conditions. Most cells operate effective in the pH range of

6 to 8, however, many common buffers have problems in this range. For instance, phosphate can participate in or inhibit metabolic reactions. Borate can complex many metabolites and carbonate has limited solubility. A wide range of buffers are available so the investigator should choose one that best fits the requirements of the experiment.

Below are formulas for several common buffers. Directions are given for preparing stock solutions which are then combined in varying proportions to produce a buffer of the desired pH.

CITRIC ACID BUFFER (McIlvaine)

Stock Solution A 0.1 M Citric Acid (anhydrous)

(19.212g Citric Acid in 1000ml H20)

Stock Solution B 0.2M Disodium Phosphate

(28.392g Disodium Phosphate in 1000 ml H20) ml A

19.6

17.76 ml B

0.4

1.24 pH

2.2

2.4 ml A

9.28

8.85 ml B`

10.72

11.15 pH

5.2

5.4

17.82

16.83

15.89

15.06

14.3

13.56

12.9

12.29

2.18

3.17

4.11

4.94

5.7

6.44

7.1

7.71

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

8.4

7.91

7.37

6.78

6.15

5.45

4.55

3.53

11.6

12.09

12.63

13.22

13.85

14.55

15.45

16.47

5.6

5.8

6.0

6.2

6.4

6.6

6.8

7.0

1


11.72

11.18

10.65

10.14

8.28

8.82

9.35

9.86

4.2

4.4

4.6

4.8

2.61

1.83

1.27

0.85

17.39

18.17

18.73

19.15

7.2

7.4

7.6

7.8

9.7 10.3 5.0 0.55 19.45 8.0

CARBON DIOXIDE

Carbon dioxide, CO

2

, is one of the products of cellular respiration. Because it is a gas, whose volume is easily measured, production of CO

2

is frequently used as an indicator of the rate of respiration. Similarly, CO

2

is one of the reactants in photosynthesis, therefore, decrease in the volume of this gas can be used to indicate the rate of photosynthesis.

Indicating CO

2

Change

In aquatic organisms, changes in CO

2

can be monitored by the pH of the solution. Carbon dioxide dissolves in water to form carbonic acid, CO

2

+ H

2

O



H

2

CO

3

. Therefore, as CO

2

is released by organisms during respiration, it dissolves in water, forming a weak acid and thus lowering the pH.

A simple way to indicate if either photosynthesis or respiration is occurring is to place some tissue in an indicator dye solution and watch for a color change. Phenol Red is such an indicator.

In a water solution with a pH >8.4 it will be red in color. Add enough of the dye powder to make a red solution. As the pH shifts to more acidic, the color changes to orange and finally yellow when it reaches levels <6.8. You can demonstrate this by blowing bubbles through a straw into a glass of red solution. It will gradually change to yellow as you continue to blow.

-Measuring CO

2

Levels

The simplest way to measure CO

2 changes in an aqueous solution is to measure pH change using pH paper or a pH meter (see pH, MEASURING pH).

It is a more involved process to determine changes in CO

2

in a nonaqueous system. You must either set up two respirometers, similar to the one diagrammed below, or run a single respirometer twice. Basically, a respirometer places living tissue (or organisms) inside a closed system and measures the change in gas volume within the system. In the diagram below, if there is a net decrease in gas volume (more O

2

is used than CO

2

is produced), the water drop in the pipette will be drawn towards the test tube. On the other hand, if more CO

2

is being produced than O

2

is being consumed, the net volume of gas inside the system will increase and the water drop will be forced towards the open pipette end. If there is no net change, the water will not move.

One tube must be set up with KOH (or some other strong base like NaOH) in the bottom to react with CO

2

to form K

2

CO

3

and water, 2KOH + CO

2



K

2

CO

3

+ H

2

O. In this tube you can directly measure how much oxygen is consumed because no CO

2

is released into the enclosed atmosphere. A second tube is run without KOH to determine any net change between O

2 consumed and CO

2

released. CO

2

is determined by the difference between the two tubes.

Technically, a third tube should also be set up as a control. What should it contain? What would it be controlling for?

To use this setup, assemble the respirometer with the tissue or organisms inside the vessel or tube on the bottom. Be sure that the valve is open from the tube to the pipette ( the red arrow on the valve handle points in the "open" direction). Allow the apparatus

2

BO213 REVISION DATE : 06/16/04 3 to equilibrate for a few minutes, then draw a bead of water into the pipette by holding the open end under water and drawing a cm or so of water into the pipette by withdrawing the syringe plunger.

Lift the end of the pipette out of the water and continue to draw in on the plunger until the bead of water is near the middle of the pipette. Begin readings by noting the position of one end of the meniscus bead and making periodic measurements of its change.

Note: the apparatus shown uses a valve assembly and a 1-hole stopper. A 2-hole stopper can be used with the syringe in one hole and the pipette in the second.

If the meniscus is moving off scale, quickly reposition it by pushing or drawing on the syringe plunger to move the water bead in the appropriate direction. Be sure to note the beads position prior to readjusting and the amount of adjustment made.

CELL

This description introduces the eukaryotic cell, as seen with a light microscope. The eukaryotic cell is generally what is thought of when the term cell is mentioned. Eukaryotic means with a

"true" nucleus; eukaryotic cells are the typical cells of which most species of living things are composed. (The exceptional cases, Bacteria and Blue-green algae, are prokaryotic .) The protoplast is the "living stuff" of the cell; it consists of the nucleus and the cytoplasm . The nucleus is a large, often spherical organelle which contains the hereditary information of a cell.

One or more nucleoli are usually visible in the nucleus. During the cell division, chromosomes will also be visible in the nuclear region. The cytoplasm contains a number of smaller membrane bound organelles including: plastids (e.g. chloroplasts , chromoplasts, and leucoplasts), mitochondria and dictyosomes or Golgi . In plant cells one or more vacuoles , filled with cell sap may occupy most of the interior of the cell. Plant cells are also distinctive because of the outer cell wall . The cell wall is a non-living secretion of the protoplast consisting of two or more distinct layers. The cytoplasm may also include numerous non-living particles such as starch grains and crystals . In addition there are many other smaller organelles and membrane systems, referred to collectively as ultrastructure , which are not visible with the light microscope.

During some of your investigations you will probably want to examine living cells, therefore it will first be necessary to learn different preparation techniques. The most common and useful techniques are outlined below.

-Techniques for Examining Living Cells

Hand Sectioning

Hand sectioning is a rapid way to obtain information about the

Make a Hand Section cells comprising relatively firm tissues. Your early attempts may not produce perfect results, but even your mistakes will help to illustrate the three-dimensional relationships in the materials studied, and with practice excellent results may be obtained.

Select an appropriate specimen, a new razor blade, and prepare a small dish of water.

3

Make an Epidermal Peel


Hold the part to be sectioned firmly between your thumb and index finger. Small or fragile parts may be sandwiched between pieces of potato or carrot.

Expose fresh tissue by making a preliminary cut in the plane of the sections you eventually want to examine. This and subsequent cuts should be made by slicing (using as much blade surface as possible) toward you.

Quickly make a series of sections trying to make each as thin as possible. Place each section in your dish of water. Although the ideal hand-section should include the entire part, keep the pieces too - they frequently offer the thinnest pieces of tissue.

Select the thinnest sections for examination - flat toothpicks make good section lifters.

Making a Water Mount

Place a drop of water on a slide and add the specimen to be examined.

Holding a coverslip between your thumb and index finger, touch one edge to the slide and bring it in contact with the water drop.

Make a Hand Section

Using a dissecting needle or pencil, slowly lower the coverglass to the slide thus preventing air bubbles from being trapped around the specimen.

Excess water can be blotted using a paper towel. Additional water may be added by placing a drop at the edge of the coverslip.

To change solutions under a coverslip, place a drop or two of the new solution at one edge of the coverslip and use a paper towel at the opposite edge to blot up old solution. The blotting action will draw new solution under the coverslip. This also works for drawing stain under a coverslip.

Making Epidermal Peels

Single layers of epidermal cells, the outer "skin" of plant parts, can easily be obtained from thick, fleshy plant organs using the following procedure:

Break the tissue in half (a shallow cut through the opposite side from the one to be examined will help) so that only the epidermis connects the two pieces. (See Figures)

Gently pull one half down the side of the other so that the

Make an Epidermal Peel epidermis is pulled away from the tissue of the latter.

Lay the exposed epidermis on a drop of water and cut away the remaining tissue.

Make a water mount of the epidermal strip.

Making Epidermal Scrapes

Individual cells, and small groups of cells, lining animal organs may be obtained by scraping the surface with a scalpel, razor, or even a wooden toothpick. Scrape the tissue to be examined, then

4

BO213 REVISION DATE : 06/16/04 5 rinse the scraper in a drop of water on a microscope slide. Add stain, if desired, a coverslip, and examine.

CONTROL

When designing an experiment you want something to compare your results against - this is the control. For instance, if you are interested in the effect of a particular color of light on the rate of photosynthesis, you would design an experiment using particular colored light filters. As controls you would used white light (all colors combined) and complete dark (no light). By comparing your experimental results against the controls, you would be able to determine if a particular color had any effect. When designing your experiment, be sure to keep all variables constant, except the one you are interested in examining. For instance, in an effect of light quality (color) experiment, all treatments, including the control, would be run at the same temperature, with the same amount of nutrients, etc.

DEDUCTION

Deduction is a conclusion based on reasoning from a general case to specifics. Conclusions based on scientific experiments are examples of deductive reasoning. The lay public usually associates the scientific method exclusively with deductive reasoning, proving hypotheses, and discovery of "facts" (but, see HYPOTHESIS and INDUCTION).

DEPENDENT VARIABLE - (see VARIABLE).

DILUTION – (see PIPETTES AND PIPETTING)

ERROR

This term has a common usage which is equally applicable in biology -- making a mistake. In science, however, there are other, more specific definitions. When analyzing the results of an experiment, we are interested in the experimental error - that error due to the specific design of the experiment or the equipment used. For instance, if we are using a thermometer to record temperatures during an experiment, and the instrument was out of calibration, our results will be consistently in error. Another example of experimental error would arise if different members of a group make successive readings of an instrument and they do not read consistently. For instance, one person may misread the meter by not viewing it direct on while another person may round off readings. A third person may interpolate (estimate a fraction between two numbers on the scale) to one additional significant figure, while a fourth may interpolate two additional significant figures. When the data from this group is pooled, there will be an inherent experimental error due to the different instrument reading techniques of the individual group members. Additional errors commonly encountered in biology have to do with statistical testing.

We use statistical tests to help us determine if observed results are sufficiently close to the expected results to be accepted or sufficiently different to be rejected. A type I error is when we reject a null hypothesis (see HYPOTHESIS) when it is true. The probability of making a type I error is the level of significance of a statistical test. A type II error is when we accept a null hypothesis when, in fact, the alternative is true. We can avoid a type I error by making our statistical test more rigorous - but of course, that increases the likelihood of making a type II error!

EXPERIMENTAL DESIGN

Experimental design deals with selection of variables to be studied and the choice of a sampling program. It does not deal with experimental techniques used to gather data. The most commonly used experimental design is the two-sample comparison. To do this you select two situations in

5

BO213 REVISION DATE : 06/16/04 6 which all conditions but one are the same. One situation, usually more "normal" serves as the control and is the basis for comparison. The other situation is the experimental in which you vary the factor of interest. By comparing data obtained from the experimental situation with the control, you can make some conclusions about the effect of the variable you altered on the organism being studied. Be careful, though, to consider other possible explanations. For instance, you may do an experiment growing plants under two different lighting conditions. The control may be normal daylight, and the experimental may have additional supplemental lighting from a floodlight. Plants in the latter situation may grow more rapidly. this may seem to support the hypothesis that the greater the amount of light, the faster a plant will grow. The supplemental floodlight certainly will provide more light intensity - but it also provides heat. Is it the light, the heat, or both that made the experimental plants grow faster?

GRADUATED CYLINDER

A graduated cylinder is a device for measuring fluid volumes quickly and relatively accurately. It is a cylinder of uniform diameter calibrated at regular intervals up to a maximum. Typical graduated cylinders have maximum volumes of 10ml, 25ml, 100 ml, 250ml, 500ml, and 1000ml.

To achieve the greatest precision, you should use a graduated cylinder whose maximum volume is as close as possible to the volume you want to measure.

To use the graduated cylinder, fill to nearly the volume you want by pouring fluid into the cylinder from a tap, a beaker or some other vessel. Stop before reaching the appropriate graduated line on the side of the cylinder. Carefully add the last bit of fluid with a squirt bottle.

Touch the edge of the squirt bottle to the side of the graduated cylinder so that as you slowly add fluid, it will run down the side of the cylinder and not cause bubbles to form which would make it difficult to read the meniscus. Add fluid slowly until the bottom of the meniscus exactly matches the calibration line you want. When pouring fluid from the graduated cylinder to some other vessel, do so slowly so as not to lose any of the fluid you so carefully measured.

GRAPHS

Data from an experiment is usually presented either in the form of a graph or a table - but NOT both. A graph is the preferable method of presenting the data when a trend, relationship or pattern is evident. By convention the independent variable, for instance time, is plotted on the horizontal "x" axis and the dependent variable, such as measurement data, is plotted along the vertical, "y" axis. There are four types of graphs commonly used in reporting scientific results: line graph, bar graph, histogram, and scatter plot. Each format implies different things about the data and each is appropriate for certain kinds of information. The kind of data you have will determine the type of graph to use.

-Line Graphs

A line graph is used when the dependent variable represents a continuous function of the independent variable. For instance, we could look at the length of a leaf measured at daily intervals. The data could be collected in a table such as the one below.

6


Collection Number (day) Average Leaf Length (mm)

1 10 ± 1

15 ± 2.5

2

3

18 ± 2

4

24 ± 0.5

26

24

22

20

Line Graph

18

16

14

12

10

8

6

4

2

0

1 2

Collection Number (day)

3 4

In this case, leaf length is a continuous variable. If you sampled at 1.5 days, leaf length would be somewhere between 10 and 15 mm; at 3.75 days, length would be between 18 and 24, etc. By plotting the data as a line graph, we indicate that at intermediate times we would expect intermediate lengths as a function of the relationship illustrated by the graph - the curve or line.

In a line graph, the data points are not connected by a series of chords. Rather a single curve

(line) of best fit is plotted to the data. The slope of this line is actually the value at which change is occurring (see RATE). For methods of determining and plotting the line of best fit (see

STATISTICS - REGRESSION).

-Bar Graph

Bar graphs are frequently used when the independent variable depicts qualitative (non-numerical) categories such as different species. The dependent variable is still quantitative and is plotted along a scale on the y-axis. For example, the data in the table below represents the results of an experimental and a control situation on four species of flowering plants where the mean height, ± standard error, is plotted.

7


Species Control Height (cm) Experimental Height (cm)

A 22 ± 1

14 ± 2

18 ± 2

5 ± 2

B

C

14 ± 1 13 ± 3

D

20 ± 0.5 15 ± 4

A bar graph of this data is illustrated below.

25

Bar Graph

Legend

23

21

19

17

15

13

11

9

Control Height (cm)

Experimental Height

7

5

3

A B

Species

C D

-Histograms

Histograms represent frequency distributions, showing the frequency of observations falling into a series of numerical categories plotted on the x-axis. For instance, prior to sampling you may arbitrarily decide on certain size classes, such as <5', 5'-5'6", 5'6"-6", >6'. The table below represents such a hypothetical collection of data.

Size Class, Height

<5'

5'-5'6"

5'6"-6'

>6'

Number of Individuals

4

15

13

8

8


This data is graphed below as a histogram. Notice that rather than having the bars separated from each other, as in a bar graph, the bars are adjacent indicating that the size classes form a

Histogram

10

9

8

7

6

5

4

3

Number of Individuals

17

16

15

14

13

12

11

< 5' 5' - 5'6"

Size Class, Height

5'6" - 6' > 6' continuum.

-Scatter Plot

Scatter plot is an accurate description of this type of graph. Every individual data point collected, as opposed to mean values, is plotted directly on the graph. Frequently it is used to show correlation or strength of association between two variables. For instance, in the graph below, leaf length is plotted against leaf width in a single plant.

9

10 BO213 REVISION DATE : 06/16/04

9

8

7

6

5

4

3

Scatter Plot

2

1

0

0.0

0.2

0.4

0.6

Leaf Width (cm)

0.8

1.0

Graphs are not necessary when trends or relationships are not significant or when data are so sparse or repetitive that they can be easily incorporated into the text - unless this repetitiveness or lack of significance is precisely what you want to illustrate.

1.2

Graphs should be understandable on their own. Be sure that the axes are labelled appropriately, including units, and that the legend provides enough information for a reader to be able to interpret the graph. The legend is usually written as an incomplete sentence with only the first word capitalized. Be sure that the data is plotted accurately and clearly. If you a making the graph by hand, use graph paper and a straight-edge. Computers are increasingly being used to generate quick and accurate graphs of data.

HYPOTHESIS

An hypothesis is a tentative statement or assumption which is made in order to be tested. To formulate a hypothesis is to make a testable prediction about the relationship between variables.

A hypothesis is usually stated before any sensible investigation or experiment is performed because the hypothesis provides guidance to an investigator about the data to collect. A hypothesis is an expression of what the investigator thinks will be the effect of the manipulated

(independent) variable on the responding (dependent) variable. A workable hypothesis is stated in such a way that , upon testing, its credibility can be established or refuted. Hypotheses can usually be formed as an "if...then" statement.

Because it is not possible to prove a hypothesis scientifically, in the same way a mathematician can prove a theorem, scientists frequently phrase their hypothesis as a null hypothesis (H:

O

), in opposition to an alternative hypothesis (H:

A

). A null hypothesis is simply a statement of "no

10

BO213 REVISION DATE : 06/16/04 11 difference" between the experimental and control. If there is a difference, we must reject the null hypothesis and accept the alternative. The concept of hypothesis testing is basic to all of science; it is also the most misunderstood by the public. The word "prove" should not exist in the scientist's vocabulary, an infinite number of examples are needed to prove a hypothesis. No matter how much evidence we gather to support a specific hypothesis, we can never be certain that the same data would not equally support any number of unknown alternative hypotheses. On the other hand, only one piece of evidence is necessary to disprove, and thus reject, a null hypothesis. If we demonstrate that the null hypothesis is invalid, then the alternative must be true

- although, in fact, this simply means we must re-examine the alternative to define and test additional null hypotheses - ever refining our understanding of the concept or process involved.

INDEPENDENT VARIABLE - see VARIABLE.

INDUCTION

Induction is reasoning from a specific case or example to the general. Scientific theories are the result of inductive reasoning when overwhelming evidence, based on the results of numerous individual experiments, all suggest a more universal applicability. For instance, the cell theory is based on innumerable experiments which demonstrate, so far without exception, that: 1) all living things are composed of cells, 2) cells are basically alike, 3) all cells come from preexisting cells, and 4) some cells may become functional only after they die. All of the individual observations and experiments, taken together, support our inductive generalization about cells. Similarly, the

Theory of Evolution is supported by induction.

INFERENCE

To infer is to make statements about objects or events based on observations but not the result of direct perception. Inferences may or may not be accurate interpretations or explanations of observations. Inferences are based on: 1) observations, 2) reasoning, and 3) past experience of the observer. Inferences require evaluations and judgment. Inferences based on one set of observations may suggest further observation which in turn requires modification of original inferences. Inferences lead to predictions.

INTERPRETATION

During any experiment some observations will be made and data will be collected. These "facts" may be discrete enough that there is no question of what they mean. A more usual case, however, is that you, as an investigator, will have to make some value judgment about how to evaluate, or even collect, this data. For instance, you may be interested in the number and trunk diameter of trees in a certain area of forest. A logical approach is to mark off an appropriately sized area in a forest and measure the diameter of each tree within that area at a certain height above the ground.

But what if a tree is partly inside and partly outside the boundary of your marked area? What if a tree trunk divides into two or more trunks below the height where you measure - should this plant be measured as a single tree or as two or more separate, smaller, trees? These cases call for interpretation of how to even collect the data. A classic case of interpretation of data concerned classification of a group of organisms called euglenoids. Euglena and its relatives are single celled organisms which have flagella and lack a cell wall (both animal-like characteristics) but which have chloroplasts and photosynthesize (a plant-like trait). How should these organisms be classified? Until about 50 years ago there were two choices - plant or animal. Botanists interpreted euglenoids as being plants because of their ability to photosynthesize. At the same time zoologists interpreted the same organisms as animals because of their motility and lack of a cell wall. Today, euglenoids are interpreted as belonging to a third kingdom of organisms, the

Protists, whose earlier members gave rise to both the plant and animal kingdoms.

11


LUGOL'S IODINE SOLUTION

A preparation which rapidly kills cells and stains starch and glycogen dark reddish-brown. To

300 ml of dH

2

O, add 2 grams of potassium iodide. Dissolve, then add 1 g iodine. To use this stain, simply place a drop on the material you want to test for the presence of starch or glycogen and wait for a minute or two.

MEASUREMENT

To measure is to quantify, using symbols and units , the extent, size, quantity, capacity, etc., of something, especially by comparison with a standard. In science, as in everyday life in every country in the world except the United States , the International System of Units (SI), or Metric

System (see METRIC SYSTEM), is used exclusively. (Interestingly, although the U.S.

Customary System remains in more common use in this country, the metric system is the only system that has actually been specifically sanctioned by congress - in 1866!

)

MENISCUS

When fluid is place in a container, especially one with a narrow diameter, the surface of the fluid will form a crescent-shaped curve. With water solutions the curve is concave and the meniscus is used to accurately measure fluid volumes. In a measuring device, such as a pipette, graduated cylinder, or volumetric flask, fluid is added until the bottom of the meniscus exactly lines up with a calibration line on the glassware, as illustrated below.

Calibration line

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BO213 REVISION DATE : 06/16/04

MICROSCOPY

-Operation and Care of the Compound Microscope

Parts of the Microscope

13

Your instructor will demonstrate the proper way to remove the microscope from its cabinet. The microscope is a precision instrument and should be handled with care. Always use two hands when carrying the microscope and carry it in an upright position.

The framework of the microscope consists of several parts which insure that the lenses, light source, and object are held firmly and in alignment. The base (B) provides a solid foundation to which the upright arm (A) is firmly attached. The stage (S) provides a solid, flat surface on which to place your specimen.

To examine the functional components of the microscope we will follow the path of a beam of light through the system. Our light source is a lamp or illuminator (L) which provides light to the microscope. A blue filter adjusts the color of light to resemble daylight. Some microscopes will also be equipped with a field diaphragm (D) directly above the light source to allow the lamp to be perfectly centered below the optics. As the light travels upward towards the stage it passes through a hole with a variable opening, the iris diaphragm (I). The size of the opening, hence the amount of light passing through, can be adjusted by moving the lever at the front of the diaphragm assembly. The light next passes through a condenser lens (C) to be focused on the specimen on the stage. For critical work the iris diaphragm and condenser must be accurately adjusted - a procedure which will be demonstrated later. For most purposes, however, simply rack the condenser up as high as it will go and use the diaphragm to adjust the light intensity to just a bit less than what seems right.

13


After passing through the specimen, the light enters into one of three objective (O) lenses mounted on a revolving turret or nosepiece.

Each of these lenses is actually a group of three to five separate lenses of different shapes and of different materials which are assembled so as to give a certain magnification with maximum clarity of detail (high resolution and low distortion).

Because of this, each objective should be handled carefully (they are quite expensive). Always begin your observations with low power (the approximate magnification is marked on the side of the lens – e.g. 4X, 10X, 40X) and increase the magnification as necessary by rotating the nosepiece to the next highest power. Modern microscopes are parfocal . This means that once the subject is in focus on low power you should be able to switch to the next higher power and have the object still in focus - or very nearly so. Initial focusing may be done with the coarse focus (F) knob; to make fine adjustments, the fine focus (f) knob should be used. The coarse focus should never be used with the 40X objective . With the high power objective in place you should only focus upward unless you are watching from the side to be certain that the front of the objective does not touch the specimen slide.

The image of the object has now been magnified by the objective lens and this image is formed inside the tube (T). An additional lens, the ocular or eyepiece (E), is now used, in exactly the same way as a magnifying glass, to further magnify the image. The magnification of the microscope is approximately equal to the magnification of the ocular X magnification of the objective being used.

The microscope should be kept clean at all times, especially the lens systems. The instructor will demonstrate how to clean the ocular lens. Remember, lenses are complex and expensive; to clean them use only the special lens paper provided for that purpose .

-Using the Microscope

Eye care

Most of our microscopes are monocular - they have only one eyepiece. This has one obvious disadvantage - only one eye can be used in making observation. However, this can be an advantage in several ways: 1) You can reduce eyestrain by switching eyes occasionally; 2) you can observe and draw the object simultaneously; and 3) you don't have to adjust the microscope to compensate for differences in vision between your eyes. Get into the habit of keeping both eyes open when using the microscope. This allows you to take advantage of the points outlined above and also reduces eyestrain. Another way to reduce eyestrain is to periodically look up from the microscope and focus on a distant object for a few seconds.

-Special Microscopy

Polarized Light

Transparent crystalline materials posses the property of optical birefringence , that is light passing through this material will be bent (refracted) into different planes from the light originally striking the material. This is of great diagnostic value in studying cell structure (cell walls, starch, spindle apparatus, and crystals are birefringent). To convert a standard light microscope into a polarizing microscope, filters (commonly called Nicols) are needed. A Nicol filter (the polarizer) absorbs all waves of light except those exactly perpendicular to the plane of the polarizing material of the filter (see Figure 1). If a second Nicol filter (the analyzer) is oriented perpendicular to the first, it will also absorb the plane polarized light (Figure 2). At the point of precise perpendicular orientation, the Nicols are said to be crossed, and the condition (maximum darkness) is called extinction . Birefringent materials are said to be optically active when viewed with crossed Nicols. This is because the birefringent material will appear light on a dark background at extinction (Figure 3).

14


To convert your compound microscope into a polarizing microscope, place a polarizer in the filter holder between the light source and the specimen and hold the analyzer between your eye and the ocular lens. Rotate the analyzer until extinction is achieved. Any birefringent material will appear bright against a dark background.

Dark Field Microscopy

Dark field microscopy increases apparent resolution of small objects by making them light against a dark background. The light entering the condenser is partially blocked so that no light passes directly through the specimen and into the objectives lens (Figure 4). Instead, the specimen is obliquely illuminated and small objects refract or reflect light into the microscope, thus appearing to produce their own light in an otherwise dark background (Figure 5). Dark field microscopy is most useful in examining bacterial cultures, pond water, etc. in which small objects are distributed throughout a liquid.

To convert your microscope into a "dark field microscope", first locate the material of interest using bright field. Then insert a field stop , a special filter with a blackened circle in the center, into the filter holder below the iris diaphragm. Adjust the iris diaphragm so that the field holder appears black. The objects in the field should now be brightly illuminated.

-Using the Microscope

Orienting Through the Microscope

Place a slide containing a newsprint letter on the microscope (be sure the low power objective is in place) and bring it into focus using the coarse adjustment knob. Is the image you observe right side up or upside down relative to the object on the stage? While you are observing the image, move the slide to the left. Which way does the image move? Now move the slide up. Which way does the image move? Record the answers to these questions, as well as what you did, in your lab notebook.

Area of the Field of View

With your newsprint letter still in place change from the low power to the medium power objective. Fine focus, if necessary, using the fine focus knob. Is the size of the letter image larger or smaller? Is the area observed in the field of view larger or smaller? Repeat this process with the high power objective -be sure to use ONLY the fine focus knob with this lens in place!

Is the image larger or smaller? Is the field larger or smaller? If you were searching a new slide for a single microscopic organism, would it be faster to scan the entire area using the low power or high power? Record the answers to these questions in your lab notebook.

List two reasons why you should always begin a microscopic examination using low power of the microscope.

Depth of Field

Place a slide containing three different colored overlapping threads on your microscope and bring them into focus under low power. Can you focus on all three at once? Switch to the medium power objective and refocus (fine focus knob). Are all three threads simultaneously in focus?

Repeat for high power (FINE FOCUS ONLY) . How many threads are in sharp focus at one time? How is depth of field related to area of the field at different magnifications? Record the answer to these and the following questions in your lab notebook.

Return to low power and look at your microscope tube from the side as you rotate the course focus knob in a clockwise direction. Are you focusing up or down?

15


Using the information you provided above, you should be able to outline a procedure to determine the order, from top to bottom, of the colored threads on your slide. Before you start, check on the feasibility of your proposed procedure with your instructor. What color is the top thread? The middle? The bottom?

Polarized Light

Make a water mount of a small bit of starch and observe your preparation with bright field. Make a sketch of two or three grains, as observed with high power, in your lab notebook. Next insert a polarizer and analyzer filter and rotate them to extinction while observing your starch grains.

Make a second sketch of the same grains as observed with polarized light.

Dark Field

Place a drop of pond water on a slide and add a cover glass. Observe your preparation and sketch two or three different organisms under bright field in your lab notebook. Next place a field stop in the filter holder and reexamine your preparation. Make new sketches of your organisms in dark field next to your bright field sketches. Is any more detail visible?

Calibrating the Field of View.

Place a plastic rule on the stage of your microscope and focus on it under low power so that you can see the mm markings. What is the diameter of your field of view? (estimate it as close as you can). Now focus on the rule under medium power and estimate the diameter of the field of view. Repeat for high power - What's the problem? It is not possible to measure directly the diameter of the field of view under high power, but you can obtain an estimate by calculation (see the formula below). Make the necessary measurements and calculations to determine the field diameter under high power. To determine the area of the field, (Area of a circle = πr 2 , π = 3.14, r = 1/2 diameter).

Field Diameter (high power) = (Field Diameter (low power) x magnification (low power) magnification (high power)

To calculate the diameter of the field, D2, use the following formula:

D

1

M

1

= D

2

M

2 or D

2

= D

1

M

1

/M

2

D

1

is a known (measured) field diameter and M

1

and M

2

are the respective magnifications of the known and unknown fields.

Table 1. Calibration of the Microscope

Magnification Measured diameter of field of view

Calculated diameter of field of view

Area of field of view low ______________X med ______________X high ______________X

If a particular cell reached half way across your field of view under high power, how long is that cell?

16


If a row of 13 cells stretched entirely across the field at medium power, how long is a single cell?

-Dissecting Microscope

A dissecting microscope, as the name suggests, is used primarily for dissecting small objects. It consists of an objective lens, which frequently has zoom capability from 1X-6X, in addition to an ocular lens, usually of 10X. Unlike the compound microscope, the image is not inverted. In effect, a dissecting microscope acts like a fine magnifying glass allowing you to observe the object you are dissecting very close up. Like a compound microscope, the total magnification is obtained by multiplying the magnification of the objective lens by the magnification of the ocular lens.

MOLAR SOLUTION

A solution in which the molecular weight of the compound (in grams) is dissolved in 1 liter of solvent. For instance, the molecular weight of NaCl is 58. A 1 molar solution would contain 58g of NaCl dissolved in 1 liter of water.

NULL HYPOTHESIS (see HYPOTHESIS).

OXYGEN

Oxygen gas, O

2

, is a byproduct of photosynthesis that is required for aerobic cellular respiration.

-Measuring Oxygen

-Respirometer

In aqueous environments, O

2

can easily be measured using an oxygen meter. Be sure that the instrument is calibrated for the water temperature and that the air concentration reading is adjusted for elevation. All meters will have instructions and a graph to calibrate the instrument to the conditions. Once the instrument is calibrated to air, you simply insert the electrode into the solution and read the scale. For direct measurement of oxygen consumption during respiration, using a respirometer, see under CARBON DIOXIDE. This technique can also be used to measure net oxygen production during photosynthesis. As for respiration you will need to run tubes both with and without KOH to account for respiration which is occurring in the living plant cells even as they undergo photosynthesis.

Leaf Disk Flotation

Leaves are the primary photosynthetic organs in plants with much of the internal volume of a leaf consisting of air spaces that are necessary for gas exchange. The principle of leaf disk flotation is to remove the air from these intercellular spaces, a process called infiltration, and replace is with a bicarbonate solution that serves as a source of CO

2

. As photosynthesis occurs, O

2

is produced which forms ever increasing bubbles trapped in the spaces. As more and more oxygen is produced, the leaf disks become buoyant and eventually float. The rate of flotation is an indirect measure of the rate of photosynthesis.

The time required for the discs to float is inversely proportional to the rate of photosynthesis.

Procedure:

1) Prepare citrate-phosphate buffer (control – see BUFFER) and 0.02M NaHCO3 in citrate-phosphate buffer (see MOLAR SOLUTION). The sodium bicarbonate solution is maintained at a pH of 6.8 by the buffer. The amount of solution you make will depend on the size and number of containers you use. For instance, if you used standard size

17


Petri dishes with three repetitions for both your experimental and control groups you would need to make at least 300 ml of buffer, half of which would be used to make bicarbonate solution. This would allow 50 ml of solution for each dish. It would be better to make extra – say 500 ml, to be sure you have enough and to make your calculations a bit easier - - 500 ml is ½ liter. (Note: for most leaves you can omit the buffer and simply add bicarbonate to water and use a water control)

2) Select several leaves from your plant of interest and use a cork borer or paper punch to cut out equal-sized leaf sections from these leaves. Avoid getting major veins in your leaf sections. The number of disks you make depends on the number of repetitions you set up and how many disks you want per repetition. (Ten is a common number per treatment simply to make calculations easier). Again, it is better to prepare more than you will need. Some will infiltrate more easily than others so it is quicker to infiltrate a bunch, then pick out the number you need from the “sinkers,” than to have to keep repeating the infiltration procedure until all disks have sunk.

3) As soon as your disks are punched out, float half the disks in a container of plain buffer and the other half in a container of buffer plus bicarbonate. You don’t want the tissue to dry out! Infiltrate the “buffer” leaf tissue by filling a syringe half full of buffer solution and adding the disks from the buffer container. Replace the plunger into the syringe, then turn it right side up so the air moves to the top and you can push the air out of the syringe by pressing on the plunger. Once the excess air has been removed, evacuate the tissue several times by plugging the tip with your finger and drawing the plunger to create a vacuum. As you do this you should see some bubbles of air come out of the leaf. After holding the vacuum for a few second, release the vacuum either by removing your finger from the tip of the syringe or by letting go of the plunger handle.

As the vacuum is released, solution will replace some of the air in the leaf. Repeat this procedure several times until enough air is removed from the leaf tissue and the discs sink. Infiltrated disks (with their internal air replaced by solution) should be uniformly dark green and appear “water-logged.” Immediately cover these disks with foil so that photosynthesis cannot occur until the bicarbonate disks are ready.

18


4) Repeat step 3 with the other half of the disks using a solution of NaHCO3 in buffer in the syringe.

5) After enough discs have sunk, distribute the infiltrated discs randomly between the three dishes for each treatment. In each dish, the disks should be resting on the bottom .

While you are preparing the sets of leaf discs, cover them so that they will not begin to photosynthesize until you are ready to start the experiment.

6) Place all six dishes containing the discs under the same intensity of light and determine

(in minutes) the average amount of time for the leaf discs in each dish to float. Record these data.

This is the baseline data your research team can now use to investigate the effect of other environmental parameters on the rate of photosynthesis. Some (but not all) effects you might consider include: 1) effect of light quantity (intensity); 2) effect of light quality

(color); 3) effect of CO

2

(bicarbonate) concentration; 4) effect of temperature; 5) effect of pH, or 6) response of different plants. pH

Technically, pH is defined as the negative logarithm of the hydrogen ion activity in a solution. In a practical sense it may be thought of in the following manner. A few H

2

O molecules in a solution of pure water are always dissociated into hydrogen ions (H + ) and hydroxyl ions (OH ).

Free hydrogen ions are acidic, therefore, pH is a scale used to indicate how acidic or basic a solution is. In one liter of pure water 1 out of every 10 million (1/10,000,000) water molecules are dissociated into ions. In other words, there are 10 -7 hydrogen ions per water molecule (one for every ten million water molecules). Because when water dissociates into an acidic hydrogen ion,

H + , it also forms one basic hydroxyl ion, OH , pure water is neutral. The pH of pure water is 7

19


(the log of 1/10,000,000 is -7, therefore the negative logarithm of the concentration of hydrogen ions is +7). If 1 of every 1000 (1/1000) molecules is a hydrogen ion, the concentration is 10 -3 and the log is -3. This is 10,000 times more hydrogen ions than in pure water, so the solution is

10,000 times more acidic. The pH of this solution is 3. Every unit of change in pH, eg. from pH

7 to pH 8 or from pH 6 to pH 5, means there was a ten fold change in acidity- either up or down.

-Measuring pH

The simplest way to measure pH is to use indicator paper, such as P-Hyrion Paper. This is a special type of paper impregnated with an indicator dye. The dye changes color depending on the pH of the solution. Tear off about a 2 cm strip of pH paper and dip the tip into the solution in questions. Compare the color of the wet paper to the color chart on the pH paper container. The best match indicates the approximate pH.

A more accurate method is to use a pH meter. The pH meter has an electrode which must always be kept moist. When it is not in use, be sure that it is kept covered or immersed in a buffer solution. Have the meter turned on and warmed up (with the control knob in standby position) and adjust the temperature knob (if there is one) to the solution temperature.

Standardize the meter against a buffer of known pH close to the range you think you will need. If you're unsure, use a pH 7 buffer. Pour a small amount of buffer into a vessel just large enough to hold the electrode, then insert the electrode into the buffer. Allow the meter to reach a steady reading. If it does not read the same as the pH of the buffer you used, use the meter adjust knob to set the meter to the proper pH. Otherwise, follow the instructions accompanying the apparatus.

Now you are ready to make a reading on your unknown solution. Take the electrode out of the buffer (throw the buffer out), and rinse the tip of the electrode with distilled water. Hold the tip of the electrode against the outside of a glass container to allow any large drops of water to flow off the electrode. Next insert the electrode into the unknown solution and make your reading.

When you take the electrode out of the solution, rinse it again with distilled water before recovering the tip or placing the electrode back into the standing buffer.

PHOTOSYNTHESIS

The process by which plants utilize the energy of (sun) light to convert CO

2

into sugars. In addition, during this process water is split releasing oxygen gas. The overall equation of photosynthesis may be summarized as follows: 6CO

2

+ 6H

2

O + light



C

6

H

12

O

6

+ 6O

2

. Note, different plants undergo photosynthesis at different rates even under the same environmental conditions. The results obtained with one plant may be quite different from those obtained from another plant treated exactly the same way.

-Measuring Photosynthesis

Photosynthesis can be measured in the same way as CO

2

, by monitoring changes in gas composition - either decrease in CO

2

or increase in O

2

. See OXYGEN and CARBON DIOXIDE.

PIPETTES AND PIPETTING

A laboratory procedure which is used extensively in determining concentrations of substances, including organisms, in a liquid substrate is serial dilution. Serial dilution is used to obtain a series of solutions whose concentrations differ by a constant amount, or in some cases by differing known amounts. This is done by careful pipetting of a known volume of the initial starting solution and diluting it with a known amount of solvent. It is very important that extreme care is used in pipetting; small errors made at one dilution will be magnified at all successive

20

BO213 REVISION DATE : 06/16/04 21 dilutions. In making dilutions we make use of the formula V

1

M

1

= V

2

M

2

where V = volume and

M = molarity of the first and second solutions respectively.

-Preparation of a dilution series

A pipette is a measuring apparatus to transfer small volumes of liquid from one vessel to another.

There are several types.

Volumetric, or transfer, pipettes are designed to deliver a single volume precisely. Above the bulb is a marked ring. Fluid must be drawn up the pipette to above the ring, then released slowly until the bottom of the meniscus is exactly at the ring (the tip of the pipette should be touching the wall of the sample vessel as fluid is released). To transfer this volume to a second container, touch the pipette tip to the new container and allow the liquid to flow out.

Mohr, or measuring, pipettes are graduated but stop at a baseline before the pipette begins to narrow. To accurately transfer fluid with this type of pipette, the meniscus must be precisely on a calibration mark both at the beginning and at the end of a transfer.

Serological pipettes are graduated to deliver -- there is no base mark. The appropriate amount of fluid is drawn into the pipette (with the meniscus precisely on the correct mark) and the entire amount is transferred. There are two types of serological pipettes. Those with a single painted or frosted ring at the top should be allowed to simply drain with the tip placed against the side of the receiving vessel. Those with double rings are designed to be "blown out".

PRECISION

Results which are predictable and repeatable are precise, but precise results may or may not be accurate. For instance, if your measuring instrument is not calibrated properly you may get exactly the same result on ten successive measurements, which would be extremely precise, but your results would be inaccurate to the degree that the instrument was out of calibration. (see

ACCURACY)

PREDICTION

A prediction is a forecast of what future observation(s) might be; it is closely related to observation, inference and correlation. The reliability of predictions depends upon the accuracy of past and present observations and upon the nature of the event being predicted. (see

INFERENCE and STATISTICS - CORRELATION)

PROBLEM SOLVING

A logical method of identifying a problem, suggesting some possible solutions, and choosing the most likely explanation. This common sense approach is formalized in science and called "The

Scientific Method."

QUALITATIVE DATA

Data which are descriptive and highly subjective (affected by the subject collecting them), e.g.

"This cola is sweeter than the other cola."

QUANTITATIVE DATA

Data which are numerical and which are derived from measurement, e.g. "This cola contains 3.7 g of sucrose per liter; the other cola contains 3.1 g of sucrose per liter."

RANDOM

21


Random means without definite aim, direction, intention, or method. In other words, without bias. Random selection is a key assumption of statistical analysis, and as such, is critically important in designing scientific experiments and analyzing data. If one cannot be reasonably certain that samples were obtained in a randomized manner, the results obtained will be questionable.

In designing experiments, treatments should be randomized. For instance, if three pots of plants serve as a control and an additional three plants receive a fertilizer treatment, the three treatment pots should not all be next to the window while the control plants are lined up away from the window. To do so biases the experiment because the treatment plants would receive more light in addition to fertilizer. If the pots were set out in a random manner, however, it would be just as likely for a control plant as an experimental plant to be next to the window.

In sampling, it is important to decide where, how much and how many samples should be made ahead of time so as not to bias samples, eg. subconsciously choosing to sample where the largest bacterial colonies are located on a Petri dish. One way to do this is to lay out grid coordinates and then choose sample coordinates with a random numbers table.

In a table of random numbers, each integer from 0-9 has an equal and independent chance of occurring anywhere in the table. Likewise each two digit number 00-99 is randomly distributed as are three digit numbers 000-999, etc. To use the table, decide ahead of time: 1) what direction you want to read (either horizontally, vertically or diagonally, 2) how many digits are appropriate, and 3) where you want to begin in the table (the table should be entered randomly so as not to begin at the same point everytime you need to sample). For example, if you lay out grid coordinates 15 X 15, you want to use 2 digit numbers and use the first 2-digit number between 00 and 15 as your first coordinate and the second number between 00 and 15 as your second coordinate.

See Appendix A for a table of random numbers.

A crude approximation of random sampling is to blindfold a partner, disorient them, then let them

"finger" or "point" or "walk" to the sample location.

RATE

Change per unit time. For instance, miles per hour is a rate of distance traveled (miles) per unit of time (hour) or millimeters per day is a rate of elongation of a growing organ (mm) per unit time (day). Rate is frequently graphed by plotting time on the X-axis and dimension measured on the Y-axis. If there is change over time, the resulting graph will be a line with a slope not equal to zero. The slope of the line is the rate in units of the Y-dimension per unit time (X-dimension).

(see GRAPHS and STATISTICS)

REPLICATION - (see SAMPLING).

RESPIRATION

A series of metabolic reactions in which food molecules are broken down to release energy to the cells in which respiration is occurring. Respiration in some organisms, particularly bacteria, may be done in the absence of oxygen. This process is called anaerobic respiration. The byproduct of anaerobic respiration in plants, bacteria and fungi (fermentation) is alcohol and CO

2

. This explains why beer, for instance, has alcoholic content and bubbles to form a head (as the dissolved CO

2

is released). In animals the byproduct of anaerobic respiration is lactic acid, which

22

BO213 REVISION DATE : 06/16/04 23 builds up in tissues to cause cramping. Under usual conditions, most organisms undergo aerobic respiration. The overall process of aerobic respiration is summarized by the general equation:

C

6

H

12

O

6

+ 6O

2



6CO

2

+ 6H

2

O + energy.

-Measuring Respiration - (see CARBON DIOXIDE and OXYGEN).

SAMPLING

A scientist can rarely collect all of the data about which she wants to draw conclusions. For example, it may be of interest to draw conclusions about the body weight of all 18 year old males in the United States. The only way to make statements about body weight of these men, with 100

% confidence is to weigh each individual - an impossible task. Instead, only some of the total number of 18 year old males are weighed and we infer from the results the total weights of all the individuals of interest. The men who are actually weighed are a statistical sample of the population.

The key to having a sample accurately represent the population is to obtain a random sample.

Random sampling implies that each individual in the population has an equal chance of being selects as part of the sample, that is, there is no bias for or against any individuals being sampled.

If samples are taken at random from a population, valid conclusions may be drawn about that population from a small sample - with a known chance of error . We can control the amount of error by varying the size of the sample. In general, the smaller the sample, the larger the chance of error; the larger the sample, the smaller the chance of error.

A random number table is useful in obtaining random samples (see RANDOM and APPENDIX

1). Decide ahead of time how you will use the table, eg. read the last three digits down a row or the first three digits across line, etc., then enter the table at a random point and begin to sample.

A randomly selected number could represent an individual in a row of plantings, number of feet from a starting point, number of measurements taken of a dimension, etc.

A single measurement is not adequate to draw conclusions about a population. This is because it is not possible to know how reliably a character was measured. Repeated measurements may vary greatly, especially if made by different people. Therefore a series of repeated measurements, or replicate measurements, should be taken. From the collection of replicates, the mean and standard deviation will provide an estimate for the population as a whole. There are techniques to determine how many replicates are needed to achieve a certain level of reliability.

As a general rule, three is a minimum number.

SERIAL DILUTION

A technique for obtaining a series of concentrations by stepwise dilution of specified amounts of a concentrated solution with known amounts of a less concentrated fluid, often distilled water.

For instance, if one ml of a stock solution is added to 9 ml of water, the resulting solution is 1/10 as concentrated as the original stock. One ml of the diluted solution added to another 9 ml of water produces a further 1/10 dilution so that the second dilution is now 1/100 (1/10 X 1/10) the concentration of the original solution.

There are actually three ways to prepare a 1:10 dilution. In the weight-to-weight method (w/w),

1.0 g of solute is dissolved in 9.0 g of solvent (e.g. water), giving a total of 10.0 parts by weight.

More commonly the weight to volume or volume to volume methods are employed. In weight to volume (w/v), 1.0 g of solute is made up to a volume of 10 ml by adding solvent (e.g. water). In this way 1.0 g of solid is dispersed in a total of 10 parts (by volume) of solvent. To prepare a

23

BO213 REVISION DATE : 06/16/04 24 volume to volume (v/v) dilution, 1.0 ml of solute is measured and added to 9.0 ml of solvent resulting in a 10 part solution, 1/10 of which is solute.

Per cent literally means parts per hundred and is commonly used to indicated solution concentrations. Since 1 part in 10 is the same as 10 parts per hundred, each of the solutions mentioned above is a 10% solution. Because they actually differ slightly in the actual number of solute molecules per total volume, you should always indicate how it was mixed – e.g. 10% (w/v) or 10% (v/v), etc.

SIGNIFICANCE

In science, use of this term is restricted to cases where a statistical test has been done and that test shows that there is a statistical difference between observed and expected results. (see

STATISTICS - Student's t-test and Goodness of Fit)

SOLUTION

A mixture of one chemical dissolved in another. The dissolved chemical is called the solvent and the dissolving chemical is called the solute. Both the solute and solvent may be either a solid, liquid, or gas. For example, atmospheric air is a solution of many different gases, tap water is a solution of gases, such as O

2

and solid minerals in water. Water is called the universal solvent because so many difference chemicals will dissolve in it.

-making a solution

Solutions are usually described in terms of percent (%) or molarity (M). See SERIAL

DILUTION for instructions on making a percent solution.

A molar solution is made by weighing out the molecular weight of a compound, in grams, and diluting to 1 liter with solvent. For instance, table salt (NaCl) has a molecular weight of 28. To mix a 1M solution, 28 grams of salt would be dissolved in 1L of water.

STANDARD DEVIATION - (see STATISTICS)

STANDARD ERROR - (see STATISTICS)

STARCH

Starch is a polysaccharide that is a common storage carbohydrate in plants. It is made up of a chain of glucose sugar molecules. Starch can easily be detected using IKI (see LUGOL’s

IODINE SOLUTION) or polarized light (see MICROSCOPY, Special Microscopy, Polarized

Light).

STATISTICS

There are three reasons statistics are important to scientists: first, they allow data to be quantitatively described and summarized; second, they allow generalized conclusions to be drawn based on relatively small sets of data; third, the differences and relationships between sets of data can be objectively analyzed. The following sections will briefly describe some of the appropriate statistics used by biologists for each of the reasons noted above.

-Descriptive Statistics

Living things are, by their nature, variable; a single individual, population, community etc. will not be exactly the same as any other. In order to describe any group of living things, statistics , descriptive measures derived from sample data, must be computed. One of the most common descriptive statistics is the mean , or average. If

“X”

represents a datum (e.g. the height of a plant

24

BO213 REVISION DATE : 06/16/04 25 in cm) the mean of a sample of several plants is

= ΣX/n where (X bar) is the symbol of the mean, ΣX (sum of X's) is the total of all the plants' heights in the sample and n

(sample size) is the number of plants sampled. e.g. The heights of five plants were 10.1, 11.4, 11.7, 12.1 and 13.3 cm respectively.

Σ X = (10.1 + 11.4 + 11.7 + 12.1 + 13.3 = 58.6) n = 5

=ΣX/n = 58.6 cm/5 = 11.72 cm

Thus the average height of the plants in this sample was 11.72 cm. If these 5 plants were randomly selected from a larger group of plants, we may assume that the average for the larger population is also approximated by 11.72 cm.

As a general rule, the mean should not be considered more accurate than 1 significant figure beyond the accuracy of the original data. In the above example each plant was measured to within 1/10 cm (0.1). Therefore, the mean may be rounded to the nearest 1/100 (0.01).

Calculating a mean only gives a partial description of the data - the average value. It is usually necessary to also describe how much variability there is around the mean. The following two sets of data have the same mean: 1, 6, 11, 16, 21, and 10, 11, 11, 11, 12. You will probably agree that the mean is not enough to meaningfully describe both sets; some measure of variability is also necessary. Two measures of variability are commonly used, standard deviation(s) and standard error (S.E.) . In each case the first step is to calculate the sum of squares (SS) - the sum of squared deviations from the mean. SS =



(x-x) 2 For the plant height data above, SS =

(10.1 - 11.72) 2 + (11.4 - 11.72) 2 +(11.7 - 11.72) 2 + (12.1 - 11.72) 2 simpler way to calculate SS is to use the formula SS =



X 2 - (



X)

+ (13.3 - 11.72) 2 = 5.37 cm 2 . A

2 /n. Again using the data above:



X = 10.1 + 11.4 + 11.7 + 12.1 + 13.3 = 58.6 cm



X 2 = (10.1) 2 + (11.4) 2 + (11.7) 2 +(12.1) 2 + (13.3) 2 = 692.16 cm 2 n = 5

SS = 692.16 cm 2 - (58.6 cm) 2 /5

= 692.16 cm 2 - 686.79 cm 2

= 5.37 cm 2

Standard deviation =



(SS/DF) where DF (degrees of freedom) = n - 1 in our example s =



(5.37 cm 2 /4) = 1.16 cm

The standard error (S.E.) is calculated by the formula: S.E. = s/

 n, which for our example is 1.16 cm/



5 = 0.52 cm. Our data may now be accurately expressed either by stating the mean and standard deviation (x = 11.72 cm, s = 1.16 cm) or by the mean and standard error

(x = 11.72 ± 0.52 cm).

25


As you can see by the equation for standard error, the magnitude of this variation is inversely proportional to the sample size. That is, the larger the sample size, the more precise the estimate of the population mean (i.e. large samples generally give better results than small samples!)

-Calculating Mean and Standard Deviation

This is simplified with the computers in the laboratory. Enter your data into a column in the

EXCEL spreadsheet. Highlight the area and choose “TOOLS”, then “DATA ANALYSIS” finally “DESCRIPTIVE STATISTICS.” Be sure the input range includes the data in your column, then check “SUMMARY STATISTICS.” Click “OK” and the output will provide a number of descriptors including your mean, standard deviation, and standard error.

-Comparing Two Means

It is frequently of interest to compare the means of two samples to draw conclusions about similarities or differences. For instance, are the results of a particular experimental treatment significantly different from the control? In some cases the difference may be very large and obvious, but in other cases the means and variances may be quite similar and an objective method is required to determine the degree of difference or similarity.

Student's t-test is commonly used to compare two means where the null hypothesis, H o

:x

1

= x

2

, is that the means are the same.

The t-statistic is calculated as: t = | s

1 –

1

–

2

2

| where the numerator is the absolute value of the mean of experiment 1 less the mean of experiment 2. The denominator is the standard error of the difference between the means and is calculated as: s

1

-

2

= √[(s p

2 /n

1

) - (s p

2 /n

2

)] where n

1

and n

2

are the two sample sizes and

sp 2 is: SS

1

+ SS

2

DF

1

+ DF

2 where SS is the sum of squares and DF is the degrees of freedom for the two data sets.

The value obtained for "t" is now compared to the table of critical values of Students'-t. Values smaller than the critical value indicate a high probability that the null hypothesis, Ho:

1

=

2 is supported. If the calculated t-value is greater than or equal to the critical value, then the null hypothesis is rejected and the alternate hypothesis, H

A

:

1

≠

2 is accepted. The appropriate degrees of freedom, DF, is DF

1

+ DF

2

(DF

1

= N

1

-1; DF

2

= N

2

-1; DF = N

1

+ N

2

-2).

26


4

5

6

DF

1

2

3

α = 0.10

6.31

2.92

2.35

2.13

2.01

1.94

Critical Values of Students'-t

α = 0.05 DF

12.71

4.31

11

12

3.18

2.78

2.57

2.45

13

14

15

16

α = 0.10

1.80

1.78

1.77

1.76

1.75

1.75

α = 0.05

2.20

2.18

2.16

2.14

2.13

2.12

7

8

9

1.89

1.86

1.83

2.36

2.31

2.26

17

18

19

1.74

1.73

1.73

2.11

2.10

2.09

10 1.81 2.23 20 1.72 2.09

Note: About α, the level of significance. Rejecting the null hypothesis, when it is in fact true, is called a Type I error. The probability of making a Type I error is called the level of significance;

α = 0.05 means the probability of a false rejection is only 5%. Unfortunately, by reducing the probability of making a Type I error, you are increasing the chance of accepting the null hypothesis when it is not true -- a Type II error!).

-Goodness of Fit

Experiments are performed in order to test hypothesis. Rarely will biological data come out to be exactly what our hypothesis predicts (again because of the inherent variability of living things). It is therefore useful to be able to test if there is a statistically significant difference between our observed data and our hypothesis. For example, we may expect a 3:1 ratio from a particular genetic cross. After doing an experiment with 40 individuals we obtain a ratio of 27:13 - not exactly 3:1, but close. Is it close enough?

To answer this question we may employ the chi-square (χ 2 ) test, called a "goodness of fit" procedure because it tests if the observed data fits the hypothesis or if there is a significant difference. The formula for chi-square is:

χ 2

= Σ [(O-E) 2

/ E] where O is the observed frequency and E is the expected (hypothesized) frequency. In the above example the observed values are 27 and 13, while the corresponding expected values are 30 (3/4 of 40) and 10 (1/4 of 40). The value of chi square is:

χ 2 = (27-30)

2

/ 30 + (13-10)

2

/ 10 = 1.2

Note that the chi-square calculation uses frequencies only, never percentages or proportions.

Our hypothesis for the chi-square test is that the observed values are not significantly different from the expected (this is called the null hypothesis). The larger the difference between the observed and expected values, the larger the resultant chi-square, and the lower the probability that the null hypothesis is correct. The value of chi-square above which we no longer accept the null hypothesis is called the critical value. The appropriate critical value depends on the degrees of freedom (one less than the number of categories being compared) and the level of significance

(α) at which we want to test (usually 0.05 in biological experiments). These values are displayed in the table of critical values of chi-square below.

27


DF

1

2

3

4

5

6

7

8

9

10

Critical Values of Chi-Square

α = 0.05

3.84

5.99

7.81

9.49

11.07

12.59

14.07

15.51

16.92

18.31

α = 0.01

6.63

9.21

11.34

13.28

15.09

16.81

18.47

20.09

21.67

23.21

Snedecor, G.W. and W.G. Cochran 1980. Statistical Methods , 7th ed. Iowa St. Univ. Press,

Ames, Iowa. 507 pp.

In our example with two categories, d.f. = 1, α = 0.05, therefore from the table the critical value is 3.84. Our value of chi-square, 1.2, is considerably smaller than the critical value, therefore, at the 5% level there is no significant difference between what we observed and what we expected.

If, however, our calculated chi-square was 3.84 or larger, we would have to reject our hypothesis that we found a 3:1 ratio from that cross.

-Regression

In many biological experiments one set of data will be related to another and it is of interest to know what the relationship is. For example, it is reasonable to assume that in a given species growing in a given area tree diameter is related to age. It should be possible to measure the diameter of a number of trees, determine their age (e.g. by counting rings in a sample bore), and come up with a relationship between age and diameter. This statistical relationship is a regression and with it you would then be able to estimate the age of other trees based on their diameter. For example, collection data for a set of five oaks might be as follows:

Tree Age (Years) Diameter (cm)

1 4 5

2

3

6

8

7

10

4

5

10

12

12

15

In the above example diameter is assumed to be dependent on age, thus diameter is the dependent variable (conventionally plotted on the Y axis) and age is the independent variable (plotted on the

X axis).

The data may be plotted

15 in this manner:

Diameter

(cm)ˆ

12

9

6

3

3

28

6 9

Age (yrs.)

12 15


The relationship between diameter and age is expressed by the regression equation which best fits the data.

The equation for a straight line is:

Y = mX + b where Y is the dependent variable, X is the independent variable, m is the slope of the line and b is the Y-intercept. The regression equation may be determined graphically by carefully plotting the data and "eyeballing" the best fitting straight line. The slope of this line can be estimated by computing "rise over run". Choose two points on the line (e.g. 1, 2) and drop vertical lines from these points to the X-axis and horizontal lines the Y-axis as shown in the graph. In this case the values of 1 and 2 are (2, 2.3), and (12, 14.8) respectively. Rise over run = (Y

2

-Y

1

)/(X

2

-X

1

) =

12.5/10 = 1.25. Because the sign of the slope is positive, Y increases with X (if the slope were negative there would be an inverse relationship and Y would decrease as X increased). The Yintercept, b, is simply the point where the regression line intercepts the Y axis. In this case b = -

0.2.

A more accurate way of estimating the regression line is to compute the "best fit" by means of

"least squares". The slope is calculated by the equation: m = SP/SS x

.

SP =



XY -



X



Y/n



XY = (4x5) + (6x7) + (8x10) + (10x12) + (12x15) = 442



X = 40 yr



Y = 49 cm n = 5

SP = 442 - (40)(49)/5 = 50

SS x

=



X 2 - (

 x) 2 /n (the same as in calculating variance in part A)



X 2 = 4 2 + 6 2 + 8 2 + 10 2 + 12 2 = 360

(



X) 2 = 40 2 = 1600

SS x

= 360 - 1600/5 = 40 therefore slope = 50/40 = 1.25

The Y-intercept is calculated by the equation: b = Y - mX = 9.8 - (1.25)(8) = - 0.2 [Note:a regression line will always go through the points

(



, ) and (0, b)]

29


By inserting the computed values into the equation of the regression line we have:

Y = 1.25X - 0.2, enabling us to predict diameters of trees of given ages. To predict the diameter of a tree "2" years old, insert the value of "2" into the equation in place of X.

-Using the Computer

See Appendix B, Data Analysis with EXCEL

-Correlation

Correlation is similar to regression in that two sets of data vary with respect to each other. The important difference is that in correlation both data sets are independent. For example tree diameter and tree height may both be dependent upon tree age - but they are independent of each other. To determine if a correlation exists you must calculate the correlation coefficient, r: r = SP

√SS x

SS y

SP, SS

X

, and SS

Y

are computed in the same way as in regression analysis. The correlation coefficient is a number in the range from -1.0 to +1.0. A positive correlation implies a direct relationship while a negative number indicates an inverse relationship. If r = 0 there is no correlation between the two values, thus, the closer r is to ± 1, the stronger the relationship.

Because the two variables are independent, it makes no difference which is labelled X and which is Y.

THEORY

This is one of the most confusing terms used in science because it is also used in common conversation with quite a different meaning. In everyday usage, the term theory implies little more than the opinion of the speaker or writer. In science, on the other hand, the term theory means that this is a strongly supported idea which has repeatedly been tested, by many people, in many ways, and for a long period of time. Furthermore, all this testing has supported the theory - otherwise the theory would have been rejected.

VARIABLE

A variable is any factor in a situation that may change or vary. Investigators in science and other disciplines try to determine what variables influence the behavior of a system by manipulating one variable, called the independent variable and measuring its effect on another variable, called the dependent variable . As this is done, all other variables are held constant. If there is a change in only one variable and an effect is produced on another variable, then you can conclude that the effect has been brought about by the changes in the manipulated (independent) variable.

If more than one variable changes, there can be no certainly at all about which of the changing variables causes the effect on the responding variable.

30


In a scientific investigation, measurements of the variables are made; however, you, the investigator, must decide how to measure each variable. An operational definition of a variable is a definition you determine for the purpose of measuring the variable during an investigation.

Thus, different operational definitions of the same variable may be used by different investigators. For instance, in a growth rate experiment, you may decide to measure length of an organ at daily intervals while in another group, they may decide to measure the same dimension at six hour intervals. In many cases it is important that you choose an appropriate operational variable in order to observe a phenomenon. If the time interval you choose is too long, for example, you may miss an important stage of a processes you were looking for.

31

BO213 REVISION DATE : 06/16/04

00-04 05-09

15

16

17

18

19

10

11

12

13

14

05

06

07

08

09

00

01

02

03

04

96754

34357

06318

62111

47534

98614

24856

96887

90801

55165

54463

15389

85941

61149

05219

41417

28357

17783

40950

82995

25

26

27

28

29

20

21

22

23

24

45

46

47

48

49

40

41

42

43

44

75884

16777

46230

42902

81007

68089

20411

58212

70577

94522

30

31

32

33

34

42626

16051

08244

59497

97155

86819

33769

27647

04392

13428

35

36

37

89409

45476

89300

66162

8882

68799

38 50051 95137

39 361753 85178

79152

44560

38328

46939

83544

91621

91869

55751

85156

07521

03033

38804

43877

66892

00333

01122

67081

13160

42866

75628

53829

38750

83378

38689

86141

00881

67126

62515

87689

56898

17676

88040

37403

52820

09243

75993

03648

12479

21472

89522

22662

85205

40756

69440

81619

89326

94070

00015

84820

64157

10-14

85651

57194

33851

09419

40293

95769

56109

50741

91631

31310

84318

56882

80207

46134

39693

51111

89950

06468

24969

71659

77250

82635

63369

58625

15707

04900

04151

21108

95493

12236

55659

53364

49927

07243

67879

84460

44898

80621

42815

83666

56905

11885

82414

11286

10651

87719

20652

10806

29881

66164

Appendix 1 Random Numbers

Randomly Assorted Digits

15-19

88678

16752

44705

89964

00998

47420

96597

30329

66315

89642

95108

42859

88844

01432

28039

72373

16944

15718

61210

62038

20190

56540

71381

08324

96256

54224

03795

80830

88842

60277

44015

71726

57715

79931

00554

62846

09351

66223

77408

36028

70639

39226

02015

88218

67079

92294

35774

83091

85966

41180

20-24

17401

54450

94211

51211

58434

20792

25930

11685

97428

98364

75305

21460

89380

94710

10154

06902

93054

82627

76049

79643

56535

64900

39564

30459

23068

46177

59077

02263

00664

39402

47361

45690

50423

89292

23410

59844

98795

86085

37390

28420

79365

22490

13858

58928

92511

46614

16249

91530

62800

10089

25-29

03252

19031

46716

04894

01412

61527

66790

23166

12275

02306

64620

43910

32992

23474

95425

74676

87687

76999

67699

79169

18760

42912

05615

85863

04372

55309

01848

29303

55017

62315

37032

66334

67372

84767

12740

14922

18644

78285

76766

70219

67382

90669

78060

03638

59888

50948

75019

36466

70629

73417

30-34

99547

58580

11738

72882

69124

20441

65706

05400

24816

24617

91318

01175

94380

20423

2*230

96199

96693

05999

42054

44741

69942

13953

42451

20781

08467

17852

12630

37204

55539

12239

86679

60332

63116

85693

02540

48730

39465

02432

52615

81369

29085

96325

16269

52862

84502

64886

21145

39981

84740

78258

40-44

17918

54132

95374

21896

59085

11859

53634

48708

71710

83942

45375

81378

98656

60609

31782

41273

77045

96739

93758

39038

33278

18711

97507

23666

93848

89415

52068

30506

69448

11844

53249

90600

21505

22278

32949

48167

90638

42846

30268

47366

47058

60933

10389

33451

83463

97365

47286

49177

77379

88629

35-39

48769

55781

17805

82171

39435

61203

66669

65578

45153

09609

87894

03164

60137

19774

97017

87236

58680

12696

05437

32404

77448

79149

64559

09284

89496

27491

98375

96926

17771

07105

22885

48888

73947

54440

73443

70158

53342

21434

41943

89872

23248

56891

62773

72095

20002

05217

62481

62660

96488

32940

32

45-49

62880

60631

72655

83864

82859

41567

22557

03887

33258

22716

85439

40620

59637

43449

41550

21546

33848

69700

03283

13163

48805

68618

65747

91777

55376

27083

71113

87018

11551

13491

34770

44105

94771

18106

41067

08186

26927

15345

77455

75577

30976

67305

75779

90279

37231

23466

60427

97111

01117

44517

32


APPENDIX 2. DATA ANALYSIS WITH EXCEL

Enter your data into the spreadsheet with the independent variable (usually x-axis) running down a column and the corresponding dependent variables down successive columns. For instance, Times 1, 2, 3, 4, 5 min. in a rate experiment would be listed sequentially down column A. The respective readings observed would be listed down column B. In another experiment with multiple samples collected from control and experimental conditions, column A would be sample number and columns B and C would be “experimental” and “control” respectively.

To calculate descriptive statistics or do a statistical test, click on “Tools” and “Data

Analysis”

“

Descriptive Statistics

” will give you the mean, standard deviation, and standard error

(among other things). This information will allow you to quickly plot the mean

±standard error for a set of values.

“t-test:

Paired, two-sample for means

” will test if the means of two samples (two columns from your data spreadsheet - - you can select any two columns if you had more than one treatment) are significantly different from each other.

Among other things the output will calculate the mean, number of observations (n), and variance for each column. (The square root of the variance is the standard deviation; divide this by the square root of n = standard error.) You will also be given the t-value (t-

Statistic) for the two means and the critical value of t at α = 0.01. For our work we will use only the one-tailed test. If your t-value is greater than the critical value, you must reject the null hypothesis that there is no significant difference between the two sets of data and accept the alternative hypothesis that they are significantly different.

Regression

The output for regression gives the correlation coefficient (r) (labeled “Multiple R”);

Coefficient of Determination (r 2 ) (Labeled “R Square”); slope (m) (Labeled “X Variable

1, Coefficients”); and Y-intercept (b) (labeled “Intercept, Coefficients).

Plotting the regression line.

Manual method.

The Y-intercept (see above) is the point on the regression line where the value of X is 0 and you are given Y. A second point on the regression line is the point (mean of x, mean of y). Plotting these two points gives you an accurate representation of the regression line.

Using Excel’s “Chart” function. a. Choose CHART under the INSERT menu (or click on the CHART icon). b. Select XY SCATTER for chart type in the box that pops up. This will allow you to display the data points without connecting lines between them. c. Click NEXT, then click on the SERIES option.

33

BO213 REVISION DATE : 06/16/04 34 d. If you are plotting more than one regression on the same graph you will want to enter the name for the first set of data in the NAME box, then click on the red arrow to the right side of the “X-values” Box which will bring you back to your data table. e. The X-values should already be highlighted, but if not use the left button of the mouse to select (highlight) all of the data for the “X-values”. Then re-click on the red arrow to the right of the “Source Data” box to bring you back to the chart wizard. f. Now repeat steps “d and e” for the y-values. g. Click NEXT to take you to step 3 of the chart wizard. You will use several of the tabs

that pop up.

In the TITLES tab

-enter a title for your graph, e.g., Enzyme Kinetics

-enter a label for the x-axis, e.g., Time (min)

-enter a label for the y-axis, e.g., Absorbance

In the GRIDLINES tab, uncheck all the boxes.

In the LEGEND tab, unckeck “show legend” or position the legend where you would like it to appear. h. Click NEXT to step 4 which allows you to place the graph either on a new sheet or into your data table - - you choose (having it with the data is frequently useful) i. Click FINISH to produce your labeled plot. You can do some “finishing” at this point.

-To remove background color on the graph, put the arrow somewhere in the gray area and right-click. In the pop-up menu, choose FORMAT PLOT AREA and choose “none” for the Border and Area sub boxes.

-To modify the scale, position, or appearance of the axes, put the cursor arrow on

the axis you want to modify and right-click. Make the modifications you want. j. to add the regression line(s) put the cursor arrow on one of the data points on your plot and right-click. Choose ADD TRENDLINE.

-in the TYPE tab, choose LINEAR

-in the OPTIONS tab, check DISPLAY EQUATION and DISPLAY R-

SQUARED

-click OK. This will plot the least-squares regression line on your plot and insert

the equation for the line and goodness of fit parameter. You can drag these

formulas to position them where you want on the graph.

Adapted from

Biology of Plants Laboratory, 2005

Dr. Marshall D. Sundberg

34

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Scatter Plot

Calibration line

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