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LEARNING TO BE WINNERS OR LOSERS
The scientific study of animal behavior developed into a distinct discipline in the 1930s, arguably
reaching a milestone in 1973 when the Nobel Prize was awarded to Konrad Lorenz, Niko Tinbergen and
Karl VonFrisch for their pioneering studies of ethology. If you are interested, the Nobel acceptance
speeches are available on the Courses Server (or online at http://nobelprize.org/nobel_prizes/).
A major contribution of these ethologists was to supplement qualitative descriptions of behavior, which
are necessary but insufficient, with quantitative measures of behavior.
Tinbergen also presented the concept of four fundamental problems, or questions, to be addressed by the
study of behavior:
(1) Development / Ontogeny - How does the behavior arise during the lifetime of the individual?
(2) Mechanistic causation - How do internal and external causal factors elicit and control behavior in
the short term?
(3) Evolution / Phylogeny – What is the evolutionary history of the behavior?
(4) Adaptive Value (function) - What is the current utility or survival value of the behavior?
These four questions engender different experimental approaches and provide complementary insights.
The most insightful studies in animal behavior address more than one of these questions and employ
methods that blur the distinctions between them. The crayfish have been a model organism for many
studies on agonistic behaviors involving all 4 levels of investigations (e.g. Huber et al., 2001; Baranaga,
1996).
Theory
As you learned from Bob Kaplan’s lectures, evolution through natural selection works to favor traits that
increase the organism’s fitness (overall reproductive success). The theory of natural selection can be
used as a framework for developing hypotheses about the evolution of behavior. Evolution, through
natural selection, should favor those behaviors that maximize some beneficial currency (e.g. food intake,
predator avoidance, mate choice etc.) or minimize cost. Thus existing phenotypes are likely to have
high, adaptive value. Rigorous tests of this hypothesis constitute the basis of “the adaptionist approach.”
This “adaptationist approach” can be applied to agonistic interactions with conspecifics. Animals may
fight over prey, territories, mates or any other limited resource. The outcome, escalation and intensity of
agonistic contests may depend on many factors; for example, animals may differ in their relative
fighting ability, motivation, or territorial advantage. Their displays may range from ritualized fights with
threat displays through to fully escalated fights with costly physical attacks. (When would it be
advantageous (have high survival value) to not fight?) The major cost of escalated fighting is risk of
injury, and the major benefit is access to resources (e.g. territory, shelter, food, mates). If these costs and
benefits are different for particular individuals in particular encounters, then graded levels of escalation,
ranging from ritualized fighting through all-out attacks are expected. Graded levels of aggression allow
individuals to settle disputes in a less costly manner.
Empirical research on shelter-dwelling crustaceans, such as lobsters, crayfish, and hermit crabs, has
consistently demonstrated dominance hierarchies. When two individuals encounter each other, they
respond behaviorally in a manner appropriate for their rank. One question that has been difficult to
answer is how such inter-individual assessments of dominance are made. There are three plausible
explanations. First, individuals may have dominance recognition. This is the ability to quickly determine
the rank of the opponent. Second, individuals may have an internal assessment of their own dominance
rank based on past experience. Third, animals may rely on individual recognition, the ability to
recognize an individual previously encountered, remembering the relative rank of that individual.
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Animals that have recently won aggressive interactions may often be more likely to win against new
opponents that have not had recent winning experience; that is, winners keep winning. This
phenomenon has been found in a variety of taxa, including juncos, chickens, paradise fish, red deer,
spiders, and crickets (reviewed in Jackson, 1991). The proximate reasons and mechanisms for this
phenomenon are the current topic of many research programs (e.g. Stevenson et al., 2000) most recently
employing the awesome power of Drosophila genetics (Chen et al., 2002; Dierick, and Greenspan
2006). Historically, crustaceans have been used widely in agonistic behavioral investigations. The
advantageous characteristics of crustaceans include the relatively large size that facilitates behavioral
observation and measurement. Due to the concerted efforts of many researchers, the aggressive
behaviors are now well described. Furthermore, these animals are hardy and exhibit a broad range of
their natural agonistic repertoire even in a lab setting. Perhaps the most important characteristic of
crustaceans is their relatively accessible nervous system for physiological experiments. Studies examine
species-specific ritualized displays (e.g. Huber and Kravitz, 1997), inter and intra-sexual interactions
(e.g. Cushing and Reese, 1998), and how fighting behavior is influenced by the environment (e.g.
predation risk and time of day (e.g. Spanier et al., 1998)).
Many investigations of agonistic behavior in crustaceans have focused on
crayfish, which are especially easy to maintain in the laboratory. The
outcome and nature of crayfish fights are influenced by a multitude of
factors. These include differences in reproductive status; the relative
intensity of light conditions (related to circadian behavior); relative body
size; and previous contest experience. Contest experience may affect
subsequent behavior by modifying development and activity of the nervous
system (e.g. Baranaga, 1996; Huber et al., 1997). Because crayfish fights
are decided, in part by the relative size of the contestants, it is possible to
provide crayfish with a series of training fights that generate individuals
that have had either winning or losing experiences.
QUANTIFYING BEHAVIOR
Quantifying behavior is not easy, particularly if you need to watch many focal subjects, note many
behaviors, or record behaviors that occur frequently or quickly. Hence, one must choose a sampling
rule. Your task in this lab is made simpler by employing a focal animal sampling rule (i.e. you watch
just one individual). Other possible sampling rules are scan sampling, in which one periodically scores
behavior for a series of individuals, or behavior sampling, in which one scores all instances of
particular behavior(s) in a group of individuals. These different sampling rules are appropriate for
different questions, different organisms and different situations. The details guiding such decisions will
be discussed in lecture and more detail can be found in chapter 6 of Measuring Behavior by Martin and
Bateson (on reserve in the library).
Quantifying behavior also requires one to make decisions about recording rules. A continuous
recording of all behavior is impractical when many individuals or many behaviors are being scored, or
when behaviors are occurring quickly. Furthermore, continuous recording for long periods can be
tedious. Therefore, a common alternative is instantaneous recording in which the behavior is noted at
regularly spaced time points and the intervening periods are ignored. Today each student will watch
only one animal at a time and will use focal sampling with continuous recording. Try to think about
how other sampling and recording rules could yield different data.
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General Lab Instructions:
BEFORE HANDLING the animals, please thoroughly wash and rinse your hands. Lotions, soaps, and
general campus grime can be deadly to critters.
Get to Know Your Crayfish Ethogram:
An ethogram is a catalog of species-typical behaviors. In the early days
claw
of ethology, (the study of animal behavior) comprehensive ethograms of
all behaviors exhibited by a species would constitute publishable
scientific research. Today, most ethograms represent only a subset of the
behavioral repertoire that is related to the specific behavior being tested.
For example, our ethogram, will not be concerned with mating or
feeding, but rather will focus on agonistic behaviors. Each behavior
should be clearly defined and described by recognized postures and
movements. In an ethogram, the descriptions of each behavior should
avoid statements of intent, avoid anthropomorphism, and be clearly
defined by neutral characteristics.
We will spend a few minutes observing the animals on video. Discuss
the defined behaviors with your team until you are confident that you
will not introduce observer bias by disagreement on definitions.
SCORE
-3
BEHAVIOR
Tailflip
-2
-1
Tailtuck
Avoidance
0
Separate
1
Approach
2
Threat
3
Fight
DESCRIPTION
Rapid ventral movement of the tail results in the crayfish shooting
backwards (away from opponent).
Tail is tucked under the abdomen (no rapid resulting movement)
Crayfish slowly moves away from opponent (gives a wide berth)
usually moves in reverse.
Crayfish is at a distance from opponent and makes no directed
movement.
Crayfish slowly moves toward opponent (may include contact
without the claw display)
Crayfish approaches opponent with outspread claw and may strike
opponent without locking claws.
Crayfish locked claw(s) over opponent and attempt to flip opponent.
Read the ENTIRE handout before beginning your training and experiments
-Use focal sampling with continual recording (described above) for both training and testing.
-All fights will be observed for 10 minutes.
-Use the data collection sheets provided and staple these into your own lab notebook.
-Be sure that every student does at least one focal observation
-Because the team results include only 2 animals, a class data set is necessary for statistical tests.
-Be sure that crayfish are returned to the tanks and bowls where you found them.
-Students not directly doing the focal observation should, in their own lab notebook, note the location of
the raw data (the collaborator’s notebook).
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Back of Room
Front of room
Renn_lab#3_Crayfish
Figure 2. Map of work-station includes 4 experimental crayfish and represents the concerted
effort of 8 students
TRAINING Each team of 4 students will train two crayfish to be either a winner or a loser. The winner’s training is
accomplished by repeatedly fighting your focal crayfish (one of the size matched animals in the isolated
bowls) against different smaller opponents. The loser’s training is accomplished by repeatedly fighting
your focal crayfish against different larger opponents. Training is complete after 3 consecutive wins (or
losses) against 3 different individuals! After each training, store the opponent in a ziplock with water
box so that you can be sure to take a new opponent each time (you will have to share opponents with the
other training team across the bench from you). If you fight your focal crayfish for 5 trials and fail to
achieve 3 consecutive wins or losses, continue with the experiment but make note of the unexpected
fight results for final data analysis.
EXPERIMENT Winners vs. Losers
Two size-matched sized crayfish (one with winner’s training and one with loser’s training) will be tested
in the experimental fights. Because there are 4 students, you can have 2 students recording focal
behavior observations for each crayfish. How similar are your results? When you enter your data to
the class data set, enter the mean of the two scores. Another student should be timing the first
contact and first tail flip.
As you work today, in your lab notebook, record each step of your protocol, and any additional
information that helps you to define the behaviors. This information would be helpful for
reproducing your work even if you lose this handout.
PROTOCOL
Sampling and Recording for Training and Experimental Fights.
The data collection sheets (provided in lab) contain entry space for information you may not think that
you need for every experiment, but it is better to collect the data and not use it, than not collect it and
wish that you had. While it is best to always state a clear hypothesis before your experiment, you may
find there are additional hypotheses that can be addressed by your data. You will have to communicate
with your partner to identify which animal is the first to tail flip and record that event accurately.
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PROTOCOL CONT.
 Leave the tank divider in place until you are ready to begin recording your data.
 Allow crayfish a 5-minute acclimation period (be careful not to bang on the bench or tank, or
make any movements near the tank. Sit at least 2 feet back from the tank. You cannot
expect crayfish to behave naturally if they are threatened).
 Two students will work together for the training fights using a focal sample and continuous
recording rule, each student will observe a single individual crayfish.
 Remove the tank divider and start your timer to count 10 minutes.
 Use the descriptions above, and record behavioral events directly onto the data collection sheet
that will be stapled into your lab notebook.
 Each time that you observe your focal animal perform one of the described behaviors, put a tick
mark in the appropriate box on your own data collection sheet. (Do not worry about the scoring
until the end of the trial).
 The student with the timer will be responsible for noting the time and ID of the crayfish that does
the first contact as well as the first tail flip.
 Notice that the data collection sheet includes additional information: Animal ID, weight, type of
fight, as well as which animal performed the first tailflip. Because you are watching only your
own animal, you will need to verbally communicate with your partner who is watching the other
animal when this occurs. Be sure that ALL information is recorded.
 Continue recording for the entire 10 minutes.
 Replace the divider separating the two crayfish when 10 minutes has passed.
 Remove the opponent and weigh the opponent. Record the weight on the data sheet.
 Put the opponent in a ziplock box with water.
 Leave the focal animal in the tank and allow it 5 minutes of rest.
 While your focal animal is resting, tally your tick marks, and multiply the number of events by
the score for that behavior.
 REPEAT training for 3 consecutive wins (or losses) or 5 trials (which ever comes first).
Data Entry
As a team of 4, log into the computers as yourself. Connect to the Courses Server as yourself.
Drag the file crayfish data template from the Courses Server/Bio101 102/BeaviorRenn/Week3_Crayfish to your desktop.
Open it and Save As yourname_Ned_Tues_crayfish or yourname_Carey_Wed_crayfish etc.
When you finish recording and saving your data, put that file in the Crayfish data dropbox.
Don’t forget that the class is waiting for your data set.
For each fight you will enter:
 The identifier number of the focal animal (A1 – D6).
 The sex of the combatants (male, female, mixed).
 The type (not the outcome) of fight (W=winner training L=loser training E=experiment).
 Is this the first training fight (first, second, third, fourth, fifth or experiment)?
 Weight of the focal crayfish. (for the experimental fight focal = winner’s training)
 Weight of the opponent crayfish. (for the experimental fight opponent = loser’s training)
 Total Behavior Score of the focal crayfish.
 Total Behavior Score of the opponent crayfish.
 Which crayfish tailflipped first (F=focal O=opponent N=Neither tailflipped)?
 What was the highest intensity score for this fight (-3 – +3)?
 Which crayfish initiated the FIRST contact (F=focal O=opponent N=No contact)?
 Which crayfish won the fight (F=focal; O=opponent; T = tie)?
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
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What was the duration (seconds) from first contact to first tailflip?
Hypotheses and Predictions:
Many hypotheses can be tested with the data you will collect during this experiment.
You will be recording categorical data (nominal) such as winner/loser, first to tail flip, male/female.
You will also be recording numerical variables (continuous) such as the number of specific behaviors,
the overall behavioral score, the weight of the individual. For some of these variables you may be
interested in the mean value for a group of individuals, such as the mean time to first tail flip for a
winner’s training compared to a loser’s training. For other variables you may be interested in the
relationship between two continuous variables, for example, the relationship between weight of the
opponent and the duration of time until the first tailflip. Different statistical tests are appropriate for
different types of data. The following flowchart should help you decide when each test is appropriate.
While you wait for the class data set, work as a team to discuss the following questions.
Record some of your ideas in your lab notebook.
 How would you redesign this experiment in order to determine if crayfish rely on
individual recognition, the ability to recognize an individual previously encountered?
 How would you test if familiarity is more or less important that an individual’s recent
experience?
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
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How would you design an experiment to determine if relative size of the opponent is more
or less important than recent experience?
While you continue to wait for the class data set, work as a team to choose the correct statistical test for
each biological question. You can begin writing the hypothesis and methods for the assignment.
A) Chi-square test of independence (two (or more) categorical descriptions).
B) Correlation analysis (Regression) to test for a relationship between two continuous variables.
C) The unpaired t-test compares the mean of one sample set against the mean of another sample set.
D) The paired t-test compares the means of two samples in which each datum in the first set can be matched
with a corresponding datum in the second set (often the same individual measured before and after an
experimental manipulation).
During training, you fought crayfish that are not size matched.
The answers to these questions are all predictions about a staged fight. These results may support hypotheses
that are related to the adaptive value of different aspects of agonistic behavior. You will need to use the class
dataset. In most cases you will want to use data from the first training fight rather than subsequent training
fights. (Why do I suggest this?)
Which test would you use to address each of the following questions?
1) Was the type of fight independent of which animal would tailflip first?
2) Was there a relationship between the opponent's weight and the duration between first contact and tailflip?
3) Was there a relationship between the focal animal's weight and the highest score in the battle (escalation)?
4) Was the outcome of the fight independent of type of fight? (if it is, we aren't doing a very good "training")
5) Is there a difference in the mean Total Behavior Score for focal crayfish in winner and loser training?
6) Is there a difference in the mean Total Behavior Score for the opponent crayfish for the 3rd training fight
compared to the 1st training fight?
*7) Was there a relationship between the weight difference of the two individuals and the time between first
contact and tailflip? *(You would have to add a column to the data table and use a dynamic formula in order
to calculate the size difference between the focal and opponent animals.)
**8) Is there a difference in the Total Behavior Score for the focal crayfish for the 3rd training fight compared
to the 1st training fight for the focal crayfish in loser’s training?
** This would require rearrangement of the StatView template. You should be able to figure out what the
appropriate statistical test is, but you may need to seek help if you want to complete the analysis.
In the Experimental fight, the crayfish were size matched.
As a class we will test a hypothesis about the value of previous experience in agonistic encounters. If fight
outcome is not independent of past experience, we predict that the crayfish with “winner’s” training will win.
You can also ask many questions concerning specific aspects of the fight (duration, intensity, specific
behaviors etc.). Again, the type of data available to answer these questions determines what statistical test to
use.
1) Was the mean Total Behavior Score for the focal animal different for fights that were won by that animal?
2) Was the outcome of the experimental fight independent of which animal initiated contact?
3) Is there a relationship between the intensity of the fight and the duration between first contact and tailflip?
**4) Was the mean Total Behavior Score different for crayfish with winner’s training or loser’s training?
** This interesting question requires rearrangement of the StatView template. You should be able to figure
out what the appropriate statistical test is, but you may need to seek help if you want to complete the analysis.
***5) Is there a relationship between the number of “Threats” and “Strikes” for the focal animal?
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***We did not enter data for individual behaviors for the class data set, but you can determine which
statistical test is required. There is a wealth of individual variation in fighting patterns that is omitted from our
analysis.)
Assignment:
Prepare a write up as a team (the 4 students training 2 focal crayfish).
The report is due 1 week after this exercise is performed.
The report should include:
1) A formal hypothesis (one from above or one that your team devised).
2) A brief explanation (4 – 5 sentences) concerning the adaptive value of the behavior that might
explain the ultimate function of the decision to fight or not to fight. There are some primary
literature papers on the Courses Server that are referenced in this handout that may be helpful. If
you use information from those references (or others that you find on your own) don’t forget to
cite those references appropriately with the authors last name(s) and year in the text and the full
citation provided at the end of your write up.
3) A methods section that clearly states which aspects of the data set were analyzed (did your team
use the results for the first training fight for every focal animal, did your team use total
behavioral scores for all training fights, did your team use only data from the experimental fights
etc.). Clearly state the statistical analysis that was applied to the data in order to determine if
there was a significant effect.
Do not write out the training and testing methods in your Lab Report. That information should be
in your lab notebook. Unless you have changed the protocol, your write up you can simply state,
“Behavioral training, scoring and testing was conducted according to standard Bio102 Crayfish
protocol”.
4) A figure that accurately presents the data that are relevant to your hypothesis and statistical test.
5) A figure legend that sufficiently describes the experimental design so that a knowledgeable
scientist could interpret the figure without having to refer back to the rest of the report.
6) A brief discussion of your statistical results in relation to your hypothesis.
StatView Instructions for Correlation Analysis with Small Sample Size
Click Analyze / Nonparametrics and choose Spearman Correlation
In the Variables window assign the two continuous variables you are testing for correlation.
Click OK
As with ANOVA and t-tests that you have seen before, the P-value tells you if the relationship between
your two variables is significantly different than would be expected by random chance.
To graph your data: use Bivariate / Scattergram
Display a line for the Regression, but do NOT check mean or slope.
Assign one of your continuous variables to be the X Variable and the other to be the Y Variable.
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StatView Instructions for Chi-Square Test of Independence for two categorical variables
Click Analyze / New View
Choose Contingency table / and while holding down the apple key click Summary Table / Observed
Frequencies / Expected Values.
Then select Coded raw data.
Click OK.
The summary table includes the Chi-square P-value.
The Observed Frequency table includes the tally of your data
The Expected Frequency table includes the values that you would have expected if these two variables
were independent (i.e. if the null hypothesis was true).
StatView instructions on the paired and unpaired t-test are the
t-test: used to compare the means of two distributions given the between group and within group
variances
Factorial ANOVA is an extension of the t-test for >2 groups.
Analyze-> New View
Unpaired Comparisons
Unpaired t-test
Hypothesized difference: 0
Tail: Both
OK
Assign a continuous variable and a nominal variable with the Add button.
Paired t-test: used when multiple response variables are measured for each individual
Repeated measures ANOVA is an extension of the paired t-test for > 2 groups.
Analyze-> New View
Paired Comparisons
Paired t-test
Hypothesized difference: 0
Tail: Both
OK
Assign two continuous variables with the Add button.
To make your graphs, you will use Cell Plot->Point Chart to plot the two means with 95%
Confidence Intervals. While the t-test tables are still selected, Point Chart will use the same two
variables already selected.
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Acknowledgements:
This lab is, in part, based upon a protocol by Elizabeth Jakob and Chad Hoefler “Learning to be
Winners and Losers: Agonistic Behavior in Crayfish published in Exploring Animal Behavior in
Laboratory and Field. Elsevier Press 2003.
Advice on design was contributed by Donald Edwards (Univ. of Georgia) and Ed Kravitz (Harvard
Medical School).
References:
Barinaga, M. (1996). Neurobiology - Social status sculpts activity of crayfish neurons. Science
271:290-291.
Chen, S., A. Y. Lee, Bowens, N. M., Huber, R. and Kravitz, E. A. (2002). Fighting fruit flies: A model
system for the study of aggression. Proceedings of the National Academy of Sciences of the
United States of America 99:5664-5668.
Dierick, H. A. and R. J. Greenspan (2006). Molecular analysis of flies selected for aggressive behavior.
Nature Genetics 38:1023-1031.
Glass, C. W. and F. A. Huntingford (1988). Initiation and Resolution of Fights between Swimming
Crabs (Liocarcinus-Depurator). Ethology 77: 237-249.
Hofmann, H.A., and Stevenson, P.A., (2000) Glight Restores Fight in Crickets. Nature 403:613.
Huber, R., M. Orzeszyna, Cobb, J. S. and Clancy, M. (1997). Biogenic amines and aggression:
Experimental approaches in crustaceans. Brain Behavior and Evolution 50:60-68.
Huber R & EA Kravitz. 1995. A quantitative study of agonistic behavior and dominance in juvenile
American lobsters (Homarus americanus). Brain, Behav., Evol. 46:72-83
Huber, R., K. Smith, Delago, A., Isaksson, K. and Kravitz, E. A. (1997). Serotonin and aggressive
motivation in crustaceans: Altering the decision to retreat. Proceedings of the National Academy
of Sciences of the United States of America 94:5939-5942.
Jackson, W. M. (1991). Why Do Winners Keep Winning. Behavioral Ecology and Sociobiology
28:271-276.
Karavanich, C. and J. Atema (1998). Individual recognition and memory in lobster dominance. Animal
Behaviour 56:1553-1560.
Kravitz, E. A. and R. Huber (2003). Aggression in invertebrates. Current Opinion in Neurobiology
13:736-743.
Smith, I. P., F. A. Huntingford, Atkinson, R. J. A., and Taylor, A. C. (1994). Strategic Decisions During
Agonistic Behavior in the Velvet Swimming Crab, Necora Puber (L). Animal Behaviour 47:885894.
Smith, I. P. and A. C. Taylor (1993). The Energetic Cost of Agonistic Behavior in the Velvet Swimming
Crab, Necora (= Liocarcinus) puber. Animal Behaviour 45:375-391.
Spanier, E., T. P. McKenzie, Cobb, J. S. and Clancy, M. (1998). Behavior of juvenile American lobsters,
Homarus americanus, under predation risk. Marine Biology 130:397-406.
Stevenson PA, Hofmann HA, Schoch K (2000) The fight and flight responses of crickets depleted of
biogenic amines. Journal of Neurobiology 43:107-120.
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Appendix
Categorical measurement:
Categorical data fall into distinct mutually exclusive categories that lack quantitative and qualitative
intermediates. Names are assigned to the categories. For practical data processing, the names may be
numerals, but in that case the numerical value of these numerals is irrelevant. The only comparisons that
can be made between categorical values are equality and inequality. There are no "less than" or "greater
than", nor addition or subtraction among categorical data. Examples include: the marital status of a
person, the make or model of a car, a defined behavioral outcome, response vs non-response etc.
Categorical variables are also called “Nominal variables”.
Different Numerical Measurements:
Ordinal measurement:
Numbers are assigned that represent a rank order (1st, 2nd, 3rd etc.) of the entities measured. The
numbers are called ordinals. The variables are called ordinal variables or rank variables. Comparisons of
greater and less can be made, in addition to equality and inequality. However operations such as
conventional addition and subtraction are still meaningless. Examples include the results of a horse race,
which say only which horses arrived first, second, third, etc. but no time intervals; and many
measurements in psychology and other social sciences, for example attitudes like preference,
conservatism or prejudice and social class.
Interval measurement:
The numbers assigned to objects have all the features of ordinal measurements, and in addition equal
differences between measurements represent equivalent intervals. That is, differences between arbitrary
pairs of measurements can be meaningfully compared. Operations such as addition and subtraction are
therefore meaningful. The zero point on the scale is arbitrary; negative values can be used. Examples of
interval measures are the year date in many calendars, and temperature in Celsius scale or Fahrenheit
scale.
Ratio measurement:
The numbers assigned to objects have all the features of interval measurement and also have meaningful
ratios between arbitrary pairs of numbers. Operations such as multiplication and division are therefore
meaningful. The zero value on a ratio scale is non-arbitrary. Most physical quantities, such as mass,
length or energy are measured on ratio scales; so is temperature measured in Kelvins, that is, relative to
absolute zero.
Statistical Tests in Animal Behavior:
Statistics enable us to objectively evaluate our results.
Descriptive statistics are useful for exploring, summarizing, and presenting data. Descriptive statistics
include the mean, mode (most frequent data class), and median (middle value in an ordered set of data).
The variance, standard deviation, and standard error are measures of deviation from the mean. These
statistics can be used to explore your data
Inferential statistics are used for interpreting data and drawing conclusions about our hypotheses.
A variety of statistical tests can be used to determine if the data best fit our null hypothesis (a statement
of no difference) or an alternative hypothesis (the questions we ask). We calculate the test statistic
appropriate for our research methods, experimental design, and sample size in order to calculate the
probability that the pattern we see in our data is due to chance alone. This probability is called the P
value. By convention, most behavioral ecologists agree that when P is equal to or less than 0.05, we can
confidently reject the null hypothesis.
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Statistical tests are of two basic types: parametric and non-parametric.
Parametric tests, such as Student’s t-test, ANOVA, and Pearson Correlation are usually the most
powerful tests if the underlying distributions are “normal”. Parametric tests are based on certain
assumptions and often depend upon linear relationships between variables (this is why you needed to log
transform data for some of the Regression analyses earlier this year).
Non-parametric tests, such as Mann-Whitney U-test, Wilcoxon matched-pairs test, chi-square and
Spearman correlation are generally less powerful. However, because they are free form the assumptions
of parametric test they are more “robust”. These tests rely upon the rank rather than measurements on
an interval or ratio scale, and they can be used to analyze data measured on an ordinal scale.
The data obtained in animal behavior research often rely upon categorical measurement.
Furthermore, the sample sizes are often small, and the data are often not “normally” distributed.
In these cases, non-parametric statistical tests are appropriate.
The Spearman rank correlation is a non-parametric statistic requiring measurement on an ordinal
scale or higher. A statistical correlation between two variables does not mean that they are directly
related in a causal manner. Additional experimentation is required to demonstrate causation. Correlation
between two variables, A and B, can arrive for one of three reasons: A causes B; B causes A; or A and B
are independently related to a third variable C. The Spearman correlation coefficient is denoted by the
Greek letter ρ (rho). It is a measure of how well an arbitrary function could describe the relationship
between two variables, it does not require a linear relationship between the two variables, and it can be
used for variables measured at the ordinal level. Significance is determined by calculating the
probability that the correlation would be greater than or equal to the observed ρ, given the null
hypothesis. This can be done repeatedly randomizing the data set in a technique called “permutation
testing”, or comparing the observed ρ with published tables for various levels of significance. StatView
will do this for you.
Chi-square is a non-parametric test of statistical significance appropriate for categorical data. It can be
used for more than two variables. First a table is constructed and the observed frequencies are entered
into the appropriate cells. These values are used to calculate the expected frequencies if the variables
were independent (i.e. if the null hypothesis is true).
For each cell in the table the expected value is calculated by the following equation.
column total x row total
grand total
The difference of the observed frequency and expected frequency squared divided by the expected
frequency is then calculated for every cell in the table. The Chi-square test statistic is equal to the sum of
these values.
In order to determine significance (P-value), the Chi-square value is compared with a published table
that takes into account the number of variables that were tested. Again, StatView does all of this for you
(So don’t bad mouth StatView too much).
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