(The Basics)
Why Stats?
• Scientists analyze data collected in an experiment to look
for patterns or relationships among variables. If we think
we see a pattern or a relationship, we must complete one
more step before we can be sure of the results. In order to
determine that the patterns we observe are real, and not
due to chance and our own preconceived notions, we must
test the perceived pattern for significance.
• Statistical analysis allows scientists to test whether or not
patterns are real, and not due to chance or preconceived
notions of the observer. We can never be 100% sure, but
we can set some level of certainty to our observations. A
level of certainty accepted by most scientists is 95%. We
will be using tests that allow us to say we are 95%
confident in our results
Types of Data
• Quantitative Data- measurements made using a
scale with equal intervals (temp of water in
Celsius degrees). Quantitative data consists of
numbers representing counts or measurements.
• Qualitative Data- data using non-standard scales
(descriptions of leaf quality). Qualitative data are
placed into categories that may be discrete
categories represented by word or number
labels. It can also be measurements made with a
nonstandard scale with unequal intervals.
Quantitative Data
Qualitative Data
Descriptive Statistics
• Descriptive statistics are statistics that
describe both the most typical values and the
variations that exists within sets of data.
• Include the mode, mean, median, range,
variance, standard deviation, frequency
distribution, and number.
Descriptive Stats
Mode- value that occurs most often (in a tie, use both)
Median- middle value when ranked highest to lowest
Mean (x)- mathematical average
Range- difference between the smallest and largest average
Variance- average squared distance from the mean (how spread out the
values in a set of data are).
Standard Deviation (SX)- a measure of how closely the individual points of
data cluster around the mean.
Frequency Distribution - # of cases falling into each category of the variable
Number (n)- number of data points
Descriptive Stats
Inferential Statistics
• Inferential statistics are done to determine if
the data is statistically significant. They limit
the possibility that the data differences
occurred by random chance or due to some
unknown, uncontrolled variable. If the data is
shown to be statistically significant then the
data differences can be explained by changes
in the independent variable.
Inferential Stats
Statistical Tests
• The t-test (or Analysis of Variance): An analysis of variance is used
when you have two or more groups and you want to compare
measurements of each group. The t-test analyzes the relationship
between two groups.
• The Chi-square test: This test is used when you have counts that
can be placed into yes or no categories, or other simple categories
such as quadrants.
• The Pearson R Correlation: The Pearson R Correlation allows you
to test how the values of one event or object relates to the values
of another event or object
Inferential Stats
• One-tailed- the probability distribution only
involves one end, either the upper or lower
• Two-tailed- the probability distribution
involves both the upper and lower ends.
• For most of you, the “two-tailed” test is
applicable to your projects.
Level of Significance
• Level of Significance We will use 0.05
which means that the probability of error in
the research is 5/100 (95%).
Null Hypothesis
• Basically states that there is no difference
between the mean of your control group and the
mean of your experimental group. Therefore any
observed difference between the two sample
means occurred by chance and is not significant.
• If you can disprove your null hypothesis then
there is a significant difference between your
control and experimental groups.
Helpful Resources
• APPENDIX B - Statistics for Science Research:
Hints, Tips, Examples (this can be found on my
staff webpage, provided much of the info found
in this PowerPoint, and contains instructions on
how to calculate stats using Excel).
• For calculating t-test values, the following
website is also useful: