1. Statistical Analysis Determining the Significance of Data
Accepting or Rejecting the Null Hypothesis

2. Analysis of Variance (ANOVA) Test
statistical method used to test general differences between two or more means.
Allows you to make a general conclusion regarding your Null Hypothesis :
If You Accept the Null using this test, all the means are the same or very close
If you Reject the Null using this test, at least one of the means is significantly different at least one other mean.

3. Analysis of Variance (ANOVA) Test
This statistical method provides you with a p-value (a probability).
Based on the concept of sampling (gathering data on a sample that should represent the whole population).
Need a cut-off point for the p-value
Common “cut points”: 0.05, 0.01, .001
Most Biologists use 0.05 for a p-value
A p-value < 0.05 means we are 95% or more confident our data IS significantly different, therefore we reject the Null Hypothesis.
A p-value > 0.05 means our data is NOT significantly different, therefore we do not reject the Null Hypothesis.

4. Analysis of Variance (ANOVA) Test
Let’s look at an example using Redi’s experiment which he used to disprove Spontaneous Generation.
Table 1:
# of flies present around Jars with different covers
no cover
mesh
sealed
Jar 1 36 30 1
Jar 2 42 45
Jar 3 38 44
Jar 4 47 2
Jar 5 33
mean
St. Dev

5. Analysis of Variance (ANOVA) Test
Finding Mean using Excel:
Select the Cell next to “mean”.
Type =average(
select the data you want to average
type )
press enter.
Finding Standard Deviation (how spread out the #’s are):
Select the Cell next to “St. Dev”
Type =stdev(
select the data you want
press enter

6. Analysis of Variance (ANOVA) Test
Enter labels for each column of data
Enter data in all columns
From top ribbon, select Data, then Data Analysis
If your computer does not have Data Analysis, Select File, Select Options, Add-ins.
Select Analysis Tool Pac, Select Go….Check Analysis Too Pac
Now from the ribbon, select Data and then Data Analysis

7. Analysis of Variance (ANOVA) Test
Select ANOVA: Single Factor
Click on Input Range Icon (A)
Highlight all raw data including labels in the 1st row (area in yellow) (do not include trials column)
Click Input Range Icon again
Check the box for Labels in First Row (B)
Important: Click in the circle for Output Range (C)
Click on a Cell where you want the table to appear
Click OK (E)
If P<0.05, then do T-tests to identify significance
If P>0.05, then there is no significant difference and Null is accepted

8. T-Test: Statistical Significance
A t-test’s indicates whether or not the difference between two groups’ means are significantly different in the population from which the groups were sampled
A statistically significant t-test result is one in which a difference between two groups is unlikely to have occurred because the sample happened to be atypical. Statistical significance is determined by the size of the difference between the group averages, the sample size, and the standard deviations of the groups. For practical purposes statistical significance suggests that the two larger populations from which we sample are “actually” different.

9. T-Test: Statistical Significance
A t-test also provides a p-value and compares an experimental group to the control group.
We still use the following interpretation:
A p-value < 0.05 means we are 95% or more confident our data IS significantly different, therefore we reject the Null Hypothesis.
A p-value > 0.05 means our data is NOT significantly different, therefore we do not reject the Null Hypothesis.
Is performed after receiving a p<0.05 in an ANOVA Test
Allows one to determine which experimental group(s) is causing the significant difference

10. T-Test: Statistical Significance
Let’s use Redi’s experiment again to practice running a T-test.
Add a row and Label it “ttest”
Click on the adjacent empty cell
Click on Formulas in the tool bar
Click on “More Functions” then “Statistical” then select T.Test from the menu bar (you should see a table similar to Table 2)
For “array 1” select the first column of data to be compared
For “array 2” select the second column of data to tbe compared
For “tails” select 1 since we predict that one group will be higher than the other
For “type” select 3 since the standard deviations are different for each group
Add the information, hit return and the number generated is the P-value.

11. T-Test: Statistical Significance

12. Chi Square: Goodness of Fit Test
The Chi Square Goodness of Fit Test determines if a set of data is significantly different from an expected outcome.
Calculates a chi square value!
Our Null says that the IV has NO effect on the DV
If a Chi Square Test indicates you should reject the Null, then there IS a significant difference between the expected values and the experimental group values.

13. Chi Square: Goodness of Fit Test
The Chi Square Table:

14. Chi Square: Goodness of Fit Test
Degrees of Freedom (df) = # of groups minus one

15. Chi Square: Goodness of Fit Test
Degrees of Freedom (df) = # of groups minus one
If the calculated chi-square value is greater than or equal to this critical value, then the two groups ARE significantly different, and the null hypothesis is rejected. If the null hypothesis is rejected and we are 95% confident that there is significant difference.
If the calculated chi-square value is less than this critical value, then the two groups are NOT significantly different, and the null hypothesis is not rejected/accepted.

16. Chi Square: Goodness of Fit Test
Practice: Let’s look at the number of males and females in our class. Biologically, there is a 50/50 chance of a couple having a boy or a girl. Therefore, our expected number of males and females in a class of 40 students is . In a real class of students, there were 13 boys and 27 girls. Does this significantly differ from the expected values?

17. Chi Square: Goodness of Fit Test
The Chi Square Table:

18. If Chi Square value is greater than or equal to critical value, reject the Null (is significantly different).
If Chi Square value is less than the critical value, accept the Null (not significantly different).