1. STEM Fair: Statistical Analysis

2. Summary Statistics
Mean – represents population mean (calculated same as the average)
Standard Deviation – shows the variability of an observation in a sample

3. Summary Statistics Cont.
Confidence Interval - the width of the interval shows how precisely the value of the mean is known
Shows the degree of confidence that our mean is between two values
typically a 95% CI is used

4. Steps to Completing Statistical Analysis
Data collection & input
Data summary & reduction
Data analysis: Perform statistical test(s) and draw conclusion

5. Test Assumptions
Most statistical tests have assumptions that should be met such as:
Data follows a normal population distribution &
Large enough sample size to detect change.
We are ignoring statistical test assumptions for this project.

6. Types of Statistical Tests
Paired T-Test
Unpaired T-Test
ANOVA
Chi-Square
Coefficient of Correlation

7. T-Tests
This test is used to compare the data from two different testing groups to determine if they are significantly different. There are two different types:
PAIRED: Used when the data consist of pairs of observations on the same person or object.
Example: comparing the heart rate of individuals before and after watching a scary movie.
UNPAIRED: Used when the data from one group are not directly linked to the data of the other group.
Example: comparing the effect of red light versus blue light on the growth of plants.

8. ANOVA
This test is used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups.
Example: determining whether exam performance differed based on test anxiety levels amongst students. Students are divided into three independent groups (e.g., low, medium and high-stressed students).

9. Chi-Square Test
This test is used to determine if there are differences between two or more frequency distributions. Both independent and dependent variables need to be categorical data.
Example: comparing the foraging height (upper, middle, and lower) of yellow warblers in different tree species (oak, maple, aspen, and hazel).

10. Coefficient of Correlation
This test is used to determine if the values of the dependent variable are directly related to the independent variable. You would use this test when both the variables are measured on a scale (i.e. time, temperature, length, etc.).
Example: determining the effect of pH value on the growth of plants. After you enter data, you will get an r-value, which will indicate how strongly related the two variables are. The closer the value is to 1 or -1, the stronger the relationship is.

11. Analyzing the Test Results
Two possible conclusions after carrying out a test
Reject Hypothesis
Fail to reject Hypothesis (we can never accept the alternative hypothesis)

12. Analyzing the Test Results (cont.)
P-values – one way to report the result of an analysis is by saying whether or not the hypothesis was rejected at a specified level of significance (we will use .05)
The smaller the calculated p-value, the greater the difference between the groups.
Example: the difference in means from our testing groups is statistically significant at the .05