1. Analysis based on normal distributions
Hypothesis Testing
Analysis based on normal distributions

2. Dependent Variable
The measure of the characteristic of individuals in groups
The study outcome measure
The test score

3. Independent Variable
The variable that identifies the groups that will be compared.
Normally this would be different groups of people. Do the groups represent different population?
It could be the same people before and after an intervention. Are the people in the group now members of a different population?

4. Hypothesis: A tentative explanation that accounts for a set of facts and can be tested by further investigation
Problem statement: The purpose of this study is to examine the impact of Direct Instruction reading programs on district test scores.
Hypothesis: Students who participate in direct instruction reading programs will have higher scores than those who do not.

5. Proof
Gather information on the dependent variable (test scores) and compare the scores based on the independent variable (which scores come from students in which program: DI or not).
What if most DI students were better but not all?
What about all the students from whom you did not have scores?
Proof means for all cases. You cannot prove your hypothesis.

6. What happens if this is reversed?
If your hypothesis says that there will be a difference, could you test to see if there was not a difference?
Null hypothesis: stating that no differences would be found when you really are interested in finding them.
If the hypothesis says that something is true then the null hypothesis says that it is not true.

7. Hypothesis Testing
Hypothesis: Kids with DI will have higher scores than those from other programs.
Null Hypothesis: There will be no difference between kids with DI and those from other programs.
You gather evidence and decide if the evidence says that direct instruction students had better scores.
If they do: the hypothesis is not not true.
You reject the null hypothesis.

8. Using Null Hypotheses Use a sample (otherwise we would use parameters)
Stop talking about individuals and only compare groups (mean and standard deviation)

9. Hypothesis Testing Mean of Kids without DI Mean of Kids with DI
In statistical parlance we want to know if the two groups have come from the same population (fail to reject null) or do they represent samples from different populations (reject the null).

10. Hypothesis Testing Mean of Kids without DI Mean of Kids with DI
Sampling distribution of the mean for the sample size of the kids without DI
What is the probability that the group mean difference could have appeared by chance?

11. Measure a bunch of people and if there is little difference among groups (the difference was likely to appear by chance) you say, I have been unable to find evidence that differences exist.
You have been unable to reject the null hypothesis. You have no evidence that your independent variable had any impact.
If the differences among groups are large enough you say the differences could not have happened by chance.
You have been able to reject the null hypothesis. Your independent variable becomes, for now, the best explanation for the differences.

12. Why do this?
Inferential statistics uses estimated parameters of populations to determine if differences in group means could occur by chance.
Inferential statistics is not used to prove hypotheses. It is used to demonstrate whether null hypotheses are not true.

13. Think about this as steps:
You want to know that something is true but you cannot absolutely know because you cannot test all cases.
Instead you focus on the opposite of what you want to know is true (the null hypothesis).
Start gathering evidence.
If enough cases show that something is true then saying it was not true is false.
You have rejected the null hypothesis.
For the time being, the thing you wanted to show is true (your hypothesis) is the best explanation.

14. Ok, one more semantic step and we are done:
What we are interested in knowing is whether something made two groups different.
The evidence that you gather to see if that is true are means and standard deviations of groups.
The null hypothesis always says there will be no difference between the groups.
If there is a very low probability that the difference in the groups could occur by chance, that is the evidence that the null hypothesis is wrong.
Low probabilities (p values) show that the thing you wanted to show (your hypothesis) is more likely to be true than not true. You have rejected the null hypothesis.

15. Excel Example On the course resource site download: Inquiry Science
Compare the two classes using independent sample t-test

16. Inquiry Science
What was the null hypothesis?
Can it be rejected?

17. Presenting t-Tests in Tables
Pretest Posttest Comparison of Scores on a Test of Computing Area.
Class 1
Class 2 n = 27 n = 24
36.19
31.83 * M e an
8.54
7.44 S D * p = .0 6
Results should be in table form listing means, standard deviations, and sample sizes.
In general, actual p values are presented.
Significant findings are reported in text form as well. Non-significant results are reported simply as not significant or not reported at all.

18. Descriptive Paragraph
Scores from a chapter-end unit examine were compared from classes taught using inquiry science and direct instruction. A independent samples t-test comparison was not statistically significant (p = .06).