Thinking about the t-test
With what assumption does Hinton open the last paragraph on p. 78?
Hinton assumes that if the probability is higher than the difference in the sample mean, then the null hypotheses is true.
What is the null hypothesis presented on p. 78?
The null hypothesis is that the new scheme will produce better results than the older shceme.
What statistical tool do we use to determine “what differences would we expect between two samples simply by chance alone” (78-9)?
We use the mean. We calculate both means and find the difference.
What is a t-test? (cite other sources if you need to)
A t test will test the distribution of a set of data if the null hypothesis is supported.
What are the assumptions of the t-test?
That there is normal distribution.
The example beginning on p. 83 is a related t-test, because the two sets of data come from the same people (the same group of students takes a test before lunch and after lunch). Summarize this example beginning 83 by answering the following questions:
1. What question is this teacher asking? (the answer that she predicts for this question is her research hypothesis)
That the children in her class were better at their work in the morning rather than in the afternoon.
2. What data does she collect to test her research hypothesis?
She collected data from math test which required the student’s concentration.
3. Is this a one-tailed test or a two-tailed test?
This is a one tailed test.
4. What is the statistical null hypothesis?
That the morning and afternoon tests will have the same scores.
5. What level of significance did the teacher choose?
Significance level is p = 0.05
6. Does she accept or reject her statistical null hypothesis?
She rejects the null hypothesis.
7. Does she accept or reject her research hypothesis?
She accepts her research hypothesis because her students performed better in afternoon vs. morning .
In biology, however, it’s more common that we have an independent t-test. You can, as Hinton discusses, compare how men and women respond to a sleeping pill. Answer the following questions about the example beginning on p. 88.
- What is the research hypothesis?
That the effect of the sleeping pill will be different on men rather than women.
- What data were collected to test the research hypothesis?
Six men and eight woman agreed to participate in the study. Over two weeks they either took a placebo or the bill. They did not know which they were being given. The numbers of the placebo were compared to that of the sleeping pill nights.
- Is this a one-tailed test or a two-tailed test?
Two tailed Test.
- What is the statistical null hypothesis?
That there will not be a difference between men and women.
- What level of significance was chosen?
Df = 12, p = 0.05
- Is the p-value greater than or less than the level of significance?
The p-value is the same as the level of significance of 5%. (0.05
- Should you accept or reject the statistical null hypothesis?
The null hypothesis should be accepted.
- Should you accept or reject the research hypothesis?
The results of the research hypothesis should be rejected.
What question does the t-test answer, in general?
If you should accept or reject results.
What question do you think you’ll use the t-test to explore in your research project?
If the marginal difference will have an effect on knocking off barnacles.
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