T-Test Worksheet

Hinton 1995

Science Methods and Practice

BES 301 Price

Preparing for the Data Analysis Lab

If you have questions about how to complete this worksheet, please ask for help at the Quantitative Skills Center (QSC, UW2-131), especially if you haven’t completed a statistics course. Summarize the key ideas in your lab notebook.

You’ll also want to make sure you know how to do basic things in MS Excel (which you can purchase really cheaply from the cashier’s office). I recommend taking a quick online refresher available from the QSC website: http://www.uwb.edu/qsc/workshops. Make sure you can complete the one called Introduction to Microsoft Excel. Again, go to the QSC or talk to me during office hours if you need help!

Learning Goals: Statistical concepts

By the time you take your Data Analysis Test, you’ll need to be able to

• distinguish between research hypotheses and statistical null hypotheses,
• explain when and why to use the t-test,
• classify a test as one-tailed or two-tailed,
• explain what level of significance (a) and p-values mean in plain English,
• determine when to accept or reject a statistical null hypothesis, and
• determine when to accept or reject a research hypothesis.

The reading by Hinton guides you towards these goals, but you’ll probably have to find supplementary material online, too. And you’ll most certainly need to ask lots of questions!

Thinking about the t-test

With what assumption does Hinton open the last paragraph on p. 78?

*Hinton opens with the assumptions that the students come from two sample populations of equal distribution, that the null hypothesis has not been rejected, i.e. there is no significant difference in reading performance found between the two sample populations of students taught with either the traditional teaching method or the new teaching method.   

What is the null hypothesis presented on p. 78?

*That there is no significant difference in reading performance between the group of students taught using the traditional method and the group of students taught using the new method from Europe (Hinton 78).

What statistical tool do we use to determine “what differences would we expect between two samples simply by chance alone” (78-9)?

*Calculating the mean of the data pertinent to our experiment from every possible sample at the sample size we plan to test, then comparing this to the mean of the pertinent data from every sample size we can access that is of the same sample size we plan to use for our experiment.

What is a t-test? (cite other sources if you need to)

*A t-test is the equation test run to determine a score, based on your data, which is then compared to your data table score to determine if the results of your experiment show significant statistical findings that support your hypothesis, or show that your results have no significant statistical findings and thus fail to reject the null hypothesis of your experiment.  

What are the assumptions of the t-test?

*That our test groups or samples come from adequately distributed populations, and that our experiment sample groupings have adequately similar standard deviations (Hinton 81).   

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)* Does taking a lunch break affect a decline in students’ focus for when they return to class, thus making them perform worse at math after lunch than in the morning at the start of class?

2.       What data does she collect to test her research hypothesis? *She collects the scores of two different math tests with adequately similar questions, with one test taken early in morning and the other test taken after lunch, all  by the same test subject group of 8 students in her class.  

3.       Is this a one-tailed test or a two-tailed test? *One-tailed

4.       What is the statistical null hypothesis?  *That students perform relatively the same on math tests regardless of if they take them at the beginning of the day or after lunch. ???? Or would it be more like?-Students don’t perform significantly better on math tests in the morning than after lunch.   

5.       What level of significance did the teacher choose? *The teacher chose a p= 0.05 level of significance.

6.       Does she accept or reject her statistical null hypothesis? *She rejects her statistical null hypothesis.

7.       Does she accept or reject her research hypothesis? *She accepts her research hypothesis.

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.

1. What is the research hypothesis?  *That this sleeping pill will have different effects on men and women.
2. What data were collected to test the research hypothesis? * The comparative difference of extra hours slept per night in one group of six men and one group of eight women, over a period of fourteen nights in which each of the participants received the sleeping pills for seven nights and a placebo pill for seven nights, without being made aware of which pills they were receiving on which nights.
3. Is this a one-tailed test or a two-tailed test? *Two tailed
4. What is the statistical null hypothesis?  That there will be no significant difference between the male and female extra hour sleeping responses from taking the sleeping pills.
5. What level of significance was chosen? *No significance found at the p=0.05 level. Does this mean though that p=0.05 was the chosen significance level, and they just didn’t find it, or is my first answer the correct response you are looking for?
6. Is the p-value greater than or less than the level of significance? * The p value is greater than the level of significance in this case.  As to why, I have to admit I am still a little unclear on as far as the actual mathematic manipulation goes here.
7. Should you accept or reject the statistical null hypothesis? *Accept.
8. Should you accept or reject the research hypothesis? *Reject.

What question does the t-test answer, in general?  * The t-test in general answers whether or not the data from your experiment supports or rejects your research hypothesis or your statistical null hypothesis through determining the significance level and p value of your results, based on whether or not your findings occurred beyond or within the statistically determined parameters of your experiment groups’ standard deviation, standard error, and degrees of freedom.     

What question do you think you’ll use the t-test to explore in your research project?

*Whether or not being knocked off the barnacles once per day had any significant effect on Nucella Lamellosa’s growth in total tissue weight over the course of this experiment, as compared to the standard deviation of tissue growth in the control group and the group removed from water with no food for 2 hours?

****All data, keyword references, and paraphrased concepts in the completion of this worksheet were taken from Perry R. Hinton’s (1995) “Statistics Explained: A guide for social science students.”