Math 207 Computer Lab—Inference Procedures

Getting the Needed Files

Double click on the My Computer icon on the desktop. Then double click on the campus_share on 'curtis' (U:) drive and then the Class_Share folder. Finally, double click on the Math folder and then the math_207 subfolder. Included in this folder are the Minitab files we will use in today’s lab: Billionaires.MPJ, Disease.MPJ, HomePrices.MPJ, and MentalRotation.MPJ.

As a class, we cannot access these share files (only one person can assess them at a time). Thus, you each need to copy the four files to your personal account. You can do this by simply highlighting all the files (click on the first one, then control-click on the other three—this should highlight them all). Then press Ctrl-C to copy the files. Now open the My Documents folder on the desktop (this is the My Documents folder of your personal account). Once you are in the My Documents folder, hit Ctrl-V to paste the four files into your account. To both start Minitab and open the first file, you can simply double-click on the Disease.MPJ file that you copied to your documents.

Description of Disease.MPJ

A researcher in a large city is investigating a rare disease and wants to compare the proportion of females and males infected with the disease. The researcher takes a random sample of 500 females and 650 males and tests them for infection. The data file includes the following variables:

females – results for the 500 females (0 – not infected, 1 – infected)

males – results for the 650 males (0 – not infected, 1 – infected)

Analysis

The researcher wonders if there is a difference in the population proportions of males and females who are infected with this disease. Before we carry out a large-sample inference procedure, we must check to see if the distribution of the sample proportions is well approximated by a normal curve (i.e., check if the sample number of infected and not infected is greater than 5 for both samples). Note that Minitab will carry out the large-sample test whether or not it is appropriate. It is up to you, the user of Minitab, to check any assumptions of the statistical methods. To check our rule of thumb, go to the Stat menu and select Tables>Tally Individual Variables. Enter both the females and males variables (the default is to show counts, which is what we want). Note that all sample counts are greater than 5 (just barely), so we can proceed with the large-sample test.

To carry out the test, go to the Stat menu and select Basic Statistics>2 Proportions. When using Minitab to do inference, you must be aware of how your data are set up in the worksheet. In our case, we have two separate columns. Hence, click on the “Samples in Different Columns” circle, and then enter females and males as your variables. Now click on the Options button. Here you can select your confidence level (95% is the default), the value of the difference to test in your null hypothesis (0 is always the default, which is the only situation we’ve discussed), and the direction of the alternative hypothesis (not equal is the default, which is what we want). Furthermore, there’s an option to select “Use pooled estimate of p for test.” This is the test we discussed in class (which uses a pooled estimate of p in the standard error), so select this option.

The results are then printed to the Session Window. Minitab provides the direction of the differencing, hypotheses, confidence interval, test statistic, and p-value. It is up to you to interpret these results. Is the difference statistically significant? Based on the confidence interval, do you think the difference is practically significant?

Description of MentalRotation.MPJ

Students in a previous Math 207 class took a visual spatial test twice, where they were asked to mentally rotate objects given on paper test to determine which objects were actually the same. This file includes the sex, part 1 score, part 2 score, and total score for all 27 students who participated in the study.

Analysis

Because each student took the mental rotation test twice, we can analyze these data with the paired t-test procedure (i.e., is there a practice effect? or is there a frustration effect?). Suppose the population of differences in scores (part 1 – part 2) for students at small, Midwestern, liberal arts colleges has mean . We have a sample (how representative?) from this population and we want to test the hypotheses .

From the Stat menu select Basic Statistics>Paired t. Select part 1 score as the first sample and part 2 score as the second sample. Click on the Graphs button and select a histogram of the differences (this will allow us to check the normality condition of the test). Note that you can click on the Options button to change from the default confidence level (95%) or from the default alternative hypothesis (not equal).

Based on the histogram of the differences, is it appropriate to use the t-test? Look at the results in the session window. Are the results statistically significant (i.e., is there evidence of a practice effect or a frustration effect)?

Analysis

We can also analyze these data with the two-sample t procedures. Suppose the population of mental rotation scores for women at small, Midwestern, liberal arts colleges has mean . Suppose the population of mental rotation scores for men at small, Midwestern, liberal arts colleges has mean . We have separate samples (how representative?) from these two populations and we want to test the hypotheses

First we need to determine if we should use the t procedures (we can tell Minitab to do the analysis, but we must ensure it is the right thing to do). Create separate dotplots of the scores for males and females (Graph>Dotplot>With Groups; select total score as the variable, and select sex as the categorical variable). Based on the dotplots, should we use the t-test? The graphs indicate non-normality in the female scores (although sometimes it’s difficult to tell based on only 8 observations). Hence, we will carry out the test (so you can see how to use Minitab in this way), but we should probably also conduct a nonparametric test to corroborate our results.

From the Stat menu select Basic Statistics>2-sample t. Select total score as the “Samples” and sex as the “Subscripts.” Because it’s easy for Minitab to perform the two-sample t-test that doesn’t assume equal variances, this is the test we’ll use (in practice, this is the test most often used). Hence, do not check the box that says “assume equal variances.” Look at the results in the session window. Are the results statistically significant (i.e., are the means for men and women significantly different)?

More on Inference with Minitab

Minitab allows you to perform all the tests we’ve discussed in class, plus many we haven’t discussed (e.g., nonparametric tests, Chi-square tests). It’s important that you know when to use each test and that you always check the conditions of the test (Minitab doesn’t do this for you). When running a specific test, it’s important that you understand how your data are listed in your worksheet (e.g., separate columns, single column). Finally, it’s important that you understand the output Minitab gives you and that you can provide a conclusion in layperson’s terms (not using technical statistical language).

Minitab can also perform power calculations (and sample size determination) for all the tests we’ve discussed (Stat>Power and Sample Size).