Wofford College
Using JMP 8 posted 27 October 2010 at 3:45 pm
Quick notes on conducting a T-Test with Near Point of Accommodation data for college-age men and women
and selecting p values for one-tailed and two-tailed t-tests.
Suppose the hypothesis is that “There is a difference in NPA for college-age men and women who do not wear corrective lenses.” Since this hypothesis doesn’t specify that one sex would have a greater NPA than the other, we’ll be using a two-tailed t- test.
From spreadsheet that contains all the data, select just those NPAs for men and women who don’t wear corrective lenses. To simplify matters, we’ll just use the data from the right eye (and assume there’s no difference between the left and right eyes.)
In Excel, set up two columns; the first labeled with the categories of your data (for this example it would be “sex” which corresponds to the independent variable) and the second column will have the NPA value for that person (which is the dependent variable.) In essence, we’re asking if the dependent variable actually differs by sex.
Copy and paste those two columns into a new datasheet in JMP.
Now label the columns in JMP. The left column should a character value and the right column should be numeric.
You’re ready to run your analysis now.
Under the Analyze tab, select “Fit Y by X” and then move the Sex to the X factor box and the NPA to the Y response box.
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Hit OK.
You’ll see a graph of the two sets of data.
Click on the down arrow in the upper left corner of the graph box:
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Highlight “Means/Anova/Pooled t”:
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The next box shows results of your statistical analysis (see next page.)
You’ll need the means and standard errors and n values for each of your two groups to incorporate into your abstract. Those numbers are located at the bottom of the box. The NPA for the 15 women was 91 ± 6 mm (mean ± standard error) and for the men the NPA was 94 ± 5 mm. Take a careful look at these numbers; they’re actually pretty similar by eye and there’s a fair amount of variation in the NPAs as indicated by the standard errors. To determine whether there is a statistically significant difference in NPA, we’ll need to examine the p value.
You must determine which of the three p values listed inside the red circle (next page) is appropriate to use. The choice depends on your hypothesis.
Since our hypothesis is “There is a difference in NPA for college-age men and women who do not wear corrective lenses” we’re looking for ANY difference in the averages for the two sexes, and we haven’t specified which group might have the larger NPA, so we’d use the p value for a two-tailed t-test. P values for two-tailed test are provided as “Prob > [t] = 0.7586.” You’d write this as p=0.7586 in your abstract and since this value is clearly greater than 0.05, you must accept the null hypothesis (there is no difference in NPAs for college age men and women) and reject your original hypothesis.
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But what if your hypothesis had been “College-age men have a greater NPA than college-age women who do not wear corrective lenses.” In this case, your hypothesis states that one group IS different than the other, and even predicts which group would have the greater average NAP. This hypothesis has a directionality aspect. For hypothesis that predict the direction of a difference, you should use a one-tailed t-test. Now you have to determine which one of the two remaining p values to use.
Look at the results: The mean NAP for the women was 91 mm and for the men the NAP was 94 mm. Sure enough, the average NPA for men appears to be greater than for women as the hypothesis predicted, but is the difference large enough to be statistically significant? Consulting the list of p values, we see “Prob > t = 0.3793.” This is p value for a one-tailed t-test and means that there is a 38% chance that just by random sampling we’d get a difference between men and women this large. Remember, our cutoff value is 0.05 and clearly 0.3793 is greater than 0.05, so we’d have to accept the null hypothesis (there is no difference in NPA for men and women of this age) and reject our alternate hypothesis that men have a greater NPA than women.
One last possibility: What if your hypothesis had been “College-age women have a greater NPA than college-age men who do not wear corrective lenses.” Again, the hypothesis not only proposes there is a difference, it also predicts the direction of the difference, so you must use a one-tailed t-test. Your results indicate that if there were a real difference in NPAs for the sexes, it would be more likely that men would have greater NPAs that women (94mm vs 91mm.) In other words, it would be very unlikely, given your results, that women have a greater NPA than men, and the corresponding p value from such a one-tailed t-test is “Prob < t = 0.6207.” This would be the p value to use for this last hypothesis. You’d have to conclude that the data do not support hypothesis that “College-age women have a greater NPA than college-age men who do not wear corrective lenses” (p = 0.6207; one-tailed t test.)
Admittedly, these last two examples are a bit challenging to understand, so let’s look at another set of data on NPA from men and women at age 30 where the differences are greater. (See the box on the next page.) Suppose the results of the statistical analysis are in the box below. It appears that the men have a larger NPA (104 mm) than the women (91 mm) so let’s consider the hypothesis: The average NPA for 30 year old men is greater than the average NPA for 30 year old women. Since this is a “directional” hypothesis that predicts that a particular group (the men) will have the larger NPA, we should use a one-tailed t-test. Which of those p values would be most consistent with our data? “Prob > t = 0.0317” is a p value that is less than 0.05 and indicates a statistically significant difference in the NPAs in the “direction” of our hypothesis predicts (that these men have a larger NPA than these women) so this is the appropriate p value to use.
How do we know 0.0317 is the appropriate p value to use instead of the other one (0.9683) for a one-tailed t-test? Think about it this way: If these 30 year old men had an average NPA of 104 and those 15 women had an NPA of 91, it would be very, very unlikely that 30 year old women have a greater NPA than 30 year old men based on this data. The other p value (0.9683) reflects that improbability.
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