In Ch. 8 we learned to conduct a t test to compare the mean of a sample to the mean of its population when we know the population’s mean, but we don’t know its SD. The term for this kind of t test is single sample t test or one sample t test, because it uses data from only one sample.
Example of a single sample t test
It has been suggested that reading from a light-emitting eReader before bedtime can significantly affect sleep and lower alertness the next morning. To test this finding, a researcher obtained a sample of n = 9 volunteers who agree to spend at least 15 minutes using an eReader during the hour before sleeping and then take an alertness test the next morning. For the general population, scores on the test average µ = 50 and form a normal distribution. The data from this test are in the alertness.csv file.
(1) Download alertness.csv and open it in jamovi.
(2) Make sure the Measure type and Data type are correct.
(3) From the Analyses tab, select T-Tests and One Sample T-Test.
(4) Move the alertness scores into the Dependent Variables box.
(5) From the Tests menu select Student’s.
(6) From the Hypothesis menu enter 50 in the Test value box and select ? Test value. This tells jamovi that the population mean, which is specified by the null hypothesis, is 50. This is the test value that we’ll test the sample mean against. We’re also telling jamovi that the alternative hypothesis is that the unknown mean of the treated population is NOT equal to the test value of 50. This is a non-directional or two-tailed hypothesis.
(7) From the Additional Statistics menu select Mean difference and enter 95 for Confidence interval. Also check Effect size and Descriptives. As for the confidence interval (CI), notice that jamovi calculates the CI around the mean difference. This is different from the textbook where we learned to calculate the CI around the sample mean. We can easily convert the CI around the mean difference to the CI around the sample mean by adding the lower bound and the upper bound to the test value of 50. Keep in mind that if one of these values is a negative number, that means we should subtract it from the test value of 50. The resulting values will be the lower and upper bounds of the CI around the sample mean.
(8) Save your analysis as alertness.omv, to be submitted as part of this assignment.