Understanding t-Test for Dependent Studies
Learn about t-Test for dependent studies, where the same group is measured multiple times. Explore its benefits, when to use it, and step-by-step guidelines for conducting the test with examples.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
T test for dependent A repeated-measures study (a.k.a dependent study) is one in which a single sample of individuals is measured more than once on the same dependent variable. Main benefit: two sets of data are from the same subjects. 2
Example Three professors at University of Alabama studied the effects of resource and regular classrooms on the reading achievement of learning-disabled children. A group of children was test before they take the 1-year daily instruction and after they took the 1-year daily instruction. Which statistical test we should use? 3
T test for dependent D D = t 2 2 ( ) n D 1 n D : the sum of all the difference between groups : the sum of the differences squared between groups n : the number of pairs of observations 2 D 4
T test for dependent D2 Pre-test Post-test D 3 5 4 6 5 5 4 5 3 6 7 8 7 6 7 8 8 9 9 8 7 7 6 7 8 7 8 6 7 8 9 6 6 7 8 8 7 9 4 3 2 1 3 4 2 1 4 2 1 16 9 4 1 9 16 4 1 16 4 1 1 4 -1 2 4 2 1 0 -1 -5 -4 -2 -1 3 1 4 10 16 9 9 8 8 4 4 5 6 9 8 4 1 0 1 25 16 4 1 9 1 5 12 16
T test for dependent Step1: a statement of the null and research hypotheses posttest pretest : H 0 posttest pretest : H 1 6
T test for dependent Step2: setting the level of risk (or the level of significance or Type I error) associated with null hypothesis 0.05 7
T test for dependent Step3: selection of the appropriate test statistics T test for dependent = t test for paired samples = t test for correlated samples 8
T test for dependent Step4: computation of the test statistic value t=2.45 9
T test for dependent Step5: determination of the value needed for rejection of the null hypothesis T Distribution Critical Values Table df=n-1=25-1=24 One tailed: because research hypothesis is directed 10
T test for dependent Step6: a comparison of the t value and the critical value 2.45>1.711 Reject the null hypothesis 11
T test for dependent Step7 and 8: time for a decision There is the difference between pre-test and post- test: the post-test scores are higher than the pre- test scores. 12
Excel: T.TEST function T.TEST (array1, array2, tails, type) array1 = the cell address for the first set of data array2 = the cell address for the second set of data tails: 1 = one-tailed, 2 = two-tailed type: 1 = a paired t test; 2 = a two-sample test (independent with equal variances); 3 = a two- sample test with unequal variances 13
Excel T.TEST() It does not computer the t value It returns the likelihood that the resulting t value is due to chance Less than 1% of the possibility that two tests are different due to chance the two tests are difference due to other reasons than chance. 14
Excel ToolPak t-Test: Paired Two Sample for Means option t-Test: Paired Two Sample for Means pretest posttest Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 6.32 7.52 2.976666667 3.343333333 25 25 0.050718341 0 24 -2.449489743 0.010991498 1.710882067 0.021982997 2.063898547 15
Advantages of the Repeated-Samples Design Repeated-measures design reduces or limits the variance, by eliminating the individual differences between samples. 16
Problems With the Repeated-Samples Design Carryover effect (specifically associated with repeated-measures design): subject s score in second measurement is altered by a lingering aftereffect from the first measurement. 17
Example I (select appropriate methods and make the test, the same as followings) A researcher is interested in a new technique to improve SAT verbal scores. It is known that SAT verbal scores have =500 =100. She randomly selects n=30 students from this population, and has them undergo her training technique. Students are given analogy questions, and are shocked each time they get an answer wrong. The sample then writes the SAT, and gets M = 560. 19
Example II A social psychologist is interested in whether people feel more or less hopeful following a devastating flood in a small rural community. He randomly selects n=10 people and asks them to report how hopeful the feel using a 7-point scale from extremely hopeful (1) to neutral (4) to extremely unhopeful (7) The researcher is interested in whether the responses are consistently above or below the midpoint (4) on the scale, but has no hypothesis about what direction they are likely to go. His sample reports M=4.7, s = 1.89. 20
Example III To test the hypothesis that people give out more candy to kids in cute costumes than scary ones, I hire 20 kids to work for me. Ten are randomly assigned to wear cute bunny costumes, and the other ten wear Darth Vader costumes. I drop the kids off in random parts of the city, and count the total pieces of candy each has after 1 hour of trick-or-treat. Cute bunnies: M = 120, s = 10 Darth Vaders: M = 112, s = 12 21
Example IV We are testing the effects of moderate amounts of alcohol on driving performance. We make the hypothesis that even a small amount of beer will degrade driving performance (an increase in obstacles hit). To test our hypothesis, we have n=5 subjects drive around a course on Big Wheels covered with cardboard cutouts of children and furry animals, and we record the number of cutouts they hit. Then, they drink one beer, and do the course again; again we record the number of cutouts hit. What is a potential confound with this experiment? 22
Example V We want to determine if IU LIS faculty publish more than the national average of 4 papers per year (per person). We take a random sample of n=12 IU LIS professors and survey the number of papers each has published, obtaining M=6.3, s=1.13. 23
Example VI I want to know which dog is responsible for the holes in my yard. I buy 10 German Shepherds, 10 Beagles, and randomly assign each dog to its own yard. At the end of the day, the Beagles have dug M=11.3 holes, s=2.1, and the Shepherds have dug M=5.4 holes, s=1.9. Test my hypothesis that Beagles dig more holes than German Shepherds. 24
Example VII We want to know if noise affects surgery performance. We randomly select a sample of 9 surgeons, and have them perform a hand-eye coordination task (not while performing surgery, of course). The surgeons first perform the task in a quiet condition, and then we have them perform the same task under a noisy condition. Test the hypothesis that noise will cause poorer performance on the task. 25
Example VIII ETS reports that GRE quantitative scores for people who have not taken a training course are =555, =139. We take a sample of 10 people from this population and give them a new preparation course. Test the hypothesis that their test scores differ from the population. 26
