T-Test for Two Dependent Samples (Matched Pairs)

pdf

School

Harvard University *

*We aren’t endorsed by this school

Course

200

Subject

Statistics

Date

Apr 3, 2024

Type

pdf

Pages

6

Uploaded by BarristerStrawGoldfish6970

Report
Hypothesis Test: Claim about Two Dependent Samples What if the two samples we are investigating are in some way dependent on each other? Here are two examples: • Twins, where one twin is in one sample and one twin is in the other sample. Twin studies have been used to assess the heritability of things like personality, intelligence, and mental and physical disorders. (For more information on twin studies, please go to the following link: Why Twin Studies?) (https://msutwinstudies.com/why-twin-studies/) • Measurements taken on the same person at two points in time. Intervention studies often use pretest and posttest measurements to determine whether the treatment had an effect. This hypothesis test uses the following test statistic: Test Statistic Used for T-Test for Two Dependent Samples Now let's see an example of an intervention study that uses the matched pairs t- test: T-Test for Two Dependent Samples (Matched Pairs) https://leocontent.umgc.edu/content/umuc/tus/stat/stat200/2228/t-test-fo... 1 of 6 3/20/24, 11:51 PM
Example: t-test for Two Dependent (Paired) Samples (Using Summary Statistics) A random sample of 7 students took a standardized reading test before receiving tutoring and took a similar reading test after receiving tutoring. The reading test scores of these two samples are not independent. Hopefully, each student will benefit from the tutoring service. In this case, we treat these two data sets--one before tutoring and the other one after tutoring--as dependent samples. Step 1: Identify the Question/Problem to Solve Does tutoring improve reading scores at a 0.01 significance level? State the null and alternative hypotheses (H and H ): H : μ = 0 H : μ > 0 In words, the hypotheses are as follows: H : The mean reading score after tutoring is the same as the mean reading score before tutoring. H : The mean reading score after tutoring is higher than the mean reading score before tutoring. Because there is a "higher [greater] than" alternative hypothesis, this is a one- tailed test. The problem provides the significance level to use: 0.01. Step 2: Identify and Collect Data One continuous random variable that is interval level: A standardized reading test Measurements are taken twice on the same group of students, resulting in two dependent groups: before tutoring and after tutoring. The measurements are as follows: o a o d a d o a T-Test for Two Dependent Samples (Matched Pairs) https://leocontent.umgc.edu/content/umuc/tus/stat/stat200/2228/t-test-fo... 2 of 6 3/20/24, 11:51 PM
Reading score before tutoring (BT) 244 260 264 264 278 318 280 Reading score after tutoring (AT) 456 614 628 1088 943 567 536 Step 3: Select and Apply the Appropriate Method Because we are assessing the difference between two dependent sample means and meet the following assumptions, the appropriate statistical test is the dependent samples t-test. Assumptions: • A random sample of pairs was taken. A random sample of 7 students took a standardized reading test before and after a tutoring intervention. • The population of difference is normally distributed. The sample statistics are as follows: Score (AT) Score (BT) d http://polaris.umgc.edu/ ~aau/stat200/synopises/ dmdbar.gif http://polaris.umgc.edu/ ~aau/stat200/synopises/ dmdbar2.gif 456 244 212 –205.71 42,316.60 614 260 354 –63.71 4,058.96 628 264 364 –53.71 2,884.76 1088 264 824 406.29 165,071.56 943 278 656 247.29 61,152.34 567 318 249 –168.71 28,463.06 T-Test for Two Dependent Samples (Matched Pairs) https://leocontent.umgc.edu/content/umuc/tus/stat/stat200/2228/t-test-fo... 3 of 6 3/20/24, 11:51 PM
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
536 280 256 –161.71 26,150.12 Σ = 2924 Σ = 330,097.43 s = 234.56 Notice that each pretest score is subtracted from its corresponding posttest score; this give us d, which is the amount of difference that occurs between each pair of scores. Thus, this matched pairs t-test is run on the mean of the differences between the pairs of scores and the standard deviation of the differences. s = 234.56 Here is the test statistic: For a dependent samples t-test, the degrees of freedom are number of pairs - 1. In this case, there are seven pairs, so df = 7 - 1 = 6, or 6 degrees of freedom. Using the t-score calculator applet, we find that the p-value of this t-test is 0.0016. Decide whether or not to reject H The p-value of this t-test is 0.0016. This is the probability that an event, the null hypothesis, will happen.This p -value is much smaller than the given α , which is d d o. T-Test for Two Dependent Samples (Matched Pairs) https://leocontent.umgc.edu/content/umuc/tus/stat/stat200/2228/t-test-fo... 4 of 6 3/20/24, 11:51 PM
0.01. Thus there is enough evidence to reject the null hypothesis that the mean reading score after tutoring is the same as the mean reading score before tutoring Step 4: Interpret the Results and Apply to Real Life Within the context of the problem, we can say that reading test scores are significantly higher after tutoring, which supports the claim that tutoring improves reading scores (p<.01). Here is how the QuickCalcs web applet calculates the p-value from the above problem using raw data: T-Test for Two Dependent Samples (Matched Pairs) https://leocontent.umgc.edu/content/umuc/tus/stat/stat200/2228/t-test-fo... 5 of 6 3/20/24, 11:51 PM
The results show that the t-value is 4.7118, with 6 degrees of freedom, and a p- value of 0.0016. The results are consistent with the results obtained using summary statistics. (Note: The p -value calculated by the applet is for a two-tailed test.Since we are doing a one-tailed test, the p -value needs to be divided by 2; therefore, the p-value for this problem is: 0.0033/2 =0.0016.) T-Test for Two Dependent Samples (Matched Pairs) https://leocontent.umgc.edu/content/umuc/tus/stat/stat200/2228/t-test-fo... 6 of 6 3/20/24, 11:51 PM
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help

Related Documents

IMG_5128.jpeg
IMG_5130.jpeg
Solution_Describing_Data_B_Displaying_Qualitative_Data_Start.xlsx
Data Analysis Work - clean(2).xlsx
WK8AssgnGordon L.docx
1 - Graded Week 5 Homework-Mark Kasule.pdf
3 - Graded Week 6 Homework-Mark Kasule.pdf
Go - Graded Week 5 Homework-Mark Kasule.pdf
Go - Graded Week 6 Homework-Mark Kasule.pdf
T-Test for Two Independent Samples.pdf
Assignment 2.docx
Assignment 3.docx
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
SEE MORE TEXTBOOKS
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
SEE MORE TEXTBOOKS