Understanding Paired-Samples T-Tests: Hypothesis and Analysis

School

CUNY Hunter College**We aren't endorsed by this school

Course

STAT 213

Subject

Statistics

Date

Dec 10, 2024

Pages

Uploaded by ChancellorFreedom15844

CPAIRED-SAMPLES T-TESTSInstructor John WetmoreSTAT 2131

Within-Subjects Research Designs•Repeated-Measures: dependent variable is measured two or more times for each individual•The same subjects are used in all conditions.•Example: Measuring GRE performance before and after a class•Matched-Subjects: each individual in one sample is matched with an individual in the other sample•These two individuals are equivalent for a specific variable (e.g., age, gender, etc…) or are related.•Examples: Parent-Child, Patient-Caregiver, Spouse-Spouse2

Advantages and Disadvantages of Within-Subjects Research DesignsAdvantages1.Uses fewer participants2.Good for studying learning, development, and changes over time3.Reduces or eliminates individual differences between participantsDisadvantages1.Allows for extraneous factors to affect changes in scores (if measurements occur at two different times).2.Participation in first treatment can affect results in the second treatment.•Counterbalancing (AB/BA) can minimize this issue.3

Hypothesis Testing in Four Steps1.State the null and alternative hypotheses (in words and symbols)2.Set the criteria for a decision (determine and number of tails)3.Collect data and compute sample statistics(choose the right test)4.Make a decision and state results ( indicates a significant result)4

Two Ways to Write Hypotheses for Paired Samples t-TestsNull HypothesisAlternative HypothesisGeneral InterpretationThe mean for group 1 is/is not greater than the mean for group 2.The mean for group 1 is/is not less than the mean for group 2.The mean for group 1 is/is not equal to the mean for group 2.5

Practice: Stating Hypotheses for a Paired t-Test •A trainer wants to see if a new strength training program affects upper body strength. He measures the number of push-ups each participant can perform in 1 minute before and after a 6-week training program. Data is collected from 12 participants at both time points.•What is the null and alternative hypotheses in words and symbols?•H0: The training program does not affect upper body strength (). •H1: The training program does affect upper body strength ().6

Keywords for Determining Whether a Test is Two-tailed or One-Tailed Two-tailed TestsOne-tailed Test (+)One-tailed Test (–)•Different•Difference•Change•Affect•Effect•Impact•Influence•Associated with•Equal to•Not equal to•More•Improve•Increase•Higher•Strengthen•Better•Superior to•Faster•Less•Weaken•Decrease•Lower•Reduce•Worse•Inferior to•Slower7

Practice: Setting the Criteria for a Decision on a Paired Samples t-Test•A trainer wants to see if a new strength training program affects upper body strength. He measures the number of push-ups each participant can perform in 1 minute before and after a 6-week training program. Data is collected from 12 participants at both time points.•Is this a one-tailed or two-tailed test? What is the value?•Because we want to see if the program affectsstrength, it’s two-tailed.8

Calculations for Paired Samples t-Tests•Based on the mean difference between measurements.•, where is the number of pairs9

Practice: Calculating a Paired Samples t-value•Data on the 12 participants in the strength training program shows there is a mean difference of 3.83 push-ups before and after the fitness program; the sum of squares of 30.04 push-ups.•What is the value of t?10

Writing Paired Samples t-Test Results in APA Format•The distance covered in Jump #1 ( = 2.48, SE= 0.04) was significantly lower than in Jump #2 ( = 2.52, SE= 0.04), t(19) = -4.77, p< 0.001.11

Practice: Making a Decision and Stating Your Conclusion•We determined that and . On average, participants could do, in 1 minute, 18.8 (SE = 1.6) push-ups before the program and 22.6 (SE = 1.4) push-ups after the program.•Did participating in the strength program significantly affect upper body strength? State your conclusion in APA format.•The average number of push-ups participants could do in 1 minute was significantly higher after the program ( = 18.8, SE = 1.6) than before the program ( = 22.6, SE = 1.4), t(11) = 7.98, p < 0.05.12

Assumptions of the Paired Samples t-TestThe samples are paired.The samples are paired.The sample differences can be viewed as a random sample from a population of differences.The sample differences can be viewed as a random sample from a population of differences.The number of sample differences is large (), or the population distribution of differences is approximately normal.The number of sample differences is large (), or the population distribution of differences is approximately normal.13

Advanced Practice: Does tryptophan affect video game performance?•We examine how tryptophan can affect video game performance. Four student’s number of goals in a soccer game is measured before and after eating a Thanksgiving dinner. Is there a significant difference? Use a two-tailed test with .1.H0: There is no difference in video game performance after consuming tryptophan ().2.H1: There is a difference in video game performance after consuming tryptophan ().3.Fail to reject H0StudentBeforeAfterD11510-5284-435724116-514

Additional Calculations for Paired-Samples t-Tests•Measures of Effect Size:•Confidence Intervals: 15

Why is effect size important?•Some scores don't have fixed units of measurement (e.g., meters, seconds).•Statistical significance does not imply practical significance.•p-values depend on sample size.•Cohen’s d uses the standard deviation as a unit of measurement (just like z-scores).16

A Closer Look at Confidence Intervals•t-values are point estimates of the population parameter, based on sample statistics•Confidence Intervals represent the range of likelyvalues for that population parameter, based on:•The point estimate•Level of confidence (i.e., = 0.05)•Standard error•If the confidence interval contains the null value (usually 0), we know the results are not statistically significant ().17

Practice: Calculating Measures of Effect Size and 95% Cis for Paired Samples t-Tests•Four student’s video game performance is measured before and after eating a Thanksgiving dinner. •(-8.35, 2.34)•Notice that the CI includes 0  not significant.18

Practice: Writing Paired Samples t-Test Results in APA Format•Four students’ number of goals in a soccer game is measured before and after eating tryptophan in a Thanksgiving dinner. Is there a significant difference?•The number of goals scored in the soccer video game was not statistically significantly different after eating tryptophan ( = 6.75, SE = 1.25) compared to before ( = 9.75, SE = 2.14), t(3) = -1.78, p = 0.17.19

Advanced Practice: Does lowering serotonin levels change the number of aggressive actions?•One sample of rats receives a drug that lowers brain levels of serotonin, while another sample receives a placebo. The number of aggressive actions each rat displays is recorded over a week.•Conduct a hypothesis test (=0.05).1.H0: μtreatment− μcontrol= 02.H1: μtreatment− μcontrol≠ 03. 4. Low Serotonin GroupControl Groupn = 10n = 15= 14= 19SS1= 180.5SS2= 130.06. Reject H020