PSYCH243 Ch 11: t-Test for Two Related Samples

Factors the Influence Hypothesis Test Outcome

1. Sample size -larger n --> larger t 2. Size of the sample mean difference (D) -larger D --> larger t 3. Sample variance -larger variance --> smaller t

Four steps for hypothesis testing

1. State hypotheses 2. locate critical region 3. solve for t-statistic 4. state conclusion

How to find SS without the computational formula

1. Subtract MD from D 2. Square D -MD 3. Add up all squares

Assumptions of Related-Samples t-Test Assumptions

1. observations within each treatment condition must be independent 2. population distribution of difference scores (D values) must be normally distributed -this assumption is not typically a serious concern unless the sample size is small -with relatively large samples (n >30) this assumptions can be ignored

Related-Samples Designs

1. repeated-measures 2. matched samples -statistically equivalent methods -use different # of subjects --> matched sample has twice as many

How to state conclusion in APA style

1. report t-value with df - t(6)= 4.07 2. State significance - p < .05 3. Report effect size - r^2= 0.40

Steps for solving for t-statistic

1. the variance 2. find estimated standard error 3. solve for t

When to use paired t-Test

1. when IV is manipulated within-subjects (when means are from the sample group of subjects measured at different times) 2. when you have two difference groups of subjects but they are matched in some way

For which would a matched-subjects study be most appropriate? A. a group of twins is tested for IQ B. Comparing boys and girls strength at age 3 C. Evaluating the difference in self-esteem between athletes and non-athletes D. Student's knowledge is tested in September and December

C. Evaluating the difference in self-esteem between athletes and non-athletes

For which of the following would a repeated-measures study be appropriate A. a group of twins is tested for IQ B. Comparing boys and girls strength at age 3 C. Evaluating the difference in self-esteem between athletes and non-athletes D. Student's knowledge is tested in September and December

D. Student's knowledge is tested in September and December

Assuming that the sample mean difference remains the same, which of the following sets of data is most likely to produce a significant t-statistic A. n=15 and SS= 10 B. n=15 and SS=100 C. n=30 and SS=10 D. n=30 and SS= 100

D. n=30 and SS=100

True or False: a matched-samples study requires only 20 participants to obtain 20 scores in each of the conditions being compared

False

T/F: compared to independent-measures designs, repeated-measures studies reduce the variance by removing individual difference

True

T/F: the repeated-measures t-statistic can be used with either a repeated-measures or a matched-subjects design

True

What does the numerator of t-statistic measure?

the difference between the data (MD) and the hypothesis (UD)

What does the denominator of the t-statistic measure?

the standard difference that is expected if H0 is true

As the variance of the difference scores increases, the magnitude of the t-statistic decreases

True

Correlational study

-Significance test of Pearson's r should be calculated

Inconsistent treatment effect

-difference scores are more scattered -variability is high

Consistent treatment effect

-difference scores cluster together -variability is low

Disadvantages of repeated-measures design

-factors besides treatment may cause subject's score to change during the time between measurements -participation in 1st treatment may influence score in 2nd treatment (order effects) ***counterbalancing is a way to control time-related or order effects

Advantages of repeated-measures designs

-fewer subjects required -can study changes over time -reduces/eliminates influence of individual differences

Matched-Subjects Design

-two separate samples -each individual is matched one-to-one with an individual from the other sample -ensures samples are equivalent with respect to specific variables

Repeated-Measures Design

-within-subjects design -2 scores obtained from each individual in the sample -same group get both condition of independent variable

When comparing two samples and there are no matched pairs

Independent samples t-test

When comparing a sample mean to an unknown population and you don't know the standard deviation...

One Sample t-Test

when comparing two samples and both samples have the same people or have matched pairs...

Paired (related samples) t-test

When comparing a sample mean to an unknown population mean and you know standard deviation...

Z-test