PSYC 60: Chapter 9 Study Guide
The effect size in this study indicates that the drug lowered the anxiety of the participants
by 2.38 standard deviations, which is a very large effect.
How is the mean difference of scores (µD) significant?
no effect = the mean difference for all the matched pairs should be close to 0. The null hypothesis is that the mean of the difference scores is equal to 0 (µD = 0). The research hypothesis is that the mean of the difference scores is not equal to 0 (µD ≠ 0). (sampling error)
The related samples t test can be used for a study that is using
Both a matching research design and a pre-post research design.
Researchers can also form pairs of people who are similar on some variable they are interested in "controlling."
Ex: researchers might create pairs of people who have the same anxiety scores (i.e., two people with anxiety scores of 180, two people with scores of 210, etc.). Then the researchers would randomly give one person from each "matched" pair the drug and the other a placebo.
Difference scores will always be positive.
False
Which of the following values is a measure of sampling error?
SEMr
4c. Compute the Average Mean Difference Expected Due to Sampling Error
SSD=ΣD^2-(ΣD)^2/N SDD=√SSD/N-1 SEMr=SDD/√N
Related Samples t (Two-Tailed) Example
Step 1: Examine the Statistical Assumptions Step 2: State the Null and Research Hypotheses Symbolically and Verbally Step 3: Compute the Degrees of Freedom and Define the Critical Region Step 4: Compute the Test Statistic (Related Samples t Test) 4a. Compute D for Each Participant/Matched Pair 4b. Compute the Observed Mean Difference (MD) 4c. Compute the Average Mean Difference Expected Due to Sampling Error 4d. Compute the Test Statistic (Related Samples t Test) Step 5: Compute an Effect Size and Describe It Step 6: Interpreting the Results of the Hypothesis Test
As with all types of t tests (e.g., single-sample t test and others), if the null hypothesis is false, the related samples t test expects an obtained t value that is
far from 0.
If the obtained t value (i.e., in this case 2.83) is farther from 0 than the critical value, the difference between the two means is
not likely to be due to sampling error.
An important distinction between the single-sample t test and the related samples t test is that the _______ analyzes mean differences between two samples.
related samples t test
4d. Compute the Test Statistic (Related Samples t Test)
t=MD/SEMr t=mean/stand. error mean ~if obtained t value is farther from 0, than the critical value, it's in the negative critical region thus, you should reject the null.
The denominators of the single-sample t test and the related samples t test are both
the typical amount of sampling error expected in the study.
Researchers use the related samples t test to determine if ________ differ more than would be expected by sampling error.
two related sample means
Step 2: State the Null and Research Hypotheses Symbolically and Verbally
Your hypotheses depend on how you compute the difference scores. If the research hypothesis is correct and the difference scores are computed as After Drug (lower anxiety) - Before Drug (higher anxiety), the mean difference score (µD) would be negative.
Matched Samples
When using "matched" samples, you analyze the data as if each matched pair were really a single person.
Step 6: Interpreting the Results of the Hypothesis Test
You will need to compute the means for the drug and placebo groups
When computing the df for a related samples t test, the N in the formula is the
number of pairs of scores.
Related Samples t Formula
t=MD/SEMr
4d. Compute the Test Statistic (Related Samples t Test)
t=MD/SEMr -if the obtained t value is farther from 0 than the critical value, the null should be rejected.
The obtained t value in this study indicates that
the deviation between the sample means was 5.83 times larger than was expected due to sampling error. the null hypothesis should be rejected.
When computing a related samples t test, you must remember that all of the analyses are done on
the difference between the paired scores for each participant (i.e., D).
µD is the symbolic notation for
the mean of the difference scores from the population.
When writing the reporting statement of the results, the p value is written as less than .05 (i.e., p < .05) because
the obtained t value was in the critical region.
Which of the following best represents the null hypothesis for a two-tailed related samples t test?
µD=0
4b. Compute the Observed Mean Difference (MD)
MD=ΣD/N
Effect size cutoffs?
small if d is close to .2, medium if it is close to .5, and large if it is close to .8.
Step 4: Compute the Test Statistic (Related Samples t Test) 4a. Compute D for Each Participant/Matched Pair
the related samples t test analyzes difference scores (Ds) rather than raw scores. difference score for each participant is computed. All difference scores were computed by subtracting After Drug - Before Drug scores.
To compute the effect size, you divide the observed deviation between the means by
the standard deviation of the difference scores.
Step 2: State the Null and Research Hypotheses Symbolically and Verbally
~H1= must be nondirectional (it doesn't specify if it has +/- effect) ~H0= directional
How is the related-measures t test is similar to the single-sample t test?
Related-measures t test compares the deviation *between* two means to determine if it is likely to have been created by sampling error.
Step 6: Interpreting the Results of the Hypothesis Test
(M=?, SD=?)...(M=?, SD=?), t(x)=XXX, p<.05 (one-tailed), d=XXX
What are the denominator and numerator of Single-Sample and Repeated/Related Samples t Tests?
-The denominators of both the single-sample t test and the related samples t test represent the typical amount of sampling error expected. -The numerator of the single-sample t test compares a sample mean (i.e., M) with an expected value if the null hypothesis were true (i.e., µ). -The numerator of the related samples t test compares the mean difference between two sample means (i.e., MD; the D stands for difference) with the mean difference expected if the null is true (i.e., µD).
Step 1: Examine the Statistical Assumptions
-independence of data assumption requires that participants' scores within a condition do not influence the scores of others in that same condition. -the IV must identify two groups of related scores that are measured under different conditions, and the DV must be measured on an interval or ratio scale (appropriate measurement of variables assumption for related t test). -The normality assumption for a related samples t test requires that the distribution of sample mean differences be normally shaped.
In most research situations in which a related samples t test is used, the µD expected if the null is true is
0
Which of the following common statistical assumptions is not an assumption of the related samples t test?
Homogeneity of variance
What happens if the null is true? what if happens if it's rejected?
If the null hypothesis for either test were true, you would expect to get an obtained t value close to 0. If the obtained t value were farther from 0 than the critical value, the null hypothesis would be rejected.
What is the observed difference?
If the observed difference is significantly different from 0, we will always use µD = 0 because it is exceedingly rare to use a value other than 0.
Repeated/Related Samples t Test
It can be used to compare the mean of a sample of people *before* and *after* they experience a treatment. -Researchers use the same group of people to represent two different populations.
How does related samples test compare means?
Not directly comparing these means. Instead, the related samples t test uses the difference scores from each matched pair of participants.
Repeated/Related Samples t Test os also called?
Paired samples t test, matched samples t test, dependent samples t test, or a within-subjects t test.
Related Samples t Test (One-Tailed) Example
Step 1: Examine the Statistical Assumptions Step 2: State the Null and Research Hypotheses Symbolically and Verbally Step 3: Compute the Degrees of Freedom and Define the Critical Region Step 4: Compute the Test Statistic (Related Samples t Test) 4a. Compute D for Each Participant/Matched Pair 4b. Compute the Observed Mean Difference (MD) 4c. Compute the Average Mean Difference Expected Due to Sampling Error 4d. Compute the Test Statistic (Related Samples t Test) Step 5: Compute an Effect Size and Describe It Step 6: Interpreting the Results of the Hypothesis Test
Logic of the Single-Sample and Repeated/Related Samples t Tests
The logic of the related samples t test is similar to that of the single-sample t test. Single Sample t=M-µ/SEMs Repeated/related samples t= MD-µD/SEMr
How is the related-measures t test is different to the single-sample t test?
The related samples t test is different in that the two means it compares both come from the same sample (*within*), which is measured twice under different conditions.
What does the repeated-measures t test do?
The repeated-measures t test determines if the treatment changed participants' scores on a dependent variable (DV).
Why is t test called related samples t test?
The t test is called a related samples t test because each person in the first sample has something in common with or is linked to someone in the second sample (i.e., the samples are related).
When to use one tailed or two tailed tests?
Two tailed: if you did not know if the treatment would have an effect on XXX levels, One tailed: you clearly expect the treatment to reduce/increase XXX
You use a related samples t statistic when (choose two)
b. the IV defines two matched samples, and the DV is measured on an interval/ratio scale. c. the IV defines one sample measured under two different conditions, and the DV is measured on an interval/ratio scale.
The effect size in this study indicates that the anti anxiety drug raised cholesterol levels of the participants
by 1.15 standard deviations, which is a very large effect.
4b. Compute the Observed Mean Difference (MD)
compute the numerator of the t (i.e., the mean of the difference scores) by adding the Ds and dividing by the number of Ds (N): MD=ΣD/N
4c. Compute the Average Mean Difference Expected Due to Sampling Error
compute the typical mean difference expected due to sampling error. -compute sum of squares (SS) SSD=ΣD^2-(ΣD)^2/N SDD=√SSD/N-1 SEMr=SDD/√N
The first step in computing a related samples t is to compute difference scores (Ds) by
computing the D for each set of paired scores.
Step 4: Compute the Test Statistic (Related Samples t Test) 4a. Compute D for Each Participant/Matched Pair
computing the difference score (i.e., D) for each pair of scores is D is the difference between the two scores for each participant pair.
Step 5: Compute an Effect Size and Describe It
d=MD/SDD
Step 5: Compute an Effect Size and Describe It
d=MD/SDD -denominator=standard deviation of the D scores (SDD)
Step 3: Compute the Degrees of Freedom and Define the Critical Region
df=(N-1)
The related samples t test analyzes ________ rather than __________.
difference scores; raw scores
Step 3: Compute the Degrees of Freedom and Define the Critical Region
when computing the degrees of freedom (df) for a matched design, N is the number of paired scores. df=(N-1)
When interpreting the statistical results of any study
you should consider if a confounding variable might have affected the results. you should recognize that the experimental design is just as important to the scientific conclusion as the statistical results.
Which of the following could represent the null hypothesis for a one-tailed related samples t test?
µD ≥ 0~~null (H0) µD<0~~~~research (H1)
