1.Do the example data meet the assumptions for the paired samples t-test? Provid
ID: 3201001 • Letter: 1
Question
1.Do the example data meet the assumptions for the paired samples t-test? Provide a rationale for your answer.
2.If calculating by hand, draw the frequency distributions of the two variables. What are the shapes of the distributions? If using SPSS, what are the results of the Shapiro-Wilk tests of normality for the two variables?
3.What are the means for the baseline and posttreatment affective distress scores, respectively?
4.What is the paired samples t -test value?
RESEARCH DESIGNS APPROPRIATE FOR THE PAIRED SAMPLES t-TEST The term paired samples refers to a research design that repeatedly assesses the same group of people, an approach commonly referred to as repeated measures. Paired samples can also refer to naturally occurring pairs, such as siblings or spouses. The most common research design that may utilize a paired samples t-test is the one-group pretest-posttest design, wherein a single group of subjects is assessed at baseline and once again after receiving an intervention (Gliner, Morgan, & Leech, 2009). Another design that may utilize a paired samples t-test is where one group of participants is exposed to one level of an intervention and then those scores are compared with the same participants This is called a responses to another level of the intervention, resulting in paired scores one-sample crossover design (Gliner et al., 2009) Example 1: A researcher conducts a one-sample pretest-posttest study wherein she assesses her sample for health status at baseline, and again post-treatment. Her research question is: "Is there a difference in health status from baseline to post-treatment?" The dependent variable is health status. Null hypothesis: There is no difference between the baseline and post-treatment health status scores. Example 2: A researcher conducts a crossover study wherein subjects receive a randomly generated order of two medications. One is a standard approved medication to reduce blood pressure, and the other is an experimental medication. The dependent vari- able is reduction in blood pressure (systolic and diastolic, and the independent variable is medication type. Her research question is: "Is there a difference between the experimen- tal medication and the control medication in blood pressure reduction? Null hypothesis: There is no difference between the two medication trials in blood pres- sure reduction.Explanation / Answer
Answer:
1.Do the example data meet the assumptions for the paired samples t-test? Provide a rationale for your answer.
Assumptions: The difference between the paired scores are normally or approximately normally distributed.
Since both baseline and post data follows normal, assumption is met.
2.If calculating by hand, draw the frequency distributions of the two variables. What are the shapes of the distributions? If using SPSS, what are the results of the Shapiro-Wilk tests of normality for the two variables?
Tests of Normality
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
Baseline
.286
10
.020
.885
10
.149
Post
.224
10
.168
.911
10
.287
a. Lilliefors Significance Correction
Shapiro-Wilk statistic for baseline data is 0.885, P=0.149 which is > 0.05 level. Normality assumption is not violated. Shapiro-Wilk statistic for Post data is 0.911, P=0.287 which is > 0.05 level. Normality assumption is not violated.
3.What are the means for the baseline and post treatment affective distress scores, respectively?
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
Baseline
5.2000
10
.91894
.29059
Post
3.3000
10
.94868
.30000
4.What is the paired samples t -test value?
paired samples t –test =10.585
Paired Samples Test
Paired Differences
t
df
Sig. (2-tailed)
Mean
Std. Deviation
Std. Error Mean
95% Confidence Interval of the Difference
Lower
Upper
Pair 1
Baseline - Post
1.90000
.56765
.17951
1.49393
2.30607
10.585
9
.000
Tests of Normality
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
Baseline
.286
10
.020
.885
10
.149
Post
.224
10
.168
.911
10
.287
a. Lilliefors Significance Correction
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