Imagine a researcher is interested in whether teachers’ self-esteem differs at t
ID: 3170768 • Letter: I
Question
Imagine a researcher is interested in whether teachers’ self-esteem differs at the beginning and at the end of the school year. Use the data file: teachersurvey.sav to conduct a dependent-samples repeated-measures t-test (referred to as a paired-samples t-test in SPSS). In this data-set self-esteem was measured at the beginning of the school year (Score One) and at the end of the school year (Score Two) (i.e., repeated-measures with the same group). These are the variables to be used in this analysis.
SPSS output
Paired Samples Correlations
N
Correlation
Sig.
Pair 1
ScoreOne & ScoreTwo
40
.052
.752
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
ScoreOne - ScoreTwo
-6.950
8.907
1.408
-9.799
-4.101
-4.935
39
.000
Are the two main assumptions underlying repeated-measures t-tests met? Support your response with SPSS output as needed. Yes, Self-Esteem scores are improved.
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
ScoreOne
77.63
40
5.808
.918
ScoreTwo
84.58
40
7.060
1.116
What are the null and alternative hypotheses?
What are the mean and standard deviation for beginning self-esteem (Score One) and end self-esteem (Score Two) using APA style?
What is the value of Cohen’s d? Is it small, medium, or large?
Interpret the mean, standard deviation, standard error, and confidence interval in the paired-samples t-test output box.
What is the percentage of variance explained? Interpret this value.
Report the results in APA format.
What might be concluded from these results? In these conclusions, discuss possible limitations of the study and recommendations for future research.
Paired Samples Correlations
N
Correlation
Sig.
Pair 1
ScoreOne & ScoreTwo
40
.052
.752
Explanation / Answer
Checking Asumptions:
1. Dependent variable, self esteem scores is measured on continuous scale. Continuos variable refer to values which are measurable instead of countable. The continuos variable takes values over an interval. The mean self esteem score at the begining is 77.63 and self esteem score at the end of the school year is 84.58.
2. Paired data condition: The independent variable teachers are paired, because, same teachers' self esteem were measured at the begining and again at the end of the school year. The mean difference (score at begining-score at end) is -6.950.
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Hypotheses:
H0:mud=0 (there is no difference is population mean self esteem scores of teachers at the begining and at the end of the school year)
H1:mud=/=0 (there is difference is population mean self esteem scores of teachers at the begining and at the end of the school year)
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The mean and standard deviation of score 1 is represented as follows:
(M=77.63, SD=5.808)
The mean and standard deviation of score 2 is represented as follows:
(M=84.58, SD=7.060)
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Compute eta sqaured.
eta sqaured=t^2/(t^2+N-1)
=(-4.935)^2/{(-4.935)^2+40-1}
=0.38
According to Cohen's guidelines of effect size, 0.01 is small, 0.06 is medium and 0.14 is large.
Therefore, the effect is large.