1. You are interested in investigating if being above or below the median income (medloinc) impacts ACT means (act94) for schools. Complete the necessary steps to examine univariate grouped data in order to respond to the questions below. Although deletions and/or transformations may be implied from your examination, all steps will examine original variables.
a. How many subjects have missing values for medlonic and act94?
b. Is there a severe split in frequencies between groups?
According to the descriptive analysis, no severe split is detected. This is also reflected in the skewness number which is lower than .5.
c. What are the cutoff values for outliers in each group?
d. Which outlying cases should be deleted for each group?
Average ACT score 1994 Stem-and-Leaf Plot for
medloinc= below the median for low inc % 1993
Frequency Stem & Leaf
7.00 14 . 1223789
9.00 15 . 234478888
5.00 16 . 12788
4.00 17 . 1378
2.00 18 . 09
1.00 19 . 6
3.00 20 . 069
1.00 Extremes (>=22.5)
Stem width: 1.0
Each leaf: 1 case(s)
e. Analyzing histograms, normal Q-Q plots, and tests of normality, what is your conclusion regarding normality? If a transformation is necessary, which one would you use?
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Tests of Normality
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above or below median loinc
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Kolmogorov-Smirnova
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Shapiro-Wilk
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Statistic
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df
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Sig.
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Statistic
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df
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Sig.
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average ACT score 1994
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below the median for low inc % 1993
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.162
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32
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.032
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.903
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32
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.007
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above the median for low inc % 1993
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.166
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32
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.025
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.921
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32
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.023
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According to the information and the test of normality, it appears that this is a normal distribution. Therefore, for the transformation, we would select 'Square Root."
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f. Do the results from Levene's Test of Equal Variances indicate homogeneity of variance? Explain.
In running the test, there were no significant differences between the categories. Therefore; we can assume that this indicates homogeneity of variance.
2. Examination of the variable of scienc93 indicates a substantial to serve positively skewed distribution. Transform this variable using the most two appropriate methods. After examining the distribution for these transformed variables, which produced the best alteration?