## Description

Complete the following end of chapter exercises for Chapter 3. Submit your response in an MS Word document or Pdf after inserting the results from SPSS Output into your document. This exercise utilizes the data set schools-a.sav, which can be downloaded from chapter data sources referenced above.

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 participants have missing values for *medloinc* and *act94*?

b. Is there a severe split in frequencies between groups?

c. What are the cutoff values for outliers in each group?

d. Which outlying cases should be deleted for each group?

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?

f. Do the results from Levene’s test for equal variances indicate homogeneity of variance? Explain.

2- You
are interested in studying predictors (*math94me*, *loinc93*,
and *read94me*) of the percentage graduating in 1994 (*grad1994*).

a. Examine univariate normality for each variable. What are your conclusions about distributions? What transformation should be conducted?

b. After making the necessary transformations, examine multivariate outliers using Mahalanobis distance. What cases should be deleted?

c. After deleting the multivariate outliers, examine multivariate normality and linearity by creating a Scatterplot Matrix.

d. Examine the variables for homoscedasticity by creating a residuals plot (standardized vs. predicted values). What are your conclusions about homoscedasticity?

Please use APA format with references.

## Explanation & Answer

If you check the plagiarism part, you'll wonder because it has a high percentage, that was because of the questions that are copied from the book. Don't worry, I added the book as a reference for the file.

CHAPTER 3

Answers to End Exercises

This exercise utilizes the data set schools-a.sav

1. You are interested in investigating if being above or below the median income (medloinc) impacts

ACT means (act94) for schools.

a. How many participants have missing values for medloinc and act94?

For the variable medloinc there are 0 participants with missing values.

For the variable act94 there are 0 participants with missing values.

Statistics

above or below median loinc

N

Valid

Missing

64

0

Case Processing Summary

Cases

Valid

N

average ACT score 1994

Missing

Percent

64

N

100.0%

Total

Percent

0

N

0.0%

Percent

64

100.0%

b. Is there a severe split in frequencies between groups?

There is no severe split in frequencies between groups, it is 50% by 50%, and it is an

expected outcome: the name of the variable (above or below median income) implies that the

data will be distributed evenly between the two groups (knowing that the number of participants

is an even number).

Case Processing Summary

Cases

Valid

above or below median

loinc

average ACT score 1994

below the median for low

inc % 1993

above the median for low

inc % 1993

N

Missing

Percent

N

Total

Percent

N

Percent

32

100.0%

0

0.0%

32

100.0%

32

100.0%

0

0.0%

32

100.0%

c. What are the cutoff values for outliers in each group?

There are two stem-and-leaf plots below. The first one indicates that 1 participant with

the income that is below the median has ACT score above 22.5. The second plot shows that 2

participants with the income above the median has ACT scores higher than 17.

Extreme Values

above or below median loinc

average ACT score 1994

Case Number

below the median for low inc Highest

1

64

22.5

% 1993

2

38

20.9

3

39

20.6

4

60

20.0

5

35

19.6

1

24

14.1

2

42

14.2

3

9

14.2

4

13

14.3

5

55

14.7

above the median for low inc Highest

1

26

17.0

% 1993

2

57

17.0

3

43

16.8

4

30

16.4

5

48

16.0

1

50

13.6

2

20

13.8

3

2

14.0

4

16

14.1

5

5

14.3

Lowest

Lowest

average ACT score 1994 Stem-and-Leaf Plot for

medloinc= below the median for low inc % 1993

Frequency

7.00

9.00

5.00

4.00

Stem &

14

15

16

17

.

.

.

.

Value

Leaf

1223789

234478888

12788

1378

2.00

18 .

1.00

19 .

3.00

20 .

1.00 Extremes

Stem width:

Each leaf:

09

6

069

(>=22.5)

1.0

1 case(s)

average ACT score 1994 Stem-and-Leaf Plot for

medloinc= above the median for low inc % 1993

Frequency

Stem &

2.00

13

6.00

14

10.00

14

6.00

15

3.00

15

2.00

16

1.00

16

2.00 Extremes

Stem width:

Each leaf:

.

.

.

.

.

.

.

Leaf

68

013444

5556678999

000124

559

04

8

(>=17.0)

1.0

1 case(s)

d. Which outlying cases should be deleted for each group?

Below is the bloxplot for two groups that reveals all three outliers: one in the first group

and two in another one. Case numbers are: 64 (first group - income below the mean); #57 and

#26 (second group - income above the mean). We will alter the value for the outlying case #64 by

replacing it with a maximum value that falls within the accepted distribution which is 20.069 as

per stem-and-leaf plot, and will two outliers #57 and #26 from the second group will alter to 16.8.

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?

According to the Descriptive Statistics figure below, for participants with the income

below the median the skewness coefficient is .790. For participants with the income above the

median the skewness coefficient is .791. A positive skew tells us that there is a clustering of cases

to the left, and the right tail is extended with only few cases. The positive kurtosis is supported by

histograms. Normal Q-Q plots for both groups support this finding as the observed values deviate

somewhat from the straight line. The Kolmogorov-Smirnov test and Shapiro-Wilk test rejects the

hypothesis of normality of ACT scores for the population of both groups. Detrended normal Q-Q

plot shows a U-shape distribution.

To decrease the moderate positive skewness, the transformation proce...