# EXPERT SOLUTION: PART 1 Based on the PSPP Chi Square Distribution lecture answer the following question Using the

PART 1
Based on the PSPP Chi Square Distribution lecture answer the following question

Using the GSS2008 data, examine the relationship between attitudes toward the level of national assistance for childcare (NATCHILD) and the sex of the respondent (SEX). Fill in the following information:

Now perform the analysis with PSPP and find (You need to go to Analyze, Descriptives, Crosstabs–click.  Enter in the appropriate variables–click on statistics on the dialogue box where you enter the variables (for row, column) and make sure the chisq box is checked.)

Percentage of men (out of only men) stating the current level is too little ________________________

Percentage of women (out of only women) stating the current level is too little ________________________

Chi Square significance level ________________________ (Pearson Chi Square Sig)

Is the relationship statistically significant YES NO

How would interpret this result? What might explain why there is or is not a significant difference in the means between the two groups (male and female). The null hypothesis for the Chi Square test is that there is no difference between the mean percentages of the various groups or categories. So, if the result is significant, we can reject (rather than confirm) the null hypothesis and indicate that there is a significant difference.

How would the information from this exercise  be used by a lobbying group lobbying for more childcare assistance to develop an information strategy?

PART 2

Using the GSS2012 data, examine the relationship between sex (SEX) and the belief that a woman will not get a job or promotion over a man (DISCAFFW).

Fill in the following information:
Make a prediction

What percent of Americans believe women are less likely to get a job or promoted over a man:

___________

Do you think males and females vary on their perspectives on this issue?                          YES    NO

Now perform the analysis with PSPP and find (Remember how to read a table!):

Percentage of men (out of only men) saying “Somewhat Likely”                              __________________

Percentage of women (out of only women) saying “Somewhat Likely”                          __________________

Chi Square significance level         __________________

Is the relationship statistically significant                                        YES     NO

How would interpret this result?  In other words, what might explain why there is or is not a difference between the groups.  Do not just restate the statistics without any interpretation.

What do the results suggest about perceptions of Affirmative Action?

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CHAPTER 3: CHI SQUARE DISTRIBUTIONS

The next statistical procedure is the chi square distribution, which is used to determine the level
of statistical significance for relationships between variables at the nominal and ordinal level of
measurement. Specifically, The Pearson Chi-Square tests whether a particular pattern of
group frequencies is likely due to chance alone. Since the Pearson Chi-Square evaluates two
variables, a significant Chi-Square value tells two things: 1) the pattern of frequencies is
significantly different from a random pattern AND 2) that the values are significantly associated
with each other. We will also look at measures of association appropriate for nominal and
ordinal data: lambda and gamma.

ANALYZE

DESCRIPTIVE STATISTICS>CROSSTABS (click)

Graphic 3.1

A dialogue box will open with the list of variables and two areas to add the variables (row and
column).

Graphic 3.2

2

We are going to look at Click on the first variable so that it is highlighted, then type ABANY.
This should bring you down to Abortion if women wants for any reason.highlight it and
move it to row by clicking on the arrow.

Graphic 3.3

Then go back to the top, repeat but type SEX, it will go to Respondents Sex, highlight it and
move it to column

Graphic 3.4

Click on Statistics, and a new dialogue box will open. In the lower-right hand corner next to the
help button is something that looks like a dog-eared page. You can place your cursor it, right
click and drag on it and the dialogue box will expand revealing more choices. We are doing a
Chi-Square so make sure that the Chisq box is checked and we are going to include a measure
of association as well.

But wait! How do I know which measure of association to choose? The following discussion
was adapted from an exercise prepared by Ed Nelson at the Social Science Research and
Instructional Lab: There are many measures of association to choose from. Were going to limit
our discussion to those measures that PSPP will compute. When choosing a measure of
association well start by considering the level of measurement of the two variables (see chapter
2 for review of level of measurement).

3

 If one or both of the variables is nominal, then choose one of these measures.
o Contingency Coefficient [automatically calculated by PSPP]
o Phi and Cramers V
o Lambda

 If both of the variables are ordinal, then choose from this list.
o Gamma
o Somers d
o Kendalls tau-b
o Kendalls tau-c

 Dichotomies should be treated as ordinal. Most variables can be recoded into dichotomies
(also know as dummy variables, where it is either coded a 1 or a 0). For example,
marital status can be recoded into married (1) or not married (0). Race can be recoded as
white (1) or non-white (0). All dichotomies should be considered ordinal.

For this exercise, since both variables are ordinal: both the SEX variable and categories available
for ABANY (Yes, NO) are dichotomies and as such is treated as ordinal.

Therefore, you can choose any of the four options listed. We are just choosing Gamma so make
sure to click on Gamma as well. Since the GSS 2008 treats these as nominal variables, choose
Lambda, and then click Continue then click OK.

Graphic 3.5

The following output (Graphic 3.6) will appear

4

Graphic 3.6

Looking at the various parts will help better understand what is portrayed in the output. First is a
listing of the syntax as shown in Graphic 3.7:

Graphic 3.7

Next is a summary of the valid and missing cases or observations. You normally would not
report the missing cases, so you go with the Valid Cases rather than the Total when reporting the
N (Number of Observations). For this question, the N equals 1298.

Graphic 3.8

5

Graphic 3.9 displays a wealth of information but it means little of you do not understand it. To
know what it value stands for, first look at the top of table for a guide. The following appears at
the top: ABORTION IF WOMAN WANTS FOR ANY REASON*RESPONDENTS SEX
[count, row %, column %, total %. This last part is important because it indicates what each
value within a given square stands for.

Graphic 3.9

As an example, look at the row YES.

 Starting with the column for MALE, the first value, which is the count is 262. This is the
number of respondents that said YES and are MALE.

 The next value in the MALE column is the row percent. The value 47.64% is percent of
those that responded YES that are male, out of ALL those, in other words, EVERYONE
that responded YES. This value could be used to make comparisons across responses,
for example, what was the make-up of those that responded NO or YES.

 The third value in the MALE column is the column percent. The value, 44.56% is the
percent MALE that responded YES, out of ONLY MALE respondents. This is the value
one would use if they wanted to make comparisons across groups, in this case MALE
and FEMALE. IMPORTANT: Remember which variables you enter for each row and
column so that you know which is the categorical response (in this case: NO, YES) and
the GROUP (in this case: MALE, FEMALE).

 The last value: 20.18% is the percent MALE that responded YES out of the all
(TOTAL) respondents.

Regardless of whether or not there is a significant difference as indicated by the Pearson Chi-
Square (Graphic 10), the information in Graphic 3.9 can be used to provide valuable information.
Moving on to Graphic 10, the focus will be only on the top statistic: Chi Square. The following
measures of association (Lambda and Gamma) were also included.

6

Graphic 3.10

The results of various tests are provided in the first of the three tables. If you did not click on
Gamma and Lambda, this would be the only table you would see. The Pearson Chi-Square
tests whether a particular pattern of group frequencies is likely due to chance alone. Recall from
the beginning of the chapter that a significant Pearson Chi-Square value tells us two things: 1)
the pattern of frequencies is significantly different from a random pattern AND 2) that the values
are significantly associated with each other. This association can also be tested with gamma,
lambda, and others as listed above.

Please not that most academic journals consider a significance level of .05 or lower to be
significant (95% of confidence intervals). Although, some journals also researchers to indicate
when test statistics indicate a significance level of .1 or lower. This can vary by journal and
discipline.

Back to our example: The Pearson Chi-Square value or score is 2.10. When statisticians
calculated these scores by hand it was necessary to look up critical values to see if this value was
significant. Statistical software, like PSPP, SPSS, SAS, and STATA and many others, calculates
the significance level for you so this is unnecessary. The significance level is listed under
Asymp. (Asymptotic) Sig. (2 tailed) and is .147. This indicates that it is not significant.
Similarly, neither Gamma or Lambda are significant (based on the Chi-Square) suggesting that
the pattern of frequencies are not significantly different that what could be produced by chance
nor, as indicated by all three test statistics, that these two variables are not significantly
associated with each other.

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