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Compare Central Tendency & Variability

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Compare Central Tendency & Variability

Group comparison of

central tendency?

(e.g., lower-higher?, more-less likely?)

Measurement Level?

Ordinal

Nominal

Interval

Badly Skewed?

Yes

NO

Mode

Mean

Median

Median

Compare Central Tendency & Variability

Group comparison of

Variability?

(e.g., more or less diverse?)

Measurement Level?

Ordinal

Interval

Badly Skewed?

Yes

NO

Standard

Deviation

Range

Range

This question is asking whether the variability of the dependent variable [educ] is different depending on respondents’ marital status [marital]. Notice that the dependent variable is an interval level variable and the independent variable is a nominal level variable. You have to compare values of the appropriate variability measure, which is a standard deviation value, of the dependent variable [educ] for each group in independent variable [marital].

You can compare the variability of an interval level variable based on group difference of another variable in SPSS by clicking

Analyze > Compare Means > Means…

First, select and move the dependent variable [educ] and the independent variable [marital] to the “Dependent List:” and “Independent List:” boxes, respectively. Then, click on “Options…” button.

You will have to select statistics of your interest from the “Statistics:” box on the left and move to the “Cell Statistics:” box to ask SPSS to get the statistics for you. Then, click on “Continue” and “OK”.

SPSS output provides with a table of the standard deviation values of the dependent variable [educ] that were calculated separately for each category of the independent variable [marital]. Since there were no signs of skewness in the table, we use standard deviation as a measure of variability in this case. The SPSS output shows that survey respondents who were married had a standard deviation of 3.197, greater than the standard deviation of 2.837 for survey respondents who were never married. With this values given, you can now tell that “Survey respondents who were married had more diverse values for "highest year of school completed" than survey respondents who were never married.”

This question also asks the variability of [tvhours] by [sex].

You do the same thing as you did in the last example in SPSS using [tvhours] as the dependent variable and [sex] as the independent variable in this case though.

Recall that we used Analyze > Compare Means > Means… function in SPSS. Now, select the dependent and independent variables and move to appropriate boxes, then click “Options…” button.

You will have to select statistics of your interest from the “Statistics:” box on the left and move to the “Cell Statistics:” box to ask SPSS to get the statistics for you. Then, click on “Continue” and “OK”. Make sure to select Skewness measure to examine whether the distribution of the dependent variable was badly skewed.

Notice that the dependent variable [tvhours] was badly skewed (skewness=2.88>1). In this case, comparisons of variability should be based on the ranges, instead of standard deviations, for groups defined by the independent variable [sex]. SPSS output shows that survey respondents who were female had a range of 12, less than the range of 22 for survey respondents who were male. Now we can say that “Survey respondents who were female had less diverse values for "number of hours per day spent watching TV" than survey respondents who were male.”

Notice that this question asks which group [sex] is higher/lower in “feelings toward Hispanics” [feelhsps], i.e., to compare central tendency measures of [feelhsps] for each [sex] group. Also notice that [feelhsps] is an ordinal level variable and the preferred measure of central tendency for ordinal level variables is median.

You can compare the central tendency of an interval level variable based on group difference of another variable in SPSS by clicking

Analyze > Compare Means > Means…

First, select and move the dependent variable [feelhsps] and the independent variable [sex] to the “Dependent List:” and “Independent List:” boxes, respectively. Then, click on “Options…” button.

You will have to select statistics of your interest from the “Statistics:” box on the left and move to the “Cell Statistics:” box to ask SPSS to get the statistics for you.

Select Median in this case. Then, click on “Continue” and “OK”.

SPSS output shows that survey respondents who were female had a median of 7.00, greater than the median of 6.00 for survey respondents who were male. Survey respondents who were female have warmer feelings toward Hispanics than survey respondents who were male.

Notice that this question asks which group in [marital] is higher/lower in “number of hours per day spent watching TV” [tvhours], i.e., to compare central tendency measures of [tvhours] for each [marital] group. Also notice that [tvhours] is an interval level variable and the preferred measure of central tendency for an interval level variable that is not badly skewed is mean. If it is badly skewed, however, the preferred measure of central tendency is median.

After selecting dependent and independent variables, we have to choose Median and Skewness measures as well as Mean in the “Means: Option” window. It is because we might need median value in case the dependent variable is badly skewed.

Notice that the dependent variable [tvhours] was badly skewed (total skewness=2.880>1) and, in this case, the preferred measure of central tendency is medians, instead of means, for groups defined by the independent variable "marital status" [marital].

Given that indication, SPSS output shows that survey respondents who were married had a median of 2.00, less than the median of 3.00 for survey respondents who were never married. Now, we can say “Survey respondents who were married watched fewer hours of TV than survey respondents who were never married.”

Notice that this question asks which group in [sex] is higher/lower in “age” [age], i.e., to compare central tendency measures of [age] for each [sex] group. Also notice that [age] is an interval level variable and the preferred measure of central tendency for an interval level variable that is not badly skewed is mean. If it is badly skewed, however, the preferred measure of central tendency is median.

The result of analysis, Analyze > Compare Means > Means…, with [age] as a dependent variable and [sex] independent variable shows that there is no sign of bad skewness (skewness=.454<1) so we use means of age for each group of [sex] to compare the groups in terms of age. SPSS output shows that survey respondents who were female had a mean of 46.54, less than the mean of 46.63 for survey respondents who were male. Thus, we can conclude that “Survey respondents who were female were younger than survey respondents who were male.”

This question asks which was the most likely group of [sex] in a group of [marital], for example, “married” and “never married” groups. In other words, we have to identify the modal group of [sex] in each category of [marital].

Notice that we will use cross tabulation to answer to this question as both the variables were nominal level variables.

Recall that we can get the crosstabulation table in SPSS by clicking

Analyze > Descriptive Statistics > Crosstabs…

Since we want to identify modal [sex] in each group of [marital], we move [sex] to row and [marital] to column of the crosstabulation and, then, ask SPSS to provide Column percentages in the “Cells…” window as shown in the “Crosstabs: Cell Display” window.

Notice that survey respondents who were married were most likely to have been female. The modal category contained 51.8% of the cases in the 'married' category of the independent variable "marital status" [marital]. Also, SPSS output shows that survey respondents who were never married were most likely to have been female. The modal catgory contained 54% of the cases in the 'never married' category of the independent variable "marital status" [marital].

Yes

Yes

Yes

Yes

No

Yes

Yes

Question: one group defined by independent variable had higher/lower values on dependent variable

Is the variable nominal level?

Is the variable ordinal level?

Is the variable interval level?

No

No

Is the dependent variable badly skewed?

Comparison of medians correct

Comparison of modes correct?

Yes

False

No

No

Comparison of means correct?

False

True

False

True

Note: to say one specific value is the mode, the distribution must not have multiple modes. If there is more than one mode, the answer to the problem will be false.

No

False

True

Yes

Yes

Yes

Yes

Yes

No

Question: one group defined by independent variable was more/less diverse on dependent variable

Is the variable nominal level?

Is the variable ordinal level?

Is the variable interval level?

No

No

Comparison of ranges correct

Incorrect application (no measure in SPSS)

Dep. variable badly skewed?

Yes

False

No

Comparison of standard deviations correct?

False

True

No

False

True