SW318 Social Work Statistics Slide 1 Compare Central Tendency & Variability Group comparison of central tendency? Measurement Level? Badly Skewed? MedianMeanMedian Interval Ordinal NO Yes (e.g., lower-higher?, more-less likely?) Mode Nominal

SW318 Social Work Statistics Slide 2 Compare Central Tendency & Variability Group comparison of Variability? Measurement Level? Badly Skewed? Range Standard Deviation Range Interval Ordinal NO Yes (e.g., more or less diverse?)

SW318 Social Work Statistics Slide 3 Compare Variability: Ordinal or Interval (1) 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].

SW318 Social Work Statistics Slide 4 Compare Variability in SPSS (1) 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…

SW318 Social Work Statistics Slide 5 Compare Variability in SPSS (2) 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.

SW318 Social Work Statistics Slide 6 Compare Variability in SPSS (3) 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”.

SW318 Social Work Statistics Slide 7 Compare Variability in SPSS (4) 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 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.”

SW318 Social Work Statistics Slide 8 Compare Variability: Ordinal or Interval (2) 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.

SW318 Social Work Statistics Slide 9 Compare Variability in SPSS (5) 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.

SW318 Social Work Statistics Slide 10 Compare Variability in SPSS (6) 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.

SW318 Social Work Statistics Slide 11 Compare Variability in SPSS (7) 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.”

SW318 Social Work Statistics Slide 12 Compare Central Tendency: Ordinal 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.

SW318 Social Work Statistics Slide 13 Compare Central Tendency in SPSS: Ordinal(1) 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…

SW318 Social Work Statistics Slide 14 Compare Central Tendency in SPSS: Ordinal(2) 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.

SW318 Social Work Statistics Slide 15 Compare Central Tendency in SPSS: Ordinal(3) 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”.

SW318 Social Work Statistics Slide 16 Compare Central Tendency in SPSS: Ordinal(4) 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.

SW318 Social Work Statistics Slide 17 Compare Central Tendency: Interval(1)- Skewed Variable 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.

SW318 Social Work Statistics Slide 18 Compare Central Tendency in SPSS: Interval(1) 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.

SW318 Social Work Statistics Slide 19 Compare Central Tendency in SPSS: Interval(2) 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.”

SW318 Social Work Statistics Slide 20 Compare Central Tendency: Interval(2) Non-Skewed Variable 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.

SW318 Social Work Statistics Slide 21 Compare Central Tendency in SPSS: Interval(3) 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 for survey respondents who were male. Thus, we can conclude that “Survey respondents who were female were younger than survey respondents who were male.”

SW318 Social Work Statistics Slide 22 Group Comparison-Nominal 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.

SW318 Social Work Statistics Slide 23 Group Comparison in SPSS-Nominal (1) Recall that we can get the crosstabulation table in SPSS by clicking Analyze > Descriptive Statistics > Crosstabs…

SW318 Social Work Statistics Slide 24 Group Comparison in SPSS-Nominal (2) 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.

SW318 Social Work Statistics Slide 25 Group Comparison in SPSS-Nominal (3) 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].

SW318 Social Work Statistics Slide 26 Steps in comparing central tendency Question: one group defined by independent variable had higher/lower values on dependent variable Is the variable nominal level? Yes False No Comparison of modes correct? True Yes Is the variable ordinal level? Is the variable interval level? Yes No Comparison of medians correct Is the dependent variable badly skewed? Comparison of means correct? No Yes False No False True Yes True No False 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.

SW318 Social Work Statistics Slide 27 Steps in comparing variability Question: one group defined by independent variable was more/less diverse on dependent variable Is the variable nominal level? Yes False Yes Is the variable ordinal level? Is the variable interval level? Yes No Comparison of ranges correct Dep. variable badly skewed? Comparison of standard deviations correct? No Yes No False True Yes True No False Incorrect application (no measure in SPSS)