Chi-Square SPSS Test Assignment

Assignment Task

Basic Chi-Square Test

This test is run through the Analyze menu, under Nonparametric Tests → Legacy Dialogues → Chi-Square. Run this test to determine if the occurrences of a categorical variable (the number of cases which fall into each level of the variable) follow a predicted ratio.

Note: Often times, you will be predicting that the occurrences of each level of the variable are equal (which would be a ratio of 1:1:1...).   Other times, however, you can test for other ratios (e.g., 2:1 if predicting that there will be twice as many males in a group as females).

The following steps are needed to run this test:

• Select the variable you want by pulling it over into the Test Variable List You can run Chi-squares of multiple variables at once; you have to be predicting the same value ratio for each variable.
• You can specify the range of values you want to run, but you will normally get your range from the data (runs test on all values).
• Under Expected Values, leave All Categories Equal selected if you are predicting an even ratio across all variable

Note: If you are not predicting an even ratio, then you need to enter the ratio that you are predicting, starting with the ratio value for the first variable value and so on.

Ex: If you are predicting twice as many females as males in a data set, males are coded 1 and females are coded 2, you would:

1. Select Values
2. Enter 1 into the values box and click on Add
3. Enter 2 into the values box and click on Add

This will test for a ratio of 1 male to every 2 females. If you are predicting an uneven ratio for a variable that has more that 2 values, you must enter a ratio value for each variable value. In other words, if your variable has 5 values, the test will not run unless you select and add 5 values into your "Values" section of the Chi-square test (hope that makes sense).

Chi-Square Test for Independence 

This test is run through the Analyze menu, under Descriptive Statistics → Crosstabs. Run this test when trying to determine if 2 categorical variables are independent of one another. The following steps are needed to run this test:

1. Select the variables you want to run a Chi-square on (put one in the column box and one in the row box).

[Note: You can run multiple Chi-squares at once by putting more than one variable into either the column or row boxes, but there is no need to do this unless you're running multiple Chi-squares comparing 1 variable to several others. Also, don't worry about the layer box, this if for a function of Crosstabs that is not related to Chi-squares.]

2. Click on the Statistics tab and click on the Chi-square box located in the upper left. You can also select from a number of other statistics to print (Phi and Cramer's V are the only ones that we'll be using).

3. Under the Cells tab, you can select what info you want to print on your Crosstabulation tables. Select row/column percentages, observed and expected scores. 

4. Under the Format tab, you just select between ascending or descending order. (It really doesn't matter which one you choose.)

5. Click OK to run or Paste to run from syntax.

When running a Chi-square, 3 different significance figures may come up. Just worry about the
"Pearson chi-square" Test (this is the only one that comes up when running a Chi-square on larger tables).

Example Syntax:

CROSSTABS 

/TABLES=row_variable  BY column_variable 

/FORMAT= AVALUE TABLES

  /STATISTIC=CHISQ PHI 

/CELLS= COUNT EXPECTED 

/COUNT ROUND CELL.

Interpreting Chi-Square Results Before you start to interpret what the significance levels mean, first consider what your hypothesis is for a particular chi-square test. Based on the hypothesis, use the significance level to tell you if the data matches your predicted hypothesis. See examples below…

Basic Chi-Square Example: 

Hypothesis: There are an equal number of graduate students and undergraduate students in a particular sample

Procedure: Run a Basic Chi-Square test and leave All Categories Equal to predict an even ratio across all variable levels (in this case, graduate and undergraduate).

• If the Chi-Square probability (Asymp.sig) level is LESS THAN .05, then Chi-square is said to be significant, meaning that there is not an equal ratio of graduate students and undergraduate students in your sample.
• If the Chi-Square probability (Asymp.sig) level is GREATER THAN .05, then Chi-square is not significant, meaning that there is an equal ratio of graduate students and undergraduate students in your sample.

Chi-Square Test for Independence Example: Hypothesis: There is no relationship between gender and assignment to remedial or advanced math classes in high school.Procedure: Run a Chi-Square test for Independence to determine if gender and assignment to remedial or advanced math classes in high school are independent of each other.

• If the Chi-Square probability (Asymp.sig) level is LESS THAN .05, then Chi-square is said to be significant, and you would conclude that there is a significant relationship between gender and remedial/advanced math class assignment. That is, gender and remedial/advanced assignment are not independent of one another.
• If the Chi-Square probability (Asymp.sig) level is GREATER THAN .05, then Chi-square is not significant, and you would conclude that there is not a relationship between gender and remedial/advanced math class assignment. That is, gender and remedial/advanced assignment are independent of one another.

Helpful Hints

Tip: If you can’t figure out what the significant test means (i.e., whether the data fits your hypothesis or not), look at the pattern of expected/observed frequencies in your chi-square table to help you determine the meaning of your results

.Keep in mind:

• If an Expected frequency is less than 5, it is probably not appropriate to run a chi-square test. Therefore, you are severely limited in the conclusions that can be drawn. However, we are not going to worry about that for this assignment (but it is worth noting when running research studies).
• If you have a very large sample, the Chi-square may be significant simply because you have large power. However, the significant results may not be meaningful if the differences between expected/observed frequencies are practically small. Therefore, when dealing with large sample sizes, you must interpret results carefully, and should probably verify your results with more conservative statistical evidence.

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