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Statistics_are in the eye of the Manipulator
Introduction
The Chi-Square (X2) statistic may be used to determine if two categorical (nominal or ordinal variables with less than 5 rankings) variables are related. For example, you may hypothesize that gender influences a person’s political party identification. You can determine some of this information by looking at the cross tabulation and comparing the percentages of men and women for each party identification. This statistic involves comparing your actual results with the results you would expect to have if there were NO difference between women and men in terms of their political party affiliation.
Assumptions
When you choose to analyse your data using a chi-square test for independence, you need to make sure that the data you want to analyse “passes” two assumptions. These two assumptions are:
- Assumption #1: Your two variables should be measured at an ordinal or nominal level (i.e., categorical data). You can learn more about ordinal and nominal variables in our article: Types of Variable.
- Assumption #2: Your two variable should consist of two or more categorical, independent groups. Example independent variables that meet this criterion include gender (2 groups: Males and Females), ethnicity (e.g., 3 groups: Caucasian, African American and Hispanic), physical activity level (e.g., 4 groups: sedentary, low, moderate and high), profession (e.g., 5 groups: surgeon, doctor, nurse, dentist, therapist), and so forth.
- Assumption #3: One of the requirements for Chi-Square is that each and every cell has a frequency of 5 or greater.
Chi-Square Test Procedure in SPSS
We show you how to interpret the results from your chi-square test for independence.
- Click Analyze > Descriptives Statistics > Crosstabs… on the top menu
- You will be presented with the following Crosstabs dialogue box:
- Transfer one of the variables into the Row(s): box and the other variable into the Column(s): box. In our example, we will transfer the Gender variable into the Row(s): box and Preferred_Learning_Medium into the Column(s): box. There are two ways to do this. You can either: (1) highlight the variable with your mouse and then use the relevant
buttons to transfer the variables; or (2) drag-and-drop the variables. How do you know which variable goes in the row or column box? There is no right or wrong way. It will depend on how you want to present your data.If you want to display clustered bar charts (recommended), make sure that Display clustered bar charts checkbox is ticked.
- Click on the
button. You will be presented with the following Crosstabs: Statistics dialogue box: - Select the Chi-square and Phi and Cramer’s V options (for Nominal data) or Somers’d for Ordinal data.
- Click the
button. - Click the
button. You will be presented with the following Crosstabs: Cell Display dialogue box:Published with written permission from SPSS Statistics, IBM Corporation. - Select Observed from the –Counts– area, and Row, Column and Total from the –Percentages– area, check Observed.
- Once you have made your choice, click the button.
Click the
button to generate your output.
Output
You will be presented with some tables in the Output Viewer under the title “Crosstabs”. The tables of note are presented below:
The Crosstabulation Table (Gender*Preferred Learning Medium Crosstabulation)
This table allows us to understand that both males and females prefer to learn using online materials versus books.The Chi-Square Tests Table
When reading this table we are interested in the results of the “Pearson Chi-Square” row. We can see here that χ(1) = 0.487, p = .485. This tells us that there is no statistically significant association between Gender and Preferred Learning Medium; that is, both Males and Females equally prefer online learning versus books.In short, Now look at the “Pearson Chi-Square Asymp. Sig (2 sided)”*. Since Chi-Square is testing the null hypothesis, the Sig value must be .05 or less for there to be a significant statistical for the relationship between the variables. In this example, the Sig. is .485, so there is no statical significance.
Look at the “Continuity Correction” line below. This will appear if you are examing variables that each have 2 possible responses. The corrected significance is .216; therefore, this also suggests that there is statistical significance between the relationship of the two variables.
The Symmetric Measures Table
The most commonly used statistic is the Phi coefficient, which ranges from 0 to 1. Higher values indicate a stronger correlation between the two variables. Phi and Cramer’s V are both tests of the strength of association. We can see that the strength of association between the variables is very weak.Reference:
- https://statistics.laerd.com/spss-tutorials/chi-square-test-for-association-using-spss-statistics.php
- http://latrobe.libguides.com/SPSS/chi-square
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List of Journals:
1). International Journal Of Science & Engineering Research – IJOSER
2). International Journal Of Commerce, Economics & Management – IJOCEM
3). International Journal Of Service Quality – IJSQ
4). International Journal of Web Components, Data & Analytics – IJWCDA
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