# An explanation of the Chi-Square Test for Independence Jeffrey Marks Bhavisha Talsania California State University San Marcos.

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An explanation of the Chi-Square Test for Independence Jeffrey Marks Bhavisha Talsania California State University San Marcos

Research Question: Do veteran students take the same majors as non-veteran students? Special Considerations: --Focus on STEM majors (will help us group the variable). --Results must be understandable and explainable.

Data and Choice of Statistical Tests Data Type: Veteran Status and Major are Categorical. Major data grouped into college categories: (STEM, Social Sciences, Arts & Humanities, Business, Health and Education. Would like to see if a relationship exists between two categorical variables (nominal). Pearson’s Chi-square test for Independence.

Karl Pearson (1857-1936) Credited with Establishing Mathematical Statistics. Linear Regression, Correlation, Standard Deviation, Kurtosis. Classification of Probability Distributions. Chi-Square Distribution Rediscovery Introduced in July 1900.

Karl Pearson, 1890 and 1910

Descriptive Statistics Results Veterans tend to be male and transfer students. Freshman (3) and Postbacc veterans (11) excluded in the analysis. Choice of comparison group data: Student status (freshman vs. transfer) important, gender not. VetStatsF2013.xlsx

Chi-square Test for Independence Overview and Setup Hypotheses: H o : Veteran Status is Independent of Major. (No significant relationship between major and veteran Status). H a : Veteran Status is NOT Independent of Major. (A significant relationship exists between major and veteran status, meaning veterans take different majors than non-veterans). P-value is compared to Alpha or Calculated χ² is compared to a Critical χ² Cutoff Value from a table and determines if we reject or fail to reject Ho. Degrees of Freedom = (#rows-1)(#columns-1).

Chi Square Distribution, Statistic

Chi-Square Setup Table setup: ChiSQMajorData.xlsxChiSQMajorData.xlsx These are the Observed or Actual Values Row totals Column Totals Grand Total Expected Values for Each Cell: Row Total x Column Total Grand Total

Chi-Square Considerations Are the Data Accurate? Can You Independently Verify? 80% Rule for Expected Values. Nature/Extent of of Relationship Not Clear. When Sample Sizes Differ, Size of χ² not comparable. Hard to Compare Tables of Different Dimensions. Cramer’s V attempts to Adjust for the Above. Effect Size:.10 Low,.30 Medium,.50 Large effect size is a quantitative measure of the strength of a phenomenon.

χ² Calculation For each Cell, (8 in both Examples) we do a calculation. For All F13 Transfer Students Cell 1,1 (Row 1, Column 1): χ² = (89-91.22)² =.054 91.22 ∑ χ² =.054 + 1.44 + 6.31 +.002 +.006 +.15 +.65 +.0001 = 8.6121, this is the Chi-Square Calculated Statistic.

χ² Calculation, continued. Calculated χ² for all F13 Transfer Students: 8.6121. Calculated χ² for all New F13 Transfer Students: ∑ χ² =.11 + 1.67 + 6.49 +.07 +.009 +.14 +.54 +.006 = 9.035, this is the Chi-Square Calculated Statistic. χ² Degrees of Freedom = (row-1)(column-1) = (1)(3)=3 3 df in χ² Table with Alpha =.05 gives us 7.8147

Results Compare the Calculated χ² value vs. the Critical χ², Alternately compare the p-Value vs. Alpha. If the Calculated Value Exceeds the Critical Value we Reject H o. If the p-value is < Alpha (.05), we reject the H o. In this case, if we Reject H o, then there is a significant relationship between Veteran Status and Major. The expected and observed values were far enough apart to calculate a large χ² statistic which exceeds the critical value. Results are just an example- Do for different groups, longitudinally, compare different semesters.

Results, All Transfer Students For All Transfer Students, Calculated χ² = 8.6121 Critical χ² = 7.8147. Therefore we reject the H o that Veteran Status is Independent of Major. We can say that the variables are NOT Independent, therefore a statistically significant relationship exists between Major and Veteran Status. Veterans choose different majors this semester. χ² (3, N=4177) = 8.6121, p <.05.

Results, New Transfer Students For NEW Transfer Students, Calculated χ² = 9.035 Critical χ² = 7.8147. Therefore we reject the H o that Veteran Status is Independent of Major. We can say that the variables are NOT Independent, therefore a statistically significant relationship exists between Major and Veteran Status. Veterans choose different majors this semester. χ² (3, N=1614) = 9.035, p <.05.

SPSS Results, All Transfers To do Chi-Square in SPSS use the Crosstabs function. Analyze-Descriptives-CrossTabs Be sure to select under Statistics: Chi-Square and Cramer’s V. Results of Veteran Status vs. Major, All Fall 2013 Transfer Students ValuedfSignificance 2-sided Pearson Chi-Square8.6113.035 Cramer’s V.045.035 N of Valid Cases4177

SPSS Results, New Transfers G:\2014Pres\ChiSqMajVVet.spv ValuedfSignificance 2-sided Pearson Chi-Square8.6113.029 Cramer’s V.075.029 N of Valid Cases1614

What do we do with the Results? Potential Issues: How are major changes tracked? Is there a lag? Data Correctness and Completeness. STEM Center Faculty– very interested. Veterans Coordinator- present at meeting, she can use to help veterans get jobs.. Share with Colleagues.

Questions or Comments? How do you share your findings with others? Who do you share them with? Data concerns or considerations?

Pearson, 1930

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