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

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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.

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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.

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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.

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Karl Pearson, 1890 and 1910

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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

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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).

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Chi Square Distribution, Statistic

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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

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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.

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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.

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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

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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.

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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.

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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.

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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

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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

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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.

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

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Pearson, 1930

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