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Chi-Square Test of Independence Questions

Use the Nursing dataset to run a Chi-Square Test of Independence with Heart failure and Depression as the variables.

• Q1: What is the null and alternative hypotheses?
• Q2: What is a dependent variable(s) in this analysis?
• Q3: What are the levels of Heart failure and Depression?
• Q4: Which cells had more observations than expected? Which had fewer observations than expected?
• Q5:What does the p value of < .001 indicate?
• Q6: What do these findings indicate in plain English?

Chi-square Test of Independence

Introduction

A Chi-square Test of Independence was conducted to examine whether Heart_Failure and Depression were independent. There were 2 levels in Heart_Failure: No and Yes. There were 2 levels in Depression: No and Yes.

Assumptions

The assumption of adequate cell size was assessed, which requires all cells to have expected values greater than zero and 80% of cells to have expected values of at least five (McHugh, 2013). All cells had expected values greater than zero, indicating the first condition was met. A total of 100.00% of the cells had expected frequencies of at least five, indicating the second condition was met.

Results

The results of the Chi-square test were significant based on an alpha value of .05, ²(1) = 112.61, p < .001, suggesting that Heart_Failure and Depression are related to one another. The following level combinations had observed values that were greater than their expected values: Heart_Failure (No):Depression (No) and Heart_Failure (Yes):Depression (Yes). The following level combinations had observed values that were less than their expected values: Heart_Failure (Yes):Depression (No) and Heart_Failure (No):Depression (Yes). Table 1 presents the results of the Chi-square test.

	Depression
Heart_Failure	No	Yes	2	df	p
No	628[566.43]	89[150.57]	112.61	1	< .001
Yes	162[223.57]	121[59.43]
Note. Values formatted as Observed[Expected].