Introductory Statistics

Test of Independence Review Hypothesis Testing Checking Requirements & Descriptive Statistics

Test of Independence The two proportion Z procedure is limited to two rows and two columns. However, the Test of Independence is less limiting. The row variables can have as many rows as needed and the column variable can have as many columns Row Variable Column Variable

Test of Independence Review Hypothesis Testing Checking Requirements & Descriptive Statistics

Six Steps for Doing Test of Independence 1. State the Null and Alternative Hypotheses H o : Row Variable and Column variable are independent H a : Row Variable and Column variable are not independent 2. Calculate the χ 2 (the Test Statistic) 3. Determine the Degrees of Freedom for the Test df = (r-1)(c-1) 4. Calculate the P-value 5. Reject the Null Hypothesis is the P-value is less than the level of significance (α), if not, then don’t reject. 6. State the conclusion (in layman’s terms) a. If Reject H o – We have sufficient evidence to say that “state H a in English” b. If Don’t Reject H o - We have insufficient evidence to say that “state H a in English”

Six Steps for Doing Test of Independence There was a recent survey taken on whether consumers are “label users” who pay attention to label details when buying clothes. Are men and women equally likely to be label users? Determine if gender is independent of label usage. Use a level of significance of α = The data from the study are summarized in the following contingency table : 1. H o : Gender and label usage are independent H a : Gender and label usage are not independent 2. χ 2 = df = (r-1)(c-1) = (2-1)(2-1) = 1 4. P-value = P-value is less the level of significance, we would reject the null hypothesis 6. We have sufficient evidence to say that Gender and label usage are not independent.

Expected Counts Expected Cell Counts Expect in Each Cell Assuming Independence between the Row and Column Variable (the null hypothesis is true) Expected Count for each cell = Row Total * Column Total / Table Total

Six Steps for Doing Test of Independence A study was conducted to determine why patients seek chiropractic care. Patients were classified based on their motivation for seeking treatment. Using descriptions developed by Green and Krueter, patients were asked which of the five reasons led them to seek chiropractic care : Wellness: defined as optimizing health among the self-identified healthy Preventive health: defined as preventing illness among the self-identified healthy At risk: defined as preventing illness among the currently healthy who are at heightened risk to develop a specific condition Sick role: defined as getting well among those self-perceived as ill with an emphasis on therapist- directed treatment Self care: defined as getting well among those self-perceived as ill favoring the use of self vs. therapist directed strategies The data from the study are summarized in the following contingency table : The research question was whether people's motivation for seeking chiropractic care was independent of their location: Europe, Australia, or the United States. Use a level of significance of α = 0.05.

Six Steps for Doing Test of Independence 1. H o : Location and Motivation for Chiropractic Care are independent H a : Location and Motivation for Chiropractic Care are not independent 2. χ 2 = df = (r-1)(c-1) = (3-1)(5-1) = 8 4. P-value = close to zero 5. P-value is less alpha, we would reject the null hypothesis 6. We have sufficient evidence to say that Location and Motivation for Chiropractic Care are not independent.

Test of Independence Review Hypothesis Testing Checking Requirements & Descriptive Statistics

Requirements to Check and Descriptive Statistics Before Doing Hypothesis Test Requirements to Check for Test of Independence procedure All of the Expected Counts are ≥ 5 Descriptive Statistics to Use Graphical – Use a pie charts or a bar graphs (similar to the two proportion pie charts or bar graphs)

Using SPSS for Test of Independence I. Data Entry II. Use “Data -> Weight Cases” by Freq or Count variable ONLY when you have Summarized Data III. Use “Analyze -> Descriptive Statistics -> Crosstabs” to create a two way table IV. Options 1. Click Cells, then choose the following: Observed Counts, Expected Counts, 2. Click Statistics, then choose Chi-Square 3. Click Display clustered bar charts