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# Hypothesis Testing and Comparing Two Proportions

Hypothesis Testing and Comparing Two Proportions. Hypothesis Testing : Deciding whether your data shows a “real” effect, or could have happened by chance Hypothesis testing is used to decide between two possibilities: The Research Hypothesis The Null Hypothesis. H 1 and H 0.

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## Hypothesis Testing and Comparing Two Proportions

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1. Hypothesis Testing and Comparing Two Proportions • Hypothesis Testing: Deciding whether your data shows a “real” effect, or could have happened by chance • Hypothesis testing is used to decide between two possibilities: • The Research Hypothesis • The Null Hypothesis

2. H1 and H0 • H1: The Research Hypothesis • The effect observed in the data (the sample) reflects a “real” effect (in the population) • H0: The Null Hypothesis • There is no “real” effect (in the population) • The effect observed in the data (the sample) is just due to chance (sampling error)

3. Example: Comparing Proportions • H0: The proportions are not really different • H1: The proportions are really different • Example 1: Are pennies heavier on one side? • Example 2: Do males mention footware in personals ads more often than females do?

4. The Logic of Hypothesis Testing • Assume the Null Hypothesis (H0) is true • Calculate the probability (p) of getting the results observed in your data if the Null Hypothesis were true • If that probability is low (< .05) then reject the Null Hypothesis • If you reject the Null Hypothesis, that leaves only the Research Hypothesis (H1)

5. Assume the Null Hypothesis is true • The coins are fair (balanced) • Calculate the probability (p) of getting the results observed in your data if the Null Hypothesis were true • How often would you get 8/10 coins coming up heads if the coins were fair? You would get 8/10 heads less than 5% of the time. • If that probability is low (< .05) then reject the Null Hypothesis • That is unlikely, so the Null Hypothesis must be false. • If you reject the Null Hypothesis, that leaves only the Research Hypothesis • We conclude that the coins are not fair (balanced).

6. Calculating p • How do you calculate the probability that the observed effect would happen by chance if the null hypothesis were true? • Use a test statistic: • Are two proportions different? Chi-square • Are two means different? t-test • Are more than two means different? ANOVA or “F-test”

7. The Logic is Always the Same: • Assume nothing is going on (assume H0) • Calculate a test statistic (Chi-square, t, F) • How often would you get a value this large for the test statistic when H0 is true? (In other words, calculate p) • If p < .05, reject the null hypothesis and conclude that something is going on (H1) • If p > .05, do not conclude anything.

8. Demonstrating Hypothesis Testing with Chi-square • Example 1: Testing whether coins are unbalanced • Example 2: Testing whether men are more likely to mention footware in personals ads than women are. • (see Excel spreadsheet for both examples)

9. Assumptions of Chi-square Test • Each observation must be INDEPENDENT – one data point per subject • DV is categorical (often yes/no) • Calculations must be made from COUNTS, not proportions or percentages • No cell should have an “expected value” of less than 5

10. Using Chi-square in SPSS to compare two proportions • Setting up the data file – copy data from excel and paste it into SPSS data file • Performing the Chi-square test (next slide) • Interpreting the Results (separate slide) • Reporting the Results (separate slide)

11. Performing the Chi-Square Test • Name the variables using the variables tab in the SPSS data window • analyze -> descriptive statistics -> crosstabs • Use arrow button to move “gender” into “rows” box • Use arrow button to move “footware” into “columns” box • Click “Statistics” box • Check the box for “Chi-square”, then click “Continue” • Click the “Cells” box. • Under “Percentages” check the boxes for “Row” and “Column” • Click “OK”

12. Interpreting the Results • “Case Processing Summary” – look for missing data, etc. • “Gender x Footware Crosstabulation” – shows the counts of observations in each cell, and the percentages within each row and within each column. • “Chi-square Tests” – look at “Pearson chi-square” line • Value = 5.33 – This is the value of Chi-square • “Asymp Sig” = .021 – This is the p value • Compare these values to those I calculated by hand on the excel spreadsheet

13. Reporting the Results • Report the value of chi-square, the degrees of freedom (df), and the p value. Also mention how many observations there were. • EXAMPLE: “A greater proportion of men than women mentioned footware in their ads (see Table 1). Of the six ads placed by men, 83% mentioned footware. Only 17% of the six ads placed by women mentioned footware. This difference was significant by a Chi-square test, Chi-square (1) = 5.3, p < .05.”

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