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

H1 and H0 H1: The Research Hypothesis H0: The Null 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)

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? Work through the examples in the Excel file before proceeding to the next slide. Go through the first 3 sheets, then come back to the powerpoint file.

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)

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).

Calculating p How do you calculate the probability that the observed effect is just due to chance? 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” Three we will learn about in this course. (Probably just the first two actually)

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.

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)

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

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)

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”

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

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.”