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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

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H 1 and H 0 H 1 : The Research Hypothesis –The effect observed in the data (the sample) reflects a “real” effect (in the population) H 0 : 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)

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Example: Comparing ProportionsComparing Proportions H 0 : The proportions are not really different H 1 : 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?

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The Logic of Hypothesis Testing 1.Assume the Null Hypothesis (H 0 ) is true 2.Calculate the probability (p) of getting the results observed in your data if the Null Hypothesis were true 3.If that probability is low (<.05) then reject the Null Hypothesis 4.If you reject the Null Hypothesis, that leaves only the Research Hypothesis (H 1 )

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1.Assume the Null Hypothesis is true –The coins are fair (balanced) 2.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. 3.If that probability is low (<.05) then reject the Null Hypothesis –That is unlikely, so the Null Hypothesis must be false. 4.If you reject the Null Hypothesis, that leaves only the Research Hypothesis –We conclude that the coins are not fair (balanced).

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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: 1.Are two proportions different? Chi-square 2.Are two means different? t-test 3.Are more than two means different? ANOVA or “F-test”

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The Logic is Always the Same: 1.Assume nothing is going on (assume H 0 ) 2.Calculate a test statistic (Chi-square, t, F) 3.How often would you get a value this large for the test statistic when H 0 is true? (In other words, calculate p) 4.If p <.05, reject the null hypothesis and conclude that something is going on (H 1 ) 5.If p >.05, do not conclude anything.

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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)Excel spreadsheet

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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

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

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Performing the Chi-Square Test 1.Name the variables using the variables tab in the SPSS data window 2.analyze -> descriptive statistics -> crosstabs 3.Use arrow button to move “gender” into “rows” box 4.Use arrow button to move “footware” into “columns” box 5.Click “Statistics” box 6.Check the box for “Chi-square”, then click “Continue” 7.Click the “Cells” box. 8.Under “Percentages” check the boxes for “Row” and “Column” 9.Click “OK”

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Interpreting the ResultsResults “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

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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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