# Reasoning in Psychology Using Statistics Psychology 138 2015.

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Reasoning in Psychology Using Statistics Psychology 138 2015 Slide 2 Reasoning in Psychology Using Statistics Annoucements Dont forget quiz 8 due this Friday Slide 3 Reasoning in Psychology Using Statistics Chi-Square Test for Independence A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: Is there a relationship between age and watch preference? Young (under 30) Old (over 30) Slide 4 Reasoning in Psychology Using Statistics Chi-Square Test for Independence A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: Is there a relationship between age and watch preference? Young (under 30) Old (over 30) Slide 5 Reasoning in Psychology Using Statistics Decision tree Chi-square test of independence ( 2 lower-case chi ) Describing the relationship between two categorical variables or YoungOld or Slide 6 Reasoning in Psychology Using Statistics A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? Chi-Squared Test for Independence Slide 7 Reasoning in Psychology Using Statistics Chi-Squared Test for Independence Step 1 : State the hypotheses and select an alpha level H 0 : Preference is independent of age ( no relationship ) H A : Preference is related to age ( there is a relationship ) We ll set = 0.05 A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? Observed scores Slide 8 Reasoning in Psychology Using Statistics Step 2: Compute your degrees of freedom & get critical value df = (#Columns - 1) * (#Rows - 1) = (3-1) * (2-1) = 2 For this example, with df = 2, and = 0.05 Chi-Squared Test for Independence The critical chi-squared value is 5.99 Go to Chi-square statistic table and find the critical value Slide 9 Reasoning in Psychology Using Statistics Chi-Squared Test for Independence X 2 =.05 5.99 7.81 11.07 14.07 As df gets larger, need larger X 2 value for significance. Number of cells get larger. Slide 10 Reasoning in Psychology Using Statistics Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Chi-Squared Test for Independence Observed scores Slide 11 Reasoning in Psychology Using Statistics Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Chi-Squared Test for Independence Observed scores Spot check: make sure the row totals and column totals add up to the same thing Slide 12 Reasoning in Psychology Using Statistics Chi-Squared Test for Independence Under 30 Over 30 Digital AnalogUndecided 705614 30246 Observed scores Expected scores Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies (in each cell) Slide 13 Reasoning in Psychology Using Statistics Chi-Squared Test for Independence Under 30 Over 30 Digital AnalogUndecided 705614 30246 Observed scores Expected scores Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies expected frequencies - if the null hypothesis is correct, then these are the frequencies that you would expect Slide 14 Reasoning in Psychology Using Statistics Find the residuals (f o - f e ) for each cell Step 4: compute the 2 Chi-Squared Test for Independence Slide 15 Reasoning in Psychology Using Statistics Computing the Chi-square Find the residuals (f o - f e ) for each cell Step 4: compute the 2 Slide 16 Reasoning in Psychology Using Statistics Computing the Chi-square Square these differences Find the residuals (f o - f e ) for each cell Step 4: compute the 2 Slide 17 Reasoning in Psychology Using Statistics Computing the Chi-square Find the residuals (f o - f e ) for each cell Divide the squared differences by f e Step 4: compute the 2 Square these differences Slide 18 Reasoning in Psychology Using Statistics Computing the Chi-square Square these differences Find the residuals (f o - f e ) for each cell Divide the squared differences by f e Sum the results Step 4: compute the 2 Slide 19 Reasoning in Psychology Using Statistics Chi-Squared, the final step Step 5 : Compare this computed statistic (38.09) against the critical value (5.99) and make a decision about your hypotheses A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? here we reject the H 0 and conclude that there is a relationship between age and watch preference Slide 20 Reasoning in Psychology Using Statistics Chi square as a statistical test each cell = observed difference. difference expected by chance Slide 21 Reasoning in Psychology Using Statistics Chi-Square Test in SPSS Analyze Descriptives Crosstabs Slide 22 Reasoning in Psychology Using Statistics Chi-Square Test in SPSS Analyze Descriptives Crosstabs Click this to get the expected frequencies and residuals Click this to get bar chart of the results Slide 23 Reasoning in Psychology Using Statistics Chi-Square Test in SPSS Slide 24 Reasoning in Psychology Using Statistics Wrap up In lab: Gain experience using and interpreting Chi-square procedures Questions?