Reasoning in Psychology Using Statistics 2017

Don’t forget quiz 8 due this Friday Annoucements

Exam(s) 3 Lecture Exam 3 Lab Exam 3 Combined Exam 3 Mean 55.1 (55.1/75 = 73.5%) Lab Exam 3 Mean 61.3 (61.3/75 = 81.7%) Combined Exam 3 Mean 77.6% Exam(s) 3

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). Young (under 30) Old (over 30) The question: Is there a relationship between age and watch preference? Chi-Square Test for Independence

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). Young (under 30) Old (over 30) The question: Is there a relationship between age and watch preference? Chi-Square Test for Independence

Decision tree Chi-square test of independence (χ2 lower-case chi ) Describing the relationship between two categorical variables or Young Old or Decision tree

Chi-Squared 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). The question: is there a relationship between age and watch preference? Chi-Squared Test for Independence

Chi-Squared 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). The question: is there a relationship between age and watch preference? Step 1: State the hypotheses and select an alpha level H0: Preference is independent of age (“no relationship”) HA: Preference is related to age (“there is a relationship”) We’ll set α = 0.05 Observed scores Chi-Squared Test for Independence

Chi-Squared Test for Independence Step 2: Compute your degrees of freedom & get critical value df = (#Columns - 1) * (#Rows - 1) = (3-1) * (2-1) = 2 Go to Chi-square statistic table and find the critical value The critical chi-squared value is 5.99 For this example, with df = 2, and α = 0.05 Chi-Squared Test for Independence

Chi-Squared Test for Independence As df gets larger, need larger X2 value for significance. Number of cells get larger. X2 α = .05 5.99 7.81 11.07 14.07 Chi-Squared Test for Independence

Chi-Squared Test for Independence Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Observed scores Chi-Squared Test for Independence

Chi-Squared Test for Independence Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Observed scores Spot check: make sure the row totals and column totals add up to the same thing Chi-Squared Test for Independence

Chi-Squared Test for Independence Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies (in each cell) Observed scores Expected scores 70 56 14 30 24 6 Under 30 Over 30 Digital Analog Undecided Chi-Squared Test for Independence

Chi-Squared Test for Independence Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies (in each cell) Observed scores Expected scores 70 56 14 “expected frequencies” - if the null hypothesis is correct, then these are the frequencies that you would expect 30 24 6 Under 30 Over 30 Digital Analog Undecided Chi-Squared Test for Independence

Chi-Squared Test for Independence Step 4: compute the χ2 Find the residuals (fo - fe) for each cell Chi-Squared Test for Independence

Computing the Chi-square Step 4: compute the χ2 Find the residuals (fo - fe) for each cell Computing the Chi-square

Computing the Chi-square Step 4: compute the χ2 Find the residuals (fo - fe) for each cell Square these differences Computing the Chi-square

Computing the Chi-square Step 4: compute the χ2 Find the residuals (fo - fe) for each cell Square these differences Divide the squared differences by fe Computing the Chi-square

Computing the Chi-square Step 4: compute the χ2 Find the residuals (fo - fe) for each cell Square these differences Divide the squared differences by fe Sum the results Computing the Chi-square

Chi-Squared, the final step 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? Step 5: Compare this computed statistic (38.09) against the critical value (5.99) and make a decision about your hypotheses here we reject the H0 and conclude that there is a relationship between age and watch preference Chi-Squared, the final step

Chi square as a statistical test each cell = observed difference difference expected by chance Chi square as a statistical test

Chi-Square Test in SPSS Analyze  Descriptives  Crosstabs Chi-Square Test in SPSS

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 Chi-Square Test in SPSS

Chi-Square Test in SPSS

In lab: Gain experience using and interpreting Chi-square procedures Questions? Chi-squared test: https://www.youtube.com/watch?v=WXPBoFDqNVk (~12 mins) Chi-squared test: https://www.youtube.com/watch?v=SvKv375sacA (~38 mins) Chi-squared in SPSS: https://www.youtube.com/watch?v=wfIfEWMJY3s Chi-squared distribution: http://onlinestatbook.com/2/chi_square/distributionM.html Wrap up