Statistics for the Social Sciences Psychology 340 Fall 2013 Thursday, November 21 Review for Exam #4

Homework #13 (last homework) due today Ch 17 # 13, 14, 19, 20

Announcements Final project due date extended from Dec. 5 to Dec. 6. Must be turned in to psychology department by 4 p.m. Extra credit due by the start of class on Dec. 5 (the last day our class meets). Evidence of academic dishonesty regarding extra credit will be referred for disciplinary action. Exam IV (emphasizing correlation, regression, and chi- squared test) is on Tuesday, December 3 Homeworks 12 & 13 will be graded and available for you to pick up by office hours on Monday Dec. 2 at 9 a.m. Final exam: Tuesday, 12/10 at 7:50 a.m.

Statistical analysis follows design We have finished the top part of the chart! Focus on this section for rest of semester

Chi-Squared Test for Independence Step 1 : State the hypotheses – H 0 : Preference is independent of age (“no relationship”) – H A : Preference is related to age (“there is a relationship”) 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

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 For this example, with df = 2, and  = 0.05 The critical chi-squared value is 5.99 –Go to Chi-square statistic table (B-8) and find the critical value

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 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 Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Under 30 Over 30 Digital AnalogUndecided Observed scores Expected scores

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

Find the residuals (f o - f e ) for each cell Chi-Squared Test for Independence Step 3: compute the  2

Computing the Chi-square Step 3: compute the  2 Find the residuals (f o - f e ) for each cell

Computing the Chi-square Square these differences Find the residuals (f o - f e ) for each cell Step 3: compute the  2

Computing the Chi-square Square these differences Find the residuals (f o - f e ) for each cell Divide the squared differences by f e Step 3: compute the  2

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 3: compute the  2

Chi-Squared, the final step Step 4 : 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

In SPSS Analyze => Descriptives => Crosstabs Select the two variables (usually they are nominal or ordinal) you want to examine and click the arrow to move one into the “rows” and one into the “columns” box. Click on “statistics” button, and check the “Chi- square” box. Click “continue.” Click “OK.”

SPSS Output Look at the “Chi-square tests” box. The top row of this box gives results for “Pearson’s Chi-Square” “Value” is the value of the χ 2 statistic, “df” is the degrees of freedom for the test “Asymp. Sig. (2-sided)” is the probability (p- value) associated with the test. The chi-squared distribution, like the F- distribution, is “squared” so 1-tailed test is not possible.

Exam IV (Monday 12/5) Covers first 17 chapters (emphasis on chapters ) Similar format and guidelines as past exams

Old Material Ways to describe distributions (using tables, graphs, numeric summaries of center and spread) Z-scores Probability Characteristics of the normal distribution Use of the unit normal table Central Limit Theorem & distribution of sample means Standard error of the mean ( σ M ) Hypothesis testing (four steps)

Old Material: t-tests Effect sizes and power Type I and Type II error Similarities/differences among four inferential tests: One-sample Z test One-sample t-test Independent samples t-test Paired samples t-test When to use which test Formulae for each statistic Numerator (difference between means) Denominator / standard error Degrees of freedom Use of the t-table with various alpha levels and one-tailed and two-tailed scenarios

Old Material: t-tests Assumptions of the t-tests Levene’s test for equality of variance Using SPSS/Excel to conduct t-tests Setting up the data properly Knowing which commands to use Interpreting the output Estimation and confidence intervals with t formulae

One-Way ANOVA Calculating total, between, and within condition SS, df, and MS Calculating and interpreting the F-Ratio, using the F table Effect sizes, assumptions, and how to write the results in a research paper Experiment-wise error, Post hoc tests and planned comparisons (know what they are, why they are used, and how to conduct and interpret them using SPSS - no by-hand calculations) Old Material: ANOVA

Repeated Measures ANOVA Calculating total, between condition, within condition, between participants, and error SS, df, and MS Calculating and interpreting the F-Ratio, using the F table Effect sizes, assumptions, and how to write the results in a research paper Know why a repeated measures ANOVA is more powerful than a between-groups ANOVA Old Material: ANOVA

Factorial ANOVA Understanding and interpreting main effects and interaction effects in a two-factor scenario Calculating total, between condition, Factor A, Factor B, interaction, and within condition SS, df, and MS Calculating and interpreting the three F-Ratios, using the F table Effect sizes, assumptions, and how to write the results in a research paper Old Material: ANOVA

ANOVA in SPSS Know how to conduct one-way, repeated measures, and factorial ANOVAs using spss. Know how to set up the data for each kind of ANOVA Know how to inerpret the output for each type of ANOVA In general: Be able to fill in ANOVA tables for each kind of ANOVA Be able to tell which type of test to conduct (Z, one-sample t, related-samples t, one-way ANOVA, repeated measures ANOVA, factorial ANOVA) based on description of a study or details of a data set (study the flow chart!) Old Material: ANOVA

Scatterplots Direction, strength, and shape of correlation (and associated r values) How to calculate a Pearson’s correlation coefficient, and assess its statistical significance. What kind of variables are appropriate for correlation How to set up the data, run the analysis, and interpret the output in SPSS & Excel (for scatter plots and correlations) New Material: Correlations

Be familiar with linear regression formula with both standardized and unstandardized regression coefficients. Know how to calculate the slope and intercept by hand for simple linear regression (one X and one Y), and using SPSS for both simple and multiple regression. Know how to set up the data, run the analysis, and interpret the results. Be able to write the regression equation, based on SPSS output (need to identify the regression coefficients). Know how to find predicted values of Y, as well as residuals, given a regression equation and associated values of X (for simple and multiple regression). Know how to evaluate a regression model, and how to make comparisons among different models (need to know about R 2, and tests of significance associated with change in R 2 ) New Material: Regression

Know the formula for the chi-squared statistic. Know how to calculate expected frequencies and residuals within each cell. Know how to calculate the degrees of freedom for a chi- squared test. Know what kinds of variables are appropriate for the chi- squared test. Know how to set up the data in SPSS, and how to run the analysis and interpret the output. New Material: Chi-Squared Test of Independence

You have to know when to use which test (Review the flow chart) Also, don’t forget