Lecturer’s desk INTEGRATED LEARNING CENTER ILC 120 Screen Row A Row B Row C Row D Row E Row F Row G Row H Row I Row J Row K Row L Computer Storage Cabinet Cabinet Table broken desk
Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall, 2014 Room 120 Integrated Learning Center (ILC) 10: :50 Mondays, Wednesdays & Fridays.
Reminder A note on doodling
Schedule of readings Before next exam (November 21 st ) Please read chapters 7 – 11 in Ha & Ha Please read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence
No homework due – Monday (November 17 th ) Just work on ANOVA projects
Labs continue Next week
By the end of lecture today 11/14/14 Use this as your study guide Hypothesis testing with Analysis of Variance (ANOVA) Constructing brief, complete summary statements
One way analysis of variance Variance is divided Total variability Within group variability (error variance) Between group variability (only one factor) Remember, 1 factor = 1 independent variable (this will be our numerator – like difference between means) Remember, error variance = random error (this will be our denominator – like within group variability Remember, one-way = one IV
Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses Step 2: Decision rule Alpha level? ( α =.05 or.01)? Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed t (or F) is bigger then critical t (or F) then reject null Step 5: Conclusion - tie findings back in to research problem Critical statistic (e.g. z or t or F or r) value? MS Within MS Between F = Still, difference between means Still, variability of curve(s)
Sum of squares (SS): The sum of squared deviations of some set of scores about their mean Mean squares (MS): The sum of squares divided by its degrees of freedom Mean square within groups: sum of squares within groups divided by its degrees of freedom Mean square between groups: sum of squares between groups divided by its degrees of freedom Mean square total: sum of squares total divided by its degrees of freedom MS Within MS Between F =
Writing Assignment - Quiz 1. When do you use a t-test and when do you use an ANOVA 2. What is the formula for degrees of freedom in a two-sample t-test 3. What is the formula for degrees of freedom “between groups” in ANOVA 4. What is the formula for degrees of freedom “within groups” in ANOVA 8. Draw and match each with proper label Between Group Variability Within Group Variability Total Variability 5. Daphne compared running speed for three types of running shoes What is the independent variable? What is the dependent variable? How many factors do we have (what are they)? How many treatments do we have (what are they)? 6. How are “levels”, “groups”, “conditions” “treatments” related? 7. How are “significant difference”, “p< 0.05”, “we reject the null”, and “we found a main effect” related?
Writing assignment worksheet Propose an experiment that would consist of one independent variable (IV) and one dependent variable (DV). The IV should have three groups (or more). The design should be appropriate for an analysis that uses an ANOVA 1.What is your question / What is your prediction 2.What is your IV 3.How many levels does it have 4.What are the levels 5.What is your DV 6.How many subjects do you think you can gather data on? 7.Sketch a bar graph of your predicted results
Extra Credit - Due November 24 th - There are five parts 1. A one page report of your design (includes all of the information from the writing assignment) Describe your experiment: what is your question / what is your prediction? State your Independent Variable (IV), how many levels there are, and the operational definition State your Dependent Variable (DV), and operational definition How many participants did you measure, and how did you recruit (sample) them Was this a between or within participant design (why?) 2. Gather the data Try to get at least 10 people (or data points) per level If you are working with other students in the class you should have 10 data points per level for each member of your group 3. Input data into Excel (hand in data) 4. Complete ANOVA analysis hand in ANOVA table 5. Statement of results (see next slide for example) and include a graph of your means (just like we did in the homework)
The average number of cookies sold for three different incentives were compared. The mean number of cookie boxes sold for the “Hawaii” incentive was 14, the mean number of cookies boxes sold for the “Bicycle” incentive was 12, and the mean number of cookies sold for the “No” incentive was 10. An ANOVA was conducted and there appears to be no significant difference in the number of cookies sold as a result of the different levels of incentive F(2, 12) = 2.73; n.s. How to report the findings for an ANOVA One paragraph summary of this study. Describe the IV & DV, and present the means, which type of test was conducted, and the statistical results. Start summary with two means (based on DV) for two levels of the IV Describe type of test (t-test versus anova) with brief overview of results Type of test with degrees of freedom Value of observed statistic p<0.05 = “significant”