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Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2018 Room 150 Harvill Building 10:00 - 10:50 Mondays, Wednesdays.

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Presentation on theme: "Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2018 Room 150 Harvill Building 10:00 - 10:50 Mondays, Wednesdays."— Presentation transcript:

1 Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2018 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays. Welcome 11/2/18

2 .. The Green Sheets

3 Before next exam (November 16th)
Schedule of readings Before next exam (November 16th) Please read chapters in OpenStax textbook Please read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

4 Lab sessions This Week Project 3

5

6 Study Type 3: One-way Analysis of Variance (ANOVA)
We are looking to compare two means Study Type 2: t-test Study Type 3: One-way Analysis of Variance (ANOVA) Comparing more than two means

7 Study Type: One-way ANOVA
Single Independent Variable comparing more than two groups Single Dependent Variable (numerical/continuous) Used to test the effect of the IV on the DV Ian was interested in the effect of incentives for girl scouts on the number of cookies sold. He randomly assigned girl scouts into one of three groups. The three groups were given one of three incentives and looked to see who sold more cookies. The 3 incentives were 1) Trip to Hawaii, 2) New Bike or 3) Nothing. This is an example of a true experiment How could we make this a quasi-experiment? Independent Variable: Type of incentive Levels of Independent Variable: None, Bike, Trip to Hawaii Dependent Variable: Number of cookies sold Levels of Dependent Variable: 1, 2, 3 up to max sold Between participant design Causal relationship: Incentive had an effect – it increased sales

8 Study Type: One-way ANOVA
Single Independent Variable comparing more than two groups Single Dependent Variable (numerical/continuous) Used to test the effect of the IV on the DV Ian was interested in the effect of incentives for girl scouts on the number of cookies sold. He randomly assigned girl scouts into one of three groups. The three groups were given one of three incentives and looked to see who sold more cookies. The 3 incentives were 1) Trip to Hawaii, 2) New Bike or 3) Nothing. This is an example of a true experiment Sales per Girl scout Sales per Girl scout None New Bike Trip Hawaii None New Bike Trip Hawaii Dependent variable is always quantitative In an ANOVA, independent variable is qualitative (& more than two groups)

9 One-way ANOVA versus Chi Square
Be careful you are not designing a Chi Square If this is just frequency you may have a problem This is an Chi Square Total Number of Boxes Sold Sales per Girl scout This is an ANOVA None New Bike Trip Hawaii None New Bike Trip Hawaii These are just frequencies These are just frequencies These are just frequencies These are means These are means These are means

10 Study Type: One-way ANOVA
Number of cookies sold None Bike Hawaii trip Incentives One-way ANOVAs test only one independent variable - although there may be many levels “Factor” = one independent variable “Level” = levels of the independent variable treatment condition groups “Main Effect” of independent variable = difference between levels Note: doesn’t tell you which specific levels (means) differ from each other A multi-factor experiment would be a multi-independent variables experiment

11 sample size and effect size .
A note on variance, sample size and effect size . Variability of curve(s) Variability of curve(s) Variability of curve(s) Within Groups

12 sample size and effect size Difference between means
Groups . A note on variance, sample size and effect size Difference between means Difference between means Difference between means . Variability of curve(s) Variability of curve(s) Variability of curve(s)

13 Comparing ANOVAs with t-tests
Similarities still include: Using distributions to make decisions about common and rare events Using distributions to make inferences about whether to reject the null hypothesis or not The same 5 steps for testing an hypothesis Tells us generally about number of participants / observations Tells us generally about number of groups / levels of IV The three primary differences between t-tests and ANOVAS are: 1. ANOVAs can test more than two means 2. We are comparing sample means indirectly by comparing sample variances 3. We now will have two types of degrees of freedom t(16) = 3.0; p < F(2, 15) = 3.0; p < 0.05 Tells us generally about number of participants / observations

14 One way analysis of variance Variance is divided
Difference between groups One way analysis of variance Variance is divided Remember, one-way = one IV Differences within groups Total variability Between group variability (only one factor) Within group variability (error variance) 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

15 ANOVA: Analysis of Variance Between groups Within groups Total
Between Groups Variability Total Variability Variability between groups F = Within Groups Variability Variability within groups 15

16 ANOVA: Analysis of Variance
Variability between groups F = Variability within groups Variability Between Groups “Between” variability bigger than “within” variability so should get a big (significant) F Variability Within Groups Variability Within Groups Variability Between Groups Variability Within Groups “Between” variability getting smaller “within” variability staying same so, should get a smaller F Variability Between Groups “Between” variability getting very small “within” variability staying same so, should get a very small F Variability Within Groups

17 ANOVA: Analysis of Variance
A girl scout troop leader wondered whether providing an incentive to whoever sold the most girl scout cookies would have an effect on the number cookies sold. She provided a big incentive to one troop (trip to Hawaii), a lesser incentive to a second troop (bicycle), and no incentive to a third group, and then looked to see who sold more cookies. How many levels of the Independent Variable? What is Independent Variable? Troop 1 (nada) 10 8 12 7 13 Troop 2 (bicycle) 12 14 10 11 13 Troop 3 (Hawaii) 14 9 19 13 15 What is Dependent Variable? How many groups? n = 5 x = 10 n = 5 x = 12 n = 5 x = 14

18 ANOVA: Analysis of Variance
Main effect of incentive: Will offering an incentive result in more girl scout cookies being sold? If we have a “effect” of incentive then the means are significantly different from each other we reject the null we have a significant F p < 0.05 To get an effect we want: Large “F” - big effect and small variability Small “p” - less than 0.05 (whatever our alpha is) We don’t know which means are different from which …. just that they are not all the same 18

19 Hypothesis testing: ANOVA: Analysis of Variance
Step 1: Identify the research problem Is there a significant difference in the number of cookie boxes sold between the girlscout troops that were given the different levels of incentive? Describe the null and alternative hypotheses

20 Hypothesis testing: ANOVA: Analysis of Variance Decision rule = .05
Degrees of freedom (between) = number of groups - 1 = = 2 Degrees of freedom (within) = # of scores - # of groups = (15-3) = 12* Critical F (2,12) = 3.98 *or = (5-1) + (5-1) + (5-1) = 12.

21 Critical F Scores F (2,12) α= .05 Critical F(2,12) = 3.89 21

22 ANOVA: Analysis of Variance
“SS” = “Sum of Squares” - will be given for exams - you can think of this as the numerator in a standard deviation formula ANOVA table Source df MS F SS Between ? ? ? ? Within ? ? ? Total ? ?

23 Please complete this table
ANOVA: Analysis of Variance ANOVA table Source df MS F SS Between 40 ? ? ? Within 88 ? ? Total 128 ? Please complete this table

24 ANOVA: Analysis of Variance
“SS” = “Sum of Squares” - will be given for exams ANOVA table Source df MS F SS 3-1=2 Between 40 ? 2 # groups - 1 ? ? ? 15-3=12 Within ? 88 12 ? # scores - number of groups ? Total 128 ? ? 14 # scores - 1 15- 1=14

25 ANOVA table ANOVA: Analysis of Variance SSbetween dfbetween 40 2 40 2
=20 MSbetween MSwithin ANOVA table Source df F SS MS 20 7.33 =2.73 Between 40 2 20 ? ? 2.73 Within 88 12 7.33 ? Total 128 14 SSwithin dfwithin 88 12 =7.33 88 12

26 ANOVA: Analysis of Variance
Make decision whether or not to reject null hypothesis Observed F(2,12) = 2.73 Critical F(2,12) = 3.89 2.73 is not farther out on the curve than 3.89 so, we do not reject the null hypothesis F(2,12) = 2.73; n.s. Conclusion: There appears to be no effect of type of incentive on number of girl scout cookies sold 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.

27 Writing Assignment

28 Thank you! See you next time!!

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