Introduction to Statistics for the Social Sciences SBS
Introduction to Statistics for the Social Sciences SBS 200 - Lecture Section 001, Fall 2018 Room 150 Harvill Building 10: 00 - 10: 50 Mondays, Wednesdays & Fridays. 11/2/18
The Gre e She n ets
Schedule of readings Before next exam (November 16 th) Please read chapters 1 - 11 in Open. Stax textbook Please read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence
ek e W s 3 i h t T ojec Pr
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
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
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 Dependent variable is always quantitative Sales per Girl scout 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 None New Bike Trip Hawaii In an ANOVA, independent variable is qualitative (& more than two groups)
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 Total Number of Boxes Sold Sales per Girl scout This is an ANOVA This is an Chi Square None New Bike These are means Trip Hawaii New Trip Bike Hawaii These are just frequencies None
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
. A note on variance, sample size and effect size . Variability of curve(s) Within Groups
. A note on variance, sample size and effect size Difference between means Variability of curve(s) Between. Groups
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 The three primary differences Tells us generally Tells us between generally t-tests and ANOVAS are: Tells us generally about number of 1. ANOVAs can test more than two about number of means about number of participants / 2. We are comparing sample means groups / levels of IV indirectly by participants / observations comparing sample variances observations 3. We now will have two types of degrees of freedom t(16) = 3. 0; p < 0. 05 F(2, 15) = 3. 0; p < 0. 05
Difference between groups Remember, one-way = one IV One way analysis of variance Variance is divided Differences within groups Total variability Between group variability (only one factor) Remember, 1 factor = 1 independent variable (this will be our numerator – like difference between means) Within group variability (error variance) Remember, error variance = random error (this will be our denominator – like within group variability
ANOVA: Analysis of Variance Between groups Within groups Total Between Groups Variability Total Variability Within Groups Variability F= Variability between groups Variability within groups
ANOVA: Analysis of Variance F= Variability between groups Variability within groups Variability Between Groups “Between” variability bigger than “within” variability so should get a big (significant) F Variability Within Groups Variability Between Groups “Between” variability getting smaller “within” variability staying same so, should get a smaller F Variability Within Groups Variability Between Groups “Between” variability getting very small “within” variability staying same so, should get a very small F Variability Within Groups
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 Dependent 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 n=5 x = 10 n=5 x = 12 n=5 x = 14 What is Independent Variable? How many groups?
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 We don’t know which means are different from which …. just that they are not all the same To get an effect we want: • Large “F” - big effect and small variability • Small “p” - less than 0. 05 (whatever our alpha is)
ANOVA: Analysis of Variance Hypothesis testing: 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
ANOVA: Analysis of Variance Hypothesis testing: Decision rule =. 05 Degrees of freedom (between) = number of groups - 1 =3 -1=2 Degrees of freedom (within) = # of scores - # of groups = (15 -3) = 12* Critical F (2, 12) = 3. 98 *or = (5 -1) + (5 -1) = 12.
Critical F Scores F (2, 12) α=. 05 Critical F(2, 12) = 3. 89
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 SS df MS F Between Within Total ? ? ? ?
ANOVA: Analysis of Variance ANOVA table Source Between Within Total SS df MS F 40 88 128 ? ? ? ? Please complete this table
ANOVA: Analysis of Variance “SS” = “Sum of Squares” - will be given for exams Source Between Within Total ANOVA table SS df 40 ? 88 ? ? 128 ? 2 ? 14 MS F # ? groups - 1 ? 3 -1=2 15 -3=12 # scores - number of groups ? # scores - 1 15 - 1=14
ANOVA: Analysis of Variance ANOVA table 40 SSbetween 2 ANOVA df table between Source Between Within Total SS df 40 88 128 2 12 MS 20 ? ? 7. 33 14 88 SSwithin 12 dfwithin 40 =20 2 F ? 2. 73 88 =7. 33 12 MSbetween MSwithin 20 =2. 73 7. 33
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.
Writing Assignment
- Slides: 28