Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2018 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. Welcome 4/2/18

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Before next exam (April 6th) Schedule of readings Before next exam (April 6th) Please read chapters 1 - 11 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 Study guide now online

Lab sessions Project 3 Due this week at beginning of lab

Homework #23 Postponed until Wednesday

Let’s do another one Test to see whether there is a difference in the number of units taken by 5 different majors: Geography, Sociology, Nutrition, Communication and Criminal Justice. We measured 60 students (12 students per major)

Writing Assignment – ANOVA – Part Three 1. Complete this ANOVA table 2. Find the critical F value from the table 3. Is there a main effect of major on number of units taken? 4. Is “p< 0.05”? SS df = MS ANOVA table Source SS df MS F 5. Write a summary statement of findings (all three parts) Between 218.23 ? ? ? Within 759.42 ? ? Total 977.65 ?

Degrees of Freedom Between Degrees of Freedom Within (always “round down”)

Writing Assignment – ANOVA – Another Example 1. Complete this ANOVA table 2. Find the critical F value from the table 3. Is there a main effect of major on number of units taken? 4. Is “p< 0.05”? SS df = MS ANOVA table Source SS df MS F 5. Write a summary statement of findings (all three parts) Between 218.23 4 54.56 3.95 Within 759.42 55 13.81 Total 977.65 59

Make decision whether or not to reject null hypothesis Observed F(4,55) = 3.95 Critical F(4,55) = 2.56 3.9 is larger than our critical of 2.56 so, we do reject the null hypothesis Observed F(4,55) = 3.95 Conclusion: There appears to be a main effect of type of major on number of units taken in school The average number of units taken by Geography, Sociology, Nutrition, Communication and Criminal Justice majors are 11.92, 12.50, 8.08, 12.17 and 8.58 respectively. An ANOVA was conducted and there appears to be a main effect of the number of units taken as a result of the different majors. F(4,55) = 3.95; p < 0.05

Let’s do similar problem Using MS Excel Test to see whether there is a difference in the number of units taken by 5 different majors: Geography, Sociology, Nutrition, Communication and Criminal Justice. We measured 60 students (12 students per major)

Let’s do similar problem Using MS Excel Test to see whether there is a difference in the number of units taken by 5 different majors: Geography, Sociology, Nutrition, Communication and Criminal Justice. We measured 60 students (12 students per major)

Let’s do similar problem Using MS Excel Test to see whether there is a difference in the number of units taken by 5 different majors: Geography, Sociology, Nutrition, Communication and Criminal Justice. We measured 60 students (12 students per major)

Let’s do similar problem Using MS Excel Test to see whether there is a difference in the number of units taken by 5 different majors: Geography, Sociology, Nutrition, Communication and Criminal Justice. We measured 60 students (12 students per major) SSbetween dfbetween 218 4 =55 MSbetween MSwithin “Sum of Squares” # groups - 1 55 13.8 =3.95 5-1=4 # scores - # of groups 759 55 =13.8 SSwithin dfwithin 60 – 5 = 55 # scores - 1 60-1=59

The average number of units taken by Geography, Sociology, Nutrition, Communication and Criminal Justice majors are 11.92, 12.50, 8.08, 12.17 and 8.58 respectively. An ANOVA was conducted and there appears to be a main effect of the number of units taken as a result of the different majors. F(4,55) = 3.95; p < 0.05

Hand in your writing assignment

In a one-way ANOVA we have three types of variability. Let’s try one In a one-way ANOVA we have three types of variability. Which picture best depicts the random error variability (also known as the within variability)? a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above 1. correct 2. 3.

In a one-way ANOVA we have three types of variability. Let’s try one In a one-way ANOVA we have three types of variability. Which picture best depicts the between group variability? a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above correct 1. 2. 3.

Which figure would depict the largest F ratio a. Figure 1 b. Figure 2 Variability between groups F = Let’s try one Variability within groups “F ratio” is referring to "observed F” Which figure would depict the largest F ratio a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above correct 1. 2. 3.

Winnie found an observed F ratio of .9, what should she conclude? Let’s try one Winnie found an observed F ratio of .9, what should she conclude? a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given correct 1. 2. 3.

Winnie found an observed z of .74, what should she conclude? If your observed z is within one standard deviation of the mean, you will never reject the null Let’s try one Winnie found an observed z of .74, what should she conclude? (Hint: notice that .74 is less than 1) a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given correct x x small observed z score small observed z score

Winnie found an observed t of .04, what should she conclude? Let’s try one Winnie found an observed t of .04, what should she conclude? (Hint: notice that .04 is less than 1) a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given correct x small observed t score

F(4, 25) = 3.12; p < 0.05 Let’s try one How many observations within each group? Let’s try one An ANOVA was conducted comparing different types of solar cells and there appears to be a significant difference in output of each (watts) F(4, 25) = 3.12; p < 0.05. In this study there were __ types of solar cells and __ total observations in the whole study? a. 4; 25 b. 5; 30 c. 4; 30 d. 5; 25 F(4, 25) = 3.12; p < 0.05 correct # groups - 1 # scores - # of groups # scores - 1

F(4, 25) = 3.12; p < 0.05 Let’s try one An ANOVA was conducted comparing different types of solar cells and there appears to be significant difference in output of each (watts) F(4, 25) = 3.12; p < 0.05. In this study ___ a. we rejected the null hypothesis b. we did not reject the null hypothesis correct F(4, 25) = 3.12; p < 0.05 Observed F bigger than Critical F p < .05

F(4, 25) = 3.12; p < 0.05 Let’s try one An ANOVA was conducted comparing different types of solar cells. The analysis was completed using an alpha of 0.05. But Julia now wants to know if she can reject the null with an alpha of at 0.01. In this study ___ a. we rejected the null hypothesis b. we did not reject the null hypothesis correct F(4, 25) = 3.12; p < 0.05 Comparison of the Observed F and Critical F Is no longer are helpful because the critical F is no longer correct. We must use the p value p < .05 p > .01

Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) . For each neighborhood we measured the price of four homes. Please complete this ANOVA table. Degrees of freedom between is _____; degrees of freedom within is ____ a. 16; 4 b. 4; 16 c. 12; 3 d. 3; 12 correct .

Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) . For each neighborhood we measured the price of four homes. Please complete this ANOVA table. Mean Square between is _____; Mean Square within is ____ a. 300, 300 b. 100, 100 c. 100, 25 d. 25, 100 correct .

Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) . For each neighborhood we measured the price of four homes. Please complete this ANOVA table. The F ratio is: a. .25 b. 1 c. 4 d. 25 correct .

a. reject the null hypothesis b. not reject the null hypothesis Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) . For each neighborhood we measured the price of four homes. Please complete this ANOVA table, alpha = 0.05. We should: a. reject the null hypothesis b. not reject the null hypothesis correct Observed F bigger than Critical F p < .05

Thank you! See you next time!!