Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2016 Room 150 Harvill Building 10:00 - 10:50 Mondays, Wednesdays & Fridays. Welcome http://today.msnbc.msn.com/id/33411196/ns/today-today_health/ http://www.youtube.com/watch?v=0r7NXEWpheg

Homework Assignments Homework Assignment #20 Hypothesis testing Comparing Two means (Two samples) Due Monday November 7th

Before next exam (November 18th) 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

Lab sessions Everyone will want to be enrolled in one of the lab sessions Labs continue Next week Project 3 due & Start Project 4

This lab builds on the work we did in our very first lab This lab builds on the work we did in our very first lab. But now we are using the correlation for prediction. This is called regression analysis

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)? Critical statistic (e.g. z or t) value? Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed z (or t) is bigger then critical z (or t) then reject null Step 5: Conclusion - tie findings back in to research problem

Hypothesis testing with t-tests The result is “statistically significant” if: the observed statistic is larger than the critical statistic observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x2) to be big!! the p value is less than 0.05 (which is our alpha) p < 0.05 If we want to reject the null, we want our “p” to be small!! we reject the null hypothesis then we have support for our alternative hypothesis

Independent samples t-test Are the two means significantly different from each other, or is the difference just due to chance? Independent samples t-test Donald is a consultant and leads training sessions. As part of his training sessions, he provides the students with breakfast. He has noticed that when he provides a full breakfast people seem to learn better than when he provides just a small meal (donuts and muffins). So, he put his hunch to the test. He had two classes, both with three people enrolled. The one group was given a big meal and the other group was given only a small meal. He then compared their test performance at the end of the day. Please test with an alpha = .05 Big Meal 22 25 Small meal 19 23 21 Mean= 21 Mean= 24 x1 – x2 t = 24 – 21 variability t = Got to figure this part out: We want to average the variance from 2 samples - Call it “pooled” variability 11

α = .05 Independent samples t-test Step 1: Identify the research problem Did the size of the meal affect the learning / test scores? Step 2: Describe the null and alternative hypotheses Step 3: Decision rule α = .05 Two tailed test n1 = 3; n2 = 3 Degrees of freedom total (df total) = (n1 - 1) + (n2 – 1) Critical t(4) = 2.776 = (3 - 1) + (3 – 1) = 4 12

α = .05 Independent samples t-test Step 1: Identify the research problem Did the size of the meal affect the learning / test scores? Step 2: Describe the null and alternative hypotheses Step 3: Decision rule α = .05 Two tailed test n1 = 3; n2 = 3 Degrees of freedom total (df total) = (n1 - 1) + (n2 – 1) Critical t(4) = 2.776 = (3 - 1) + (3 – 1) = 4 Step 4: Calculate observed t score 13

Notice: Simple Average = 3.5 Mean= 21 Mean= 24 Big Meal Deviation From mean -2 1 Small Meal Deviation From mean -2 2 Squared deviation 4 1 Squared Deviation 4 Big Meal 22 25 Small meal 19 23 21 Σ = 6 Σ = 8 6 3 Notice: s2 = 3.0 1 2 1 Notice: Simple Average = 3.5 8 4 Notice: s2 = 4.0 2 2 2 S2pooled = (n1 – 1) s12 + (n2 – 1) s22 n1 + n2 - 2 S2pooled = (3 – 1) (3) + (3 – 1) (4) 31 + 32 - 2 = 3.5 14

S2p = 3.5 Mean= 21 Mean= 24 Big Meal Deviation From mean -2 1 Small Meal Deviation From mean -2 2 Squared deviation 4 1 Squared Deviation 4 Participant 1 2 3 Big Meal 22 25 Small meal 19 23 21 Σ = 6 Σ = 8 = 24 – 21 1.5275 24 - 21 = 1.964 3.5 3.5 3 3 Observed t Observed t = 1.964 Critical t = 2.776 1.964 is not larger than 2.776 so, we do not reject the null hypothesis t(4) = 1.964; n.s. Conclusion: There appears to be no difference between the groups 15

Type of test with degrees of freedom Value of observed statistic We compared test scores for large and small meals. The mean test scores for the big meal was 24, and was 21 for the small meal. A t-test was calculated and there appears to be no significant difference in test scores between the two types of meals, t(4) = 1.964; n.s. Type of test with degrees of freedom n.s. = “not significant” p<0.05 = “significant” Value of observed statistic Start summary with two means (based on DV) for two levels of the IV Finish with statistical summary t(4) = 1.96; ns Describe type of test (t-test versus anova) with brief overview of results Or if it *were* significant: t(9) = 3.93; p < 0.05 16

Homework Assignment Using Excel ?

Homework Assignment Using Excel

Complete a t-test Mean= 21 Mean= 24 Participant 1 2 3 Big Meal 22 25 Small meal 19 23 21 19

Complete a t-test Mean= 21 Mean= 24 Participant 1 2 3 Big Meal 22 25 Small meal 19 23 21 20

Complete a t-test Mean= 21 Mean= 24 Participant 1 2 3 Big Meal 22 25 Small meal 19 23 21 If checked you’ll want to include the labels in your variable range If checked, you’ll want to include the labels in your variable range If checked you’ll want to include the labels in your variable range 21

Complete a t-test Finding Means Finding Means 22

Complete a t-test This is variance for each sample (Remember, variance is just standard deviation squared) Please note: “Pooled variance” is just like the average of the two sample variances, so notice that the average of 3 and 4 is 3.5 23

Complete a t-test This is “n” for each sample (Remember, “n” is just number of observations for each sample) This is “n” for each sample (Remember, “n” is just number of observations for each sample) Remember, “degrees of freedom” is just (n-1) for each sample. So for sample 1: n-1 =3-1 = 2 And for sample 2: n-1=2-1 = 2 Then, df = 2+2=4 df = “degrees of freedom” 24

Finding degrees of freedom Complete a t-test Finding degrees of freedom 25

Complete a t-test Finding Observed t 26

Complete a t-test Finding Critical t 27

Finding Critical t 28

Finding p value (Is it less than .05?) Complete a t-test Finding p value (Is it less than .05?) 29

Step 4: Make decision whether or not to reject null hypothesis Complete a t-test Step 4: Make decision whether or not to reject null hypothesis Reject when: observed stat > critical stat 1.96396 is not bigger than 2.776 “p” is less than 0.05 (or whatever alpha is) p = 0.121 is not less than 0.05 Step 5: Conclusion - tie findings back in to research problem There was no significant difference, there is no evidence that size of meal affected test scores 30

Type of test with degrees of freedom Value of observed statistic We compared test scores for large and small meals. The mean test scores for the big meal was 24, and was 21 for the small meal. A t-test was calculated and there appears to be no significant difference in test scores between the two types of meals, t(4) = 1.964; n.s. Type of test with degrees of freedom n.s. = “not significant” p<0.05 = “significant” Value of observed statistic Start summary with two means (based on DV) for two levels of the IV Finish with statistical summary t(4) = 1.96; ns Describe type of test (t-test versus Anova) with brief overview of results Or if it *were* significant: t(9) = 3.93; p < 0.05 31

Graphing your t-test results 32

Graphing your t-test results 33

Graphing your t-test results Chart Layout 34

Fill out titles 35

Thank you! See you next time!!