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

Homework due – Wednesday (November 5 th ) On class website: Please print and complete homework worksheet #18 Using Excel for hypothesis testing with t-tests

Labs continue this week with Project 2

By the end of lecture today 11/3/14 Use this as your study guide Logic of hypothesis testing Steps for hypothesis testing Levels of significance (Levels of alpha) Hypothesis testing with t-scores (two independent samples) Constructing brief, complete summary statements Using Excel for completing t-tests

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 z (or t) is bigger then critical z (or t) then reject null Step 5: Conclusion - tie findings back in to research problem One or two tailed test? Balance between Type I versus Type II error Critical statistic (e.g. z or t or F or r) value? We lose one degree of freedom for every parameter we estimate Review

.. A note on z scores, and t score: Difference between means Variability of curve(s) Difference between means Numerator is always distance between means (how far away the distributions are) Denominator is always measure of variability (how wide or much overlap there is between distributions) Variability of curve(s) Review

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 Small meal Mean= 24 Mean= 21 t = x 1 – x 2 variability t = 24 – 21 variability Got to figure this part out: We want to average from 2 samples - Call it “pooled” Review

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 What if we ran more subjects? Big Meal Small meal Mean= 24 Mean= 21 Review

We compared test scores for large and small meals. The mean test score for the big meal was 24, and was 21 for the small meal. A t-test was calculated and there was a significant difference in test scores between the two types of meals t(16) = 3.928; p < 0.05 Let’s run more subjects using our excel! Review

What happened? We ran more subjects: Increased n So, we decreased variability Easier to find effect significant even though effect size didn’t change Big sampleSmall sample This is the sample size

What happened? We ran more subjects: Increased n So, we decreased variability Easier to find effect significant even though effect size didn’t change Big sampleSmall sample This is variance for each sample (Remember, variance is just standard deviation squared) This is variance for each sample (Remember, variance is just standard deviation squared)

Another format option Independent samples t-test Big Meal versus Small Meal Will use the sort function

Another format option Independent samples t-test Big Meal versus Small Meal Will use the sort function

Independent samples t-test Male versus Female Students Another format option Will use the sort function

Independent samples t-test Male versus Female Students Another format option Will use the sort function

The mean test score for female participants was 22.2, while the mean test score for male participants was A t-test was completed and there appears to be no significant difference in the test scores as a function of gender, t(16) = ; n.s. Type of test with degrees of freedom Value of observed statistic n.s. = “not significant” p<0.05 = “significant”

One paragraph summary of this study. Describe the IV & DV. Present the two means, which type of test was conducted, and the statistical results. We compared productivity for men and women. The mean productivity level for men was 3.65 and the mean productivity for women was A t-test was calculated and there appears to be a significant difference in productivity between the two groups t(298) = 3.64; p < 0.05 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” Sample size150150

If this is less than.05 (or whatever alpha is) it is significant, and we the reject null df = (n 1 – 1) + (n 2 – 1) = ( ) + (120 -1) = 283

A survey was conducted to see whether men or women superintendents make more money 1.The independent variable is ________________ 2.The dependent variable is _________________ 3. Who made more money men or women? 4. Identify the two means and the observed t score 5. Identify the p value and state whether it is less than.05

A survey was conducted to see whether men or women superintendents make more money E-05 Equals zeros E-06 Equals zeros Are both p values less than 0.05?

A survey was conducted to see whether men or women superintendents make more money E-05 Equals zeros E-06 Equals zeros A note on scientific notation: “E-05” means move the decimal to the left 5 places E-06” means move the decimal to the left 6 places

A survey was conducted to see whether men or women superintendents make more money. The independent variable is a. nominal level of measurement b. ordinal level of measurement c. interval level of measurement d. ratio level of measurement correct

A survey was conducted to see whether men or women superintendents make more money. The dependent variable is a. nominal level of measurement b. ordinal level of measurement c. interval level of measurement d. ratio level of measurement correct

A survey was conducted to see whether men or women superintendents make more money. The independent variable is a. continuous and qualitative b. continuous and quantitative c. discrete and qualitative d. discrete and quantitative correct

A survey was conducted to see whether men or women superintendents make more money. The dependent variable is a. continuous and qualitative b. continuous and quantitative c. discrete and qualitative d. discrete and quantitative correct

A survey was conducted to see whether men or women superintendents make more money. This is a a. quasi, between subject design b. quasi, within subject design c. true, between subject design d. true, within subject design correct

A survey was conducted to see whether men or women superintendents make more money. This is a a. one-tailed test b. two-tailed test c. three-tailed test d. not enough information correct

A survey was conducted to see whether men or women superintendents make more money. The null hypothesis is a. men make more money b. women make more money c. no difference between amount of money made d. there is a difference between the amount of money made correct

A survey was conducted to see whether men or women superintendents make more money. If the null hypothesis was rejected we will conclude that a. men make more money b. women make more money c.no difference between amount of money made d. there is a difference between the amount of money made correct

A survey was conducted to see whether men or women superintendents make more money. A Type I error would be a. claiming men make more money, when they don’t b. claiming women make more money, when they don’t c.claiming no difference between amount of money made, when there is a difference d. claiming there is a difference between the amount of money made, when there is no difference correct

A survey was conducted to see whether men or women superintendents make more money. A Type II error would be a. claiming men make more money, when they don’t b. claiming women make more money, when they don’t c.claiming no difference between amount of money made, when there is a difference d. claiming there is a difference between the amount of money made, when there is no difference correct

An t-test was conducted, there were ___ men in the study and ___ women. a. 18; 21 b. 21; 18 c. 19; 19 d. 38; 38 Let’s try one correct

A t-test was conducted, which of the following best describes the results: a. t(37) = 2.02; p < 0.05 b. t(21) = 2.02; n.s. c. t(37) = 5.0; p < 0.05 d. t(21) = 5.0; n.s Let’s try one correct

A t-test was conducted, with a two tail test was there a significant difference? a. No, because 5.0 is not bigger than 6.89 b. Yes, because 5.0 is bigger than c. Yes, because 5.0 is bigger than 1.37 d. Yes, because 5.0 is bigger than 2.02 Let’s try one correct

Which is true a. p < 0.05 b. p < 0.01 c. p < d. All of the above Let’s try one correct

A survey was conducted to see whether women superintendents make more money than men. This is a a. one-tailed test b. two-tailed test c. three-tailed test d. not enough information Note the change in the problem correct

A survey was conducted to see whether women superintendents make more money than men. A t-test was conducted, which of the following best describes the results: Note the results were in the unpredicted direction a. reject the null b. do not reject the null c. not enough information Let’s try one correct

A survey was conducted to see whether women superintendents make more money than men. A t-test was conducted, which of the following best describes the results: Note the results were in the unpredicted direction a. t(21) = 2.02; p < 0.05 b. t(21) = 2.02; n.s. c. t(37) = 5.0; p < 0.05 d. t(37) = 5.0; n.s Let’s try one correct

Is there a difference in mpg between these two cars There is no difference in mpg between these two cars There is a difference in mpg between these two cars

2-tail

α =.05 (df) = 18 Critical t (18) = two tail test

2-tail S 2 pooled = (n 1 – 1) s (n 2 – 1) s 2 2 n 1 + n =.82 S 2 pooled = (10 – 1) (.80) 2 + (10 – 1) (1) = t = 17 – / /10 =

Yes There is a difference There is no difference there is no difference there is a difference

The average mpg is 18.5 for the Ford Explorer and 17.0 for the Expedition. A t-test was conducted and found this difference to be significantly different, t(18) = 3.70; p < 0.05 Expedition Explorer Type of Car Miles per gallon

. Homework Is there an increase in foot size from 1960 to 1980 Is there no difference (or a decrease) in foot size from 1960 to 1980 There is an increase in foot size from 1960 to tail

α =.05 (df) = 22 Critical t (22) = one tail test

. Homework Yes =.6201 =.4502 =.2936 S 2 pooled = (12 – 1) (.6201) 2 + (12 – 1) (4502) = 2.26 t = – / /12 = Yes The average foot size for women in 1960 is 7.7, while the average foot size for women in 1980 is 8.2. A t-test was conducted and found that the increase in foot size is statistically significant, t(22) = 2.26; p < 0.05

Year of birth Shoe Size Homework

. Homework – same problem using excel The average foot size for women in 1960 is 7.7, while the average foot size for women in 1980 is 8.2. A t-test was conducted and found that the increase in foot size is statistically significant, t(22) = 2.26; p < 0.05 Shoe Size 1-tail Yes Year of Birth