Screen Stage Lecturer’s desk Gallagher Theater Row A Row A Row A Row B 17 16 15 14 13 12 11 10 9 8 7 6 5 4 Row A 3 2 1 Row A Left handed Row B 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row B 4 3 2 1 Row B Row C 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row C 4 3 2 1 Row C Row D 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row D 4 3 2 1 Row D Row E 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row E 4 3 2 1 Row E Row F 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row F 4 3 2 1 Row F Row G 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row G 4 3 2 1 Row G Row H 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row H 4 3 2 1 Row H Row I 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row I 4 3 2 1 Row I Row J 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row J 4 3 2 1 Row J Row K 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row K 4 3 2 1 Row K Row L 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row L 4 3 2 1 Row L Row M 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row M 4 3 2 1 Row M Row N 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row N 4 3 2 1 Row N Row O 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row O 4 3 2 1 Row O Need Labels B5, E1, I16, J17, K8, M4, O1, P16 Row P 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row P 4 3 2 1 Row P Row Q 16 15 14 13 12 11 10 9 8 7 6 5 4 Row Q 3 2 1 Row Q Row R Gallagher Theater 4 3 2 Row R 26Left-Handed Desks A14, B16, B20, C19, D16, D20, E15, E19, F16, F20, G19, H16, H20, I15, J16, J20, K19, L16, L20, M15, M19, N16, P20, Q13, Q16, S4 5 Broken Desks B9, E12, G9, H3, M17 Row S 10 9 8 7 4 3 2 1 Row S
Screen Stage Social Sciences 100 Lecturer’s desk broken desk R/L handed Row A 17 16 15 14 13 12 Row B 27 26 25 24 23 Row B 22 21 20 19 18 17 16 15 14 13 12 11 10 Row C 28 27 26 25 24 23 Row C 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 Row C Row D 30 29 28 27 26 25 24 23 Row D 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 Row D Row E 31 30 29 28 27 26 25 24 23 Row E 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row E Row F 31 30 29 28 27 26 25 24 23 Row F 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row F Row G 31 30 29 28 27 26 25 24 23 Row G 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row G Row H 31 30 29 28 27 26 25 24 23 Row H 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row H Row I 31 30 29 28 27 26 25 24 23 Row I 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row I Row J 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row J Row J 31 30 29 28 27 26 25 24 23 23 Row K 22 13 12 11 10 9 8 7 6 5 2 1 Row K 31 30 29 28 27 26 25 24 21 20 19 18 17 16 15 14 4 3 Row K Row L 31 30 29 28 27 26 25 24 23 Row L 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row L Row M 31 30 29 28 27 26 25 24 23 Row M 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row M Row N 31 30 29 28 27 26 25 24 23 Row N 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row N Row O 31 30 29 28 27 26 25 24 23 Row O 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row O 23 Row P 9 8 7 6 5 4 3 2 1 Row P 31 30 29 28 27 26 25 24 22 21 20 19 18 17 16 15 14 13 12 11 10 Row P Row Q 31 30 29 28 27 26 25 24 23 Row Q 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row Q Row R 31 30 29 28 27 26 25 24 23 Row R 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row R table broken desk 9 8 7 6 5 4 3 2 1 Projection Booth
MGMT 276: Statistical Inference in Management Fall, 2014 Welcome Green sheets
Exam 2 – Thanks for your patience and cooperation The grades are posted on D2L
Reminder A note on doodling Talking or whispering to your neighbor can be a problem for us – please consider writing short notes.
Schedule of readings Before our next exam (November 6th) Lind (10 – 12) Chapter 10: One sample Tests of Hypothesis Chapter 11: Two sample Tests of Hypothesis Chapter 12: Analysis of Variance Plous (2, 3, & 4) Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence
Homework On class website: Please print and complete homework worksheets Assignment 14: Hypothesis Testing using t-tests Due: Thursday, October 30th Assignments 15 & 16: Hypothesis Testing using t-tests Due: Tuesday, November 4th
By the end of lecture today 10/28/14 Use this as your study guide By the end of lecture today 10/28/14 Logic of hypothesis testing Steps for hypothesis testing Levels of significance (Levels of alpha) what does p < 0.05 mean? what does p < 0.01 mean? t-tests
Who is taller men or women? Type I or type II error? . Independent Variable? Gender Dependent Variable? Height IV: Nominal IV: Nominal Ordinal Interval or Ratio? Who is taller men or women? DV: Nominal Ordinal Interval or Ratio? DV: Ratio IV: Continuous or discrete? IV: Discrete What would null hypothesis be? DV: Continuous or discrete? DV: Continuous No difference in the height between men and women Section 2 only - Section 1 completed this last week
Who is taller men or women? . Type I or type II error? Two –tailed One-tailed Or Two –tailed? Between Between Or within? Who is taller men or women? Quasi Quasi or True? What would null hypothesis be? No difference in the height between men and women Section 2 only - Section 1 completed this last week
Who is taller men or women? Type I or type II error? . Who is taller men or women? What would null hypothesis be? No difference in the height between men and women Type I Error Type I error: Rejecting a true null hypothesis Saying that there is a difference in height when in fact there is not (false alarm) Type II error: Not rejecting a false null hypothesis Type II Error Saying there is no difference in height when in fact there is a difference (miss) This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA t-test Section 2 only - Section 1 completed this last week
Type I or type II error? . Curly versus straight hair – which is more “dateable”? What would null hypothesis be? No difference in the dateability between curly and straight hair Type I error: Rejecting a true null hypothesis Saying that there is a difference in dateability when in fact there is not (false alarm) Type II error: Not rejecting a false null hypothesis Saying there is no difference in dateability when in fact there is a difference (miss) This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA t-test Section 2 only - Section 1 completed this last week
Writing Assignment Please watch this video describing a series of t-tests What is the independent variable? How many different dependent variables did they use? (They would conduct a different t-test for every dependent variable) http://www.everydayresearchmethods.com/2011/09/curly-or-straight-.html Section 2 only - Section 1 completed this last week http://www.youtube.com/watch?v=z7kfiA2SXMY http://www.youtube.com/watch?v=n4WQhJHGQB4
Writing Assignment Worksheet Design two t-tests Section 2 only - Section 1 completed this last week http://www.youtube.com/watch?v=z7kfiA2SXMY http://www.youtube.com/watch?v=n4WQhJHGQB4
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)? 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? 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
We lose one degree of freedom for every parameter we estimate Degrees of Freedom Degrees of Freedom (d.f.) is a parameter based on the sample size that is used to determine the value of the t statistic. Degrees of freedom tell how many observations are used to calculate s, less the number of intermediate estimates used in the calculation.
Hypothesis testing: one sample t-test Let’s jump right in and do a t-test Hypothesis testing: one sample t-test Is the mean of my observed sample consistent with the known population mean or did it come from some other distribution? We are given the following problem: 800 students took a chemistry exam. Accidentally, 25 students got an additional ten minutes. Did this extra time make a significant difference in the scores? The average number correct by the large class was 74. The scores for the sample of 25 was Please note: In this example we are comparing our sample mean with the population mean (One-sample t-test) 76, 72, 78, 80, 73 70, 81, 75, 79, 76 77, 79, 81, 74, 62 95, 81, 69, 84, 76 75, 77, 74, 72, 75
µ = 74 µ Hypothesis testing Step 1: Identify the research problem / hypothesis Did the extra time given to this sample of students affect their chemistry test scores Describe the null and alternative hypotheses One tail or two tail test? Ho: µ = 74 µ = 74 H1:
Hypothesis testing n = 25 Step 2: Decision rule = .05 Degrees of freedom (df) = (n - 1) = (25 - 1) = 24 two tail test
two tail test α= .05 (df) = 24 Critical t(24) = 2.064
µ = 74 Hypothesis testing = = 868.16 = 6.01 24 x (x - x) (x - x)2 76 72 78 80 73 70 81 75 79 77 74 62 95 69 84 76 – 76.44 72 – 76.44 78 – 76.44 80 – 76.44 73 – 76.44 70 – 76.44 81 – 76.44 75 – 76.44 79 – 76.44 77 – 76.44 74 – 76.44 62 – 76.44 95 – 76.44 69 – 76.44 84 – 76.44 = -0.44 = -4.44 = +1.56 = + 3.56 = -3.44 = -6.44 = +4.56 = -1.44 = +2.56 = -0.44 = +0.56 = -2.44 = -14.44 = +18.56 = -7.44 = +7.56 0.1936 19.7136 2.4336 12.6736 11.8336 41.4736 20.7936 2.0736 6.5536 0.3136 5.9536 208.5136 344.4736 55.3536 57.1536 Step 3: Calculations µ = 74 Σx = N 1911 25 = = 76.44 N = 25 = 6.01 868.16 24 Σx = 1911 Σ(x- x) = 0 Σ(x- x)2 = 868.16
µ = 74 Hypothesis testing = 76.44 - 74 1.20 2.03 . Step 3: Calculations µ = 74 = 76.44 N = 25 s = 6.01 76.44 - 74 = 76.44 - 74 1.20 2.03 critical t 6.01 25 Observed t(24) = 2.03
Hypothesis testing Step 4: Make decision whether or not to reject null hypothesis Observed t(24) = 2.03 Critical t(24) = 2.064 2.03 is not farther out on the curve than 2.064, so, we do not reject the null hypothesis Step 6: Conclusion: The extra time did not have a significant effect on the scores
Hypothesis testing: Did the extra time given to these 25 students affect their average test score? Start summary with two means (based on DV) for two levels of the IV notice we are comparing a sample mean with a population mean: single sample t-test Finish with statistical summary t(24) = 2.03; ns Describe type of test (t-test versus z-test) with brief overview of results Or if it had been different results that *were* significant: t(24) = -5.71; p < 0.05 The mean score for those students who where given extra time was 76.44 percent correct, while the mean score for the rest of the class was only 74 percent correct. A t-test was completed and there appears to be no significant difference in the test scores for these two groups t(24) = 2.03; n.s. Type of test with degrees of freedom n.s. = “not significant” p<0.05 = “significant” n.s. = “not significant” p<0.05 = “significant” Value of observed statistic 25
What if we had chosen a one-tail test? Step 1: Identify the research problem Did the extra time given to this sample of students increase their chemistry test scores Prediction is uni-directional Describe the null and alternative hypotheses One tail or two tail test? Prediction is uni-directional Ho: µ ≤ 74 µ > 74 H1: Step 2: Decision rule α= .05 Degrees of freedom (df) = (n - 1) = (25 - 1) = 24 α is all at one end so “critical t” changes Critical t (24) = ?????
one tail test α= .05 (df) = 24 Critical t(24) = 1.711
What if we had chosen a one-tail test? Step 1: Identify the research problem Did the extra time given to this sample of students increase their chemistry test scores Describe the null and alternative hypotheses One tail or two tail test? Ho: µ ≤ 74 µ > 74 H1: Step 2: Decision rule = .05 Degrees of freedom (df) = (n - 1) = (25 - 1) = 24 Critical t (24) = 1.711
Calculations (exactly same as two-tail test) (x - x) (x - x)2 76 72 78 80 73 70 81 75 79 77 74 62 95 69 84 76 – 76.44 72 – 76.44 78 – 76.44 80 – 76.44 73 – 76.44 70 – 76.44 81 – 76.44 75 – 76.44 79 – 76.44 77 – 76.44 74 – 76.44 62 – 76.44 95 – 76.44 69 – 76.44 84 – 76.44 = -0.44 = -4.44 = +1.56 = + 3.56 = -3.44 = -6.44 = +4.56 = -1.44 = +2.56 = -0.44 = +0.56 = -2.44 = -14.44 = +18.56 = -7.44 = +7.56 0.1936 19.7136 2.4336 12.6736 11.8336 41.4736 20.7936 2.0736 6.5536 0.3136 5.9536 208.5136 344.4736 55.3536 57.1536 Step 3: Calculations µ = 74 Σx = N 1911 25 = = 76.44 N = 25 = 6.01 868.16 24 Σx = 1911 Σ(x- x) = 0 One-tailed test has no effect on calculations stage Σ(x- x)2 = 868.16
Calculations (exactly same as two-tail test) . One-tailed test has no effect on calculations stage Calculations (exactly same as two-tail test) Step 3: Calculations µ = 74 = 76.44 N = 25 s = 6.01 76.44 - 74 = 76.44 - 74 1.20 2.03 critical t 6.01 25 Observed t(24) = 2.03
µ = 74 Hypothesis testing t(24) = 2.03 Step 3: Calculations N = 25 µ = 74 N = 25 t(24) = 2.03 = 76.44 s = 6.01 Step 4: Make decision whether or not to reject null hypothesis Observed t(24) = 2.03 Critical t(24) = 1.711 2.0 is farther out on the curve than 1.711, so, we do reject the null hypothesis Step 5: Conclusion: The extra time did have a significant effect on the scores
Hypothesis testing: Did the extra time given to these 25 students affect their average test score? Start summary with two means (based on DV) for two levels of the IV notice we are comparing a sample mean with a population mean: single sample t-test Finish with statistical summary t(24) = 2.03; ns Describe type of test (t-test versus z-test) with brief overview of results Or if it had been different results that *were* significant: t(24) = -5.71; p < 0.05 The mean score for those students who where given extra time was 76.44 percent correct, while the mean score for the rest of the class was only 74 percent correct. A one-tailed t-test was completed and there appears to be significant difference in the test scores for these two groups t(24) = 2.03; p < 0.05. Type of test with degrees of freedom n.s. = “not significant” p<0.05 = “significant” n.s. = “not significant” p<0.05 = “significant” Value of observed statistic 32
A note on z scores, and t score: . . A note on z scores, and t score: Numerator is always distance between means (how far away the distributions are or “effect size”) Denominator is always measure of variability (how wide or much overlap there is between distributions) Difference between means Difference between means Variability of curve(s) (within group variability) Variability of curve(s)
Thank you! See you next time!!