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

BNAD 276: Statistical Inference in Management Spring 2016 Green sheets

Before our next exam (March 22 nd ) OpenStax Chapters 1 – 11 Plous (10, 11, 12 & 14) Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness Schedule of readings

No homework Just study for Exam 2

Exam 2 – This Thursday, March 22 nd Study guide is online Bring 2 calculators (remember only simple calculators, we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID Stats Review by Nick and Jonathon When: Monday evening March 21 st - 6:30 – 8:30pm Where: ILC 120 Cost: $5.00 Stats Review by Nick and Jonathon When: Monday evening March 21 st - 6:30 – 8:30pm Where: ILC 120 Cost: $5.00

By the end of lecture today 3/10/16 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 One-sample versus two-sample Pooled variance Degrees of freedom Comparing means

Homework Assignment Using Excel ?

Homework Assignment Using Excel

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” Are the two means significantly different from each other, or is the difference just due to chance?

Mean= 24 Participant Big Meal Small meal Mean= 21 Complete a t-test

Mean= 24 Participant Big Meal Small meal Mean= 21 Complete a t-test

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 Mean= 24 Participant Big Meal Small meal Mean= 21 Complete a t-test

Finding Means 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 Complete a t-test

This is “n” for each sample (Remember, “n” is just number of observations for each sample) df = “degrees of freedom” 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 This is “n” for each sample (Remember, “n” is just number of observations for each sample) Complete a t-test

Finding degrees of freedom Complete a t-test

Finding Observed t Complete a t-test

Finding Critical t Complete a t-test

Finding Critical t

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

Step 4: Make decision whether or not to reject null hypothesis Reject when: observed stat > critical stat is not bigger than “p” is less than 0.05 (or whatever alpha is) p = 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 Complete a t-test

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. 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 Finish with statistical summary t(4) = 1.96; ns Or if it *were* significant: t(9) = 3.93; p < 0.05 Type of test with degrees of freedom Value of observed statistic n.s. = “not significant” p<0.05 = “significant”

Graphing your t-test results

Graphing your t-test results

Chart Layout Graphing your t-test results

Fill out titles

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 Where are we? 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.

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. This time he had two classes, both with nine 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 Independent samples t-test

Step 1: Identify the research problem Step 2: Describe the null and alternative hypotheses H o : The size of the meal has no effect on test scores One tail or two tail test? Did the size of the meal affect the test scores? H 1 : The size of the meal does have an effect on test scores Notice: Additional participants don’t affect this part of the problem Independent samples t-test

Hypothesis testing Step 3: Decision rule α =.05 Degrees of freedom total (df total ) = (n 1 - 1) + (n 2 – 1) = (9 - 1) + (9 – 1) = 16 two tailed test n 1 = 9; n 2 = 9 Critical t (16) = 2.12 Degrees of freedom total (df total ) = (n total - 2) = 18 – 2 = 16 Notice: Two different ways to think about it

α =.05 (df) = 16 Critical t (16) = 2.12 two tail test

Mean= 24 Squared Deviation Σ = 24 Big Meal Small meal Big Meal Deviation From mean Squared deviation Mean= 21 Small Meal Deviation From mean Σ = Notice: s 2 = 2.25 Notice: s 2 = 3.0 Notice: Simple Average = Step 4: Calculate observed t-score

Mean= 24 Big Meal Small meal Mean= 21 S 2 1 = 2.25 S 2 2 = 3.00 = S 2 pooled = (n 1 – 1) s (n 2 – 1) s 2 2 n 1 + n S 2 pooled = (9 – 1) (2.25) + (9 – 1) (3) S p 2 = Step 4: Calculate observed t-score

Mean= 24 Big Meal Small meal Mean= 21 S p 2 = = 24 – = S 2 1 = 2.25 S 2 2 = 3.00 Step 4: Calculate observed t-score

Step 5: Make decision whether or not to reject null hypothesis is farther out on the curve than so, we do reject the null hypothesis t(16) = 3.928; p < 0.05 Observed t = Critical t = Summarizing your t-test results

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 Summarizing your t-test results Step 6: Conclusion

Let’s run more subjects using our excel!

Finding Means Let’s run more subjects using our excel!

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 2.25 and 3 is 2.625

Let’s run more subjects using our excel! This is “n” for each sample (Remember, “n” is just number of observations for each sample) df = “degrees of freedom” Remember, “degrees of freedom” is just (n-1) for each sample. So for sample 1: n-1 =9-1 = 8 And for sample 2: n-1=9-1 = 8 Then, df = 8+8=16 This is “n” for each sample (Remember, “n” is just number of observations for each sample)

Finding degrees of freedom Let’s run more subjects using our excel!

Finding Observed t Let’s run more subjects using our excel!

Finding Critical t Let’s run more subjects using our excel!

Remember, if the “t Stat” is bigger than the “t Critical” then we “reject the null”, and conclude we have a significant effect

Finding p value (Is it less than.05?) Let’s run more subjects using our excel!

In this case, p = which is less than 0.05, so we “do reject the null” Remember, if the “p” is less than 0.05 then we “reject the null”, and conclude we have a significant effect

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!

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

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.

Homework review

. Homework Is there a difference in mpg between these two cars 2-tail There is no difference in mpg between these two cars There is a difference in mpg between these two cars

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

. Homework Is there a difference in mpg between these two cars 2-tail There is no difference in mpg between these two cars There is a difference in mpg between these two cars 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 =

. Homework 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 Yes 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 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 Yes 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

. 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

. Homework

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. Type of instruction Exam score tail p = yes CAUTION This is significant with alpha of 0.05 BUT NOT WITH alpha of 0.01 The average exam score for those with instruction was 50, while the average exam score for those with no instruction was 40. A t-test was conducted and found that instruction significantly improved exam scores, t(38) = 2.66; p < 0.05

. Homework Type of Staff Travel Expenses tail p = no The average expenses for sales staff is 142.5, while the average expenses for the audit staff was A t-test was conducted and no significant difference was found, t(11) = 1.54; n.s.

. Homework Location of lot Number of cars tail p = 0.38 no The average number of cars in the Ocean Drive Lot was 86.24, while the average number of cars in Rio Rancho Lot was A t-test was conducted and no significant difference between the number of cars parked in these two lots, t(51) = -.88; n.s. Fun fact: If the observed t is less than one it will never be significant

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 Reporting t-test results

Have a safe and happy spring break Happy Spring Break!.