Tuesday: CLT; hypothesis testing; and Type I vs II

Tuesday: CLT; hypothesis testing; and Type I vs II
Stage Screen Lecturer’s desk Row A 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 Thru slide 83 Tuesday: CLT; hypothesis testing; and Type I vs II Thursday: Review for Exam 2 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

It went really well! Exam 2 – Thanks for your patience and cooperation
The grades will be posted by Tuesday

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 worksheet #12 Due October 28th Examples of Type I and Type II Errors

By the end of lecture today 10/23/14
Use this as your study guide By the end of lecture today 10/23/14 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? One-tailed versus two-tailed test Type I versus Type II Errors

Confidence Interval of 95% Has and alpha of 5% α = .05
Where are we? Critical z -2.58 Critical z 2.58 Confidence Interval of 99% Has and alpha of 1% α = .01 99% Area outside confidence interval is alpha Critical z -1.96 Critical z 1.96 Confidence Interval of 95% Has and alpha of 5% α = .05 95% Area in the tails is called alpha Critical z -1.64 Critical z 1.64 Confidence Interval of 90% Has and alpha of 10% α = . 10 90% Critical Z separates rare from common scores Review

Rejecting the null hypothesis
The result is “statistically significant” if: the observed statistic is larger than the critical statistic (which can be a ‘z” or “t” or “r” or “F” or x2) 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 < 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

Deciding whether or not to reject the null hypothesis. 05 versus
Deciding whether or not to reject the null hypothesis .05 versus .01 alpha levels What if our observed z = 1.5? How would the critical z change? α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -1.96 or +1.96 Do Not Reject the null Not a Significant difference Remember, reject the null if the observed z is bigger than the critical z -2.58 or +2.58 Not a Significant difference Do Not Reject the null

Deciding whether or not to reject the null hypothesis .05 versus .01 alpha levels What if our observed z = -3.9? How would the critical z change? α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -1.96 or +1.96 p < 0.05 Yes, Significant difference Reject the null Remember, reject the null if the observed z is bigger than the critical z -2.58 or +2.58 p < 0.01 Yes, Significant difference Reject the null

Deciding whether or not to reject the null hypothesis .05 versus .01 alpha levels What if our observed z = -2.52? How would the critical z change? α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -1.96 or +1.96 p < 0.05 Yes, Significant difference Reject the null Remember, reject the null if the observed z is bigger than the critical z -2.58 or +2.58 Not a Significant difference Do not Reject the null

How would the critical z change?
One versus two tail test of significance: Comparing different critical scores (but same alpha level – e.g. alpha = 5%) One versus two tailed test of significance z score = 1.64 95% 95% 5% 2.5% 2.5% How would the critical z change? Pros and cons…

One versus two tail test of significance 5% versus 1% alpha levels
How would the critical z change? One-tailed Two-tailed α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 1% 5% 2.5% .5% .5% 2.5% -1.64 or +1.64 -1.96 or +1.96 -2.33 or +2.33 -2.58 or +2.58

What if our observed z = 2.0? How would the critical z change? One-tailed Two-tailed α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -1.64 or +1.64 -1.96 or +1.96 Remember, reject the null if the observed z is bigger than the critical z Reject the null Reject the null -2.33 or +2.33 -2.58 or +2.58 Do not Reject the null Do not Reject the null

What if our observed z = 1.75? How would the critical z change? One-tailed Two-tailed α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -1.64 or +1.64 -1.96 or +1.96 Remember, reject the null if the observed z is bigger than the critical z Do not Reject the null Reject the null -2.33 or +2.33 -2.58 or +2.58 Do not Reject the null Do not Reject the null

What if our observed z = 2.45? How would the critical z change? One-tailed Two-tailed α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -1.64 or +1.64 -1.96 or +1.96 Remember, reject the null if the observed z is bigger than the critical z Reject the null Reject the null -2.33 or +2.33 -2.58 or +2.58 Reject the null Do not Reject the null

90% What if we do everything right …but we make the wrong decision??
For scores that fall into the middle range, we do not reject the null Critical z 1.64 Critical z -1.64 Measurements that occur within the middle part of the curve are ordinary (typical) and probably belong there 90% 5% 5% Measurements that occur outside this middle ranges are suspicious, may be an error or belong elsewhere For scores that fall into the regions of rejection, we reject the null What percent of the distribution will fall in region of rejection Critical Values

Rejecting the null hypothesis
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 < 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 A note on decision making following procedure versus being right relative to the “TRUTH”

Procedures versus outcome Best guess versus “truth”
. Decision making: Procedures versus outcome Best guess versus “truth” What does it mean to be correct? Why do we say: “innocent until proven guilty” “not guilty” rather than “innocent” Is it possible we got a verdict wrong?

We make decisions at Security Check Points
. We make decisions at Security Check Points .

Does this airline passenger have a snow globe?
. Type I or Type II error? . Does this airline passenger have a snow globe? Null Hypothesis means she does not have a snow globe (that nothing unusual is happening) – Should we reject it???!! As detectives, do we accuse her of brandishing a snow globe?

Does this airline passenger have a snow globe?
. Does this airline passenger have a snow globe? Status of Null Hypothesis (actually, via magic truth-line) Are we correct or have we made a Type I or Type II error? True Ho No snow globe False Ho Yes snow globe You are wrong! Type II error (miss) Do not reject Ho “no snow globe move on” You are right! Correct decision Decision made by experimenter You are wrong! Type I error (false alarm) Reject Ho “yes snow globe, stop!” You are right! Correct decision Note: Null Hypothesis means she does not have a snow globe (that nothing unusual is happening) – Should we reject it???!!

The alpha you choose becomes the probability of making a Type I error
Probability of a Type I Error = alpha

Type I error (false alarm)
Type I or type II error? . Decision made by experimenter Reject Ho Do not Reject Ho True Ho False Ho You are right! Correct decision You are wrong! Type I error (false alarm) Type II error (miss) Does this airline passenger have a snow globe? Two ways to be correct: Say she does have snow globe when she does have snow globe Say she doesn’t have any when she doesn’t have any Two ways to be incorrect: Say she does when she doesn’t (false alarm) Say she does not have any when she does (miss) Which is worse? What would null hypothesis be? This passenger does not have any snow globe Type I error: Rejecting a true null hypothesis Saying the she does have snow globe when in fact she does not (false alarm) Type II error: Not rejecting a false null hypothesis Saying she does not have snow globe when in fact she does (miss)

Type I or type II error . Decision made by experimenter Reject Ho Do not Reject Ho True Ho False Ho You are right! Correct decision You are wrong! Type I error (false alarm) Type II error (miss) Does advertising affect sales? Two ways to be correct: Say it helps when it does Say it does not help when it doesn’t help Which is worse? Two ways to be incorrect: Say it helps when it doesn’t Say it does not help when it does What would null hypothesis be? This new advertising has no effect on sales Type I error: Rejecting a true null hypothesis Saying the advertising would help sales, when it really wouldn’t help people (false alarm) Type II error: Not rejecting a false null hypothesis Saying the advertising would not help when in fact it would (miss)

What is worse a type I or type II error?
. Decision made by experimenter Reject Ho Do not Reject Ho True Ho False Ho You are right! Correct decision You are wrong! Type I error (false alarm) Type II error (miss) What if we were looking at a new HIV drug that had no unpleasant side affects Two ways to be correct: Say it helps when it does Say it does not help when it doesn’t help Two ways to be incorrect: Say it helps when it doesn’t Say it does not help when it does Which is worse? What would null hypothesis be? This new drug has no effect on HIV Type I error: Rejecting a true null hypothesis Saying the drug would help people, when it really wouldn’t help people (false alarm) Type II error: Not rejecting a false null hypothesis Saying the drug would not help when in fact it would (miss)

Which is worse? Type I or type II error
. Which is worse? Type I or type II error What if we were looking to see if there is a fire burning in an apartment building full of cute puppies Two ways to be correct: Say “fire” when it’s really there Say “no fire” when there isn’t one Two ways to be incorrect: Say “fire” when there’s no fire (false alarm) Say “no fire” when there is one (miss) What would null hypothesis be? No fire is occurring Type I error: Rejecting a true null hypothesis (false alarm) Type II error: Not rejecting a false null hypothesis (miss)

Which is worse? Type I or type II error
. Which is worse? Type I or type II error What if we were looking to see if an individual were guilty of a crime? Two ways to be correct: Say they are guilty when they are guilty Say they are not guilty when they are innocent Two ways to be incorrect: Say they are guilty when they are not Say they are not guilty when they are What would null hypothesis be? This person is innocent - there is no crime here Type I error: Rejecting a true null hypothesis Saying the person is guilty when they are not (false alarm) Sending an innocent person to jail (& guilty person to stays free) Type II error: Not rejecting a false null hypothesis Saying the person in innocent when they are guilty (miss) Allowing a guilty person to stay free

. The null hypothesis is typically that something is not present, that there is no effect, that there is no difference between population and sample or between treatment and control. Null Hypothesis A measure of sickness people taking drug people not taking drug (There are two distributions here, they are just on top of each other) (overlapping) people taking drug people not taking drug A measure of sickness A measure of sickness Null is FALSE Null is TRUE Drug does have effect Something going on Nothing going on No effect of drug There is a difference between the groups There is no difference between the groups

Remember: “procedure” vs “TRUTH”
. (There are two distributions here, they are just on top of each other) (overlapping) A measure of sickness people taking drug people not taking drug people taking drug people not taking drug A measure of sickness A measure of sickness Null is FALSE Null is TRUE Score should fall in this region critical stat critical stat Score should fall in one of these regions critical stat critical stat Score should fall in one of these regions Null is FALSE Null is TRUE Drug does have effect Something going on No effect of drug Nothing going on

1. “Reject a false null hypothesis”
Two ways to be right: 1. “Reject a false null hypothesis” “there really is something going on” 2. “Do not reject a true null hypothesis” “there really is no difference between groups” Decision made by experimenter Status of Null Hypothesis (actually, via magic truth-line) Reject Ho Do not Reject Ho True Ho False Ho You are right! Correct decision You are right! Correct decision

. Two ways to be wrong: 1. “Reject a true null hypothesis” say there’s a difference when there’s not (Type I) The score fell in the tails but the null was actually “TRUE” 2. “Do not reject a false null hypothesis” say there really is no difference between groups when there really is (Type II) The score fell in the middle but the null was still “FALSE” Decision made by experimenter Status of Null Hypothesis (actually, via magic truth-line) Reject Ho Do not Reject Ho True Ho False Ho You are wrong! Type II error (miss) You are wrong! Type I error (false alarm)

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

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

. 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

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

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 1 only - Section 2 will complete this next 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) Section 1 only - Section 2 will complete this next week

Writing Assignment Worksheet
Design one t-tests Section 1 only - Section 2 will complete this next week

Thank you! See you next time!!

Tuesday: CLT; hypothesis testing; and Type I vs II

Similar presentations

Presentation on theme: "Tuesday: CLT; hypothesis testing; and Type I vs II"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

Tuesday: CLT; hypothesis testing; and Type I vs II

Similar presentations

Presentation on theme: "Tuesday: CLT; hypothesis testing; and Type I vs II"— Presentation transcript:

Similar presentations

About project

Feedback