Screen Stage Lecturer’s desk Gallagher Theater Row A Row A Row A Row B

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

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 (October 21st) Lind (5 – 11)
Study Guide is on the class website Before our next exam (October 21st) Lind (5 – 11) Chapter 5: Survey of Probability Concepts Chapter 6: Discrete Probability Distributions Chapter 7: Continuous Probability Distributions Chapter 8: Sampling Methods and CLT Chapter 9: Estimation and Confidence Interval Chapter 10: One sample Tests of Hypothesis Chapter 11: Two sample Tests of Hypothesis 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

Exam 2 – Tuesday (10/21/14) Study guide online Bring 2 calculators (remember only simple calculators, we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID

Homework No homework Just study for Exam 2

By the end of lecture today 10/16/14
Use this as your study guide By the end of lecture today 10/16/14 Confidence Intervals 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-tail versus Two-tail test Type I versus Type II Errors Review for Exam 2 One-tail versus Two-tail test Type I versus Type II Errors Will not appear on exam 2

Remember Confidence Intervals
. Remember Confidence Intervals 95% Confidence Interval: We can be 95% confident that the estimated score really does fall between these two scores Please find the raw scores that border the middle 95% of the curve 99% Confidence Interval: We can be 99% confident that the estimated score really does fall between these two scores Please find the raw scores that border the middle 99% of the curve

Standard Error of the Mean (SEM)
Remember Confidence Intervals We now know all components of actually calculating confidence intervals: When to use confidence intervals: when you are estimating (guessing) a single number by providing likely range that the number appears in How to calculate confidence intervals Simply finding the raw score that is a certain distance from the mean that is associated with an area under the curve The relevance of the Central Limit Theorem When we are predicting a value we will use the standard error of the mean (rather than the standard deviation)

Standard Error of the Mean (SEM)
Remember Confidence Intervals Confidence Intervals (based on z): We are using this to estimate a value such as a population mean, with a known degree of certainty with a range of values Subjective vs Empirical The interval refers to possible values of the population mean. We can be reasonably confident that the population mean falls in this range (90%, 95%, or 99% confident) In the long run, series of intervals, like the one we figured out will describe the population mean about 95% of the time. Greater confidence implies loss of precision. (95% confidence is most often used) Can actually generate CI for any confidence level you want – these are just the most common

Confidence Intervals (based on z): A range of values that,
with a known degree of certainty, includes an unknown population characteristic, such as a population mean How can we make our confidence interval smaller? Decrease Variability Increase sample size (This will decrease variability) Decrease variability through more careful assessment and measurement practices (minimize noise) Decrease level of confidence . 95% 95%

We will be using this same logic for “confidence intervals”
Mean = 50 Standard deviation = 10 Find the scores for the middle 95% ? ? 95% x = mean ± (z)(standard deviation) 30.4 69.6 ? .9500 .4750 Please note: We will be using this same logic for “confidence intervals” 1) Go to z table - find z score for for area .4750 z = 1.96 2) x = mean + (z)(standard deviation) x = 50 + (-1.96)(10) x = 30.4 30.4 3) x = mean + (z)(standard deviation) x = 50 + (1.96)(10) x = 69.6 69.6 Scores capture the middle 95% of the curve

is captured by the scores 48.04 – 51.96
Confidence intervals Mean = 50 Standard deviation = 10 n = 100 s.e.m. = 1 ? ? 95% Find the scores for the middle 95% 48.04 51.96 For “confidence intervals” same logic – same z-score But - we’ll replace standard deviation with the standard error of the mean ? .9500 .4750 standard error of the mean σ √ n = 10 = √ 100 x = mean ± (z)(s.e.m.) x = 50 + (1.96)(1) x = x = 50 + (-1.96)(1) x = 95% Confidence Interval is captured by the scores – 51.96

Confidence intervals ? ? Tell me the scores that border exactly
95% ? Tell me the scores that border exactly the middle 95% of the curve We know this raw score = mean ± (z score)(s.d.) Construct a 95 percent confidence interval around the mean Similar, but uses standard error the mean based on population s.d. raw score = mean ± (z score)(s.e.m.)

Confidence intervals Level of Alpha 1.96 = .05 1.64 = .10 2.58 = .01
Construct a 95 percent confidence interval around the mean Tell me the scores that border exactly the middle 95% of the curve - use z score of 1.96 Level of Alpha 1.96 = .05 1.64 = .10 90% 2.58 = .01 z scores for different levels of confidence How do we know which z score to use?

Confidence interval uses SEM
Homework Worksheet: Confidence interval uses SEM

.99 2.58 sd 2.58 sd ? 55 ? Homework Worksheet: Problem 1
29.2 Upper boundary raw score x = mean + (z)(standard deviation) x = 55 + (+ 2.58)(10) x = 80.8 80.8 Lower boundary raw score x = mean + (z)(standard deviation) x = 55 + (- 2.58)(10) x = 29.2 Standard deviation = 10 Mean = 55 2.58 sd 2.58 sd .99 29.2 ? 55 80.8 ?

.99 49 2.58 sem 2.58 sem 1.42 ? 55 ? Homework Worksheet: Problem 1
29.2 Upper boundary raw score x = mean + (z)(standard error mean) x = 55 + (+ 2.58)(1.42) x = 58.7 80.8 51.3 58.7 Lower boundary raw score x = mean + (z)(standard error mean) x = 55 + (- 2.58)(1.42) x = 51.3 Standard deviation = 10 Mean = 55 10 49 2.58 sem 2.58 sem 1.42 .99 51.3 ? 55 58.7 ?

Homework Worksheet: Problem 5
29.2 80.8 51.3 58.7 10.2 29.8 16.9 23.1 4.09 13.11 8.02 9.18 2.67 7.8 14.5 9.4

Confidence Interval of 95% Has and alpha of 5% α = .05
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% Area associated with most extreme scores is called alpha

99% 95% 90% Moving from descriptive stats into inferential stats….
Area outside confidence interval is alpha Area outside confidence interval is alpha Moving from descriptive stats into inferential stats…. 99% Measurements that occur within the middle part of the curve are ordinary (typical) and probably belong there 95% Measurements that occur outside this middle ranges are suspicious, may be an error or belong elsewhere 90%

How do we know if something is going on
How do we know if something is going on? How rare/weird is rare/weird enough? Every day examples about when is weird, weird enough to think something is going on? Handing in blue versus white test forms Psychic friend – guesses 999 out of 1000 coin tosses right Cancer clusters – how many cases before investigation Weight gain treatment – one group gained an average of pound more than other group…what if 10?

Why do we care about the z scores that define the middle 95% of the curve? Inferential Statistics
Hypothesis testing with z scores allows us to make inferences about whether the sample mean is consistent with the known population mean. Is the mean of my observed sample consistent with the known population mean or did it come from some other distribution?

Why do we care about the z scores that define the middle 95% of the curve?
If the z score falls outside the middle 95% of the curve, it must be from some other distribution Main assumption: We assume that weird, or unusual or rare things don’t happen If a score falls out into the 5% range we conclude that it “must be” actually a common score but from some other distribution That’s why we care about the z scores that define the middle 95% of the curve

I’m not an outlier I just haven’t found my distribution yet
. Main assumption: We assume that weird, or unusual or rare things don’t happen I’m not an outlier I just haven’t found my distribution yet If a score falls out into the tails (low probability) we conclude that it “must be” a common score from some other distribution

Reject the null hypothesis Support for alternative
. Reject the null hypothesis 95% .. Relative to this distribution I am unusual maybe even an outlier X 95% X Relative to this distribution I am utterly typical Support for alternative hypothesis

Rejecting the null hypothesis
. null notnull big z score x x If the observed z falls beyond the critical z in the distribution (curve): then it is so rare, we conclude it must be from some other distribution then we reject the null hypothesis then we have support for our alternative hypothesis Alternative Hypothesis If the observed z falls within the critical z in the distribution (curve): then we know it is a common score and is likely to be part of this distribution, we conclude it must be from this distribution then we do not reject the null hypothesis then we do not have support for our alternative . null x x small z score

If the observed z falls beyond the critical z in the distribution (curve): then it is so rare, we conclude it must be from some other distribution then we reject the null hypothesis then we have support for our alternative hypothesis If the observed z falls within the critical z in the distribution (curve): then we know it is a common score and is likely to be part of this distribution, we conclude it must be from this distribution then we do not reject the null hypothesis then we do not have support for our alternative hypothesis

How do we know how rare is rare enough?
Area in the tails is alpha 99% α = .01 95% α = .05 90% α = .10 How do we know how rare is rare enough? Level of significance is called alpha (α) The degree of rarity required for an observed outcome to be “weird enough” to reject the null hypothesis Which alpha level would be associated with most “weird” or rare scores? Critical z: A z score that separates common from rare outcomes and hence dictates whether the null hypothesis should be retained (same logic will hold for “critical t”) If the observed z falls beyond the critical z in the distribution (curve) then it is so rare, we conclude it must be from some other distribution

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

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

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 = 2.0? 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

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

Exam 2 Review

Thank you! See you next time!!

Screen Stage Lecturer’s desk Gallagher Theater Row A Row A Row A Row B

Similar presentations

Presentation on theme: "Screen Stage Lecturer’s desk Gallagher Theater Row A Row A Row A Row B"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

Screen Stage Lecturer’s desk Gallagher Theater Row A Row A Row A Row B

Similar presentations

Presentation on theme: "Screen Stage Lecturer’s desk Gallagher Theater Row A Row A Row A Row B"— Presentation transcript:

Similar presentations

About project

Feedback