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Unformatted text preview: 4/25/11 Announcements Last Week FR OM BE FO RE Parameters and Sta9s9cs Popula9on The Distribu9on of Sample Means The Logic of Hypothesis Tes9ng Sample ? ? A ESTIM TION X s STATISTICS (ESTIMATES) PARAMETERS 1 4/25/11 O FR M FO BE RE Sampling Error The discrepancy (or amount of error) that exists between a sample sta9s9c and the corresponding popula9on parameter O FR M FO BE RE Construc9ng a real Sampling Distribu9on for a big popula9on FR OM BE FO RE Popula9on Each Sample _ Sampling Distribu9on of X FR OM BE FO RE = 100 = 15 2 4/25/11 O FR M FO BE RE O FR M FO BE RE = 100 = 15 = 100 = 15 Random Sample X FR OM BE FO RE FR OM BE FO RE = 100 = 15 = 100 = 15 X 3 4/25/11 O FR M FO BE RE O FR M FO BE RE = 100 = 15 = 100 = 15 Random Sample X FR OM BE FO RE FR OM BE FO RE = 100 = 15 = 100 = 15 X 4 4/25/11 O FR M FO BE RE = 100 = 15 O FR M FO BE RE n = 2 n = 4 Construc9ng a real Sampling Distribu9on for a big popula9on that is not normally distributed n = 20 n = 60 n = 120 FR OM BE FO RE Popula9on Each Sample FR OM BE FO RE = 0.33 = 0.30 = 0.33 = 0.30 _ Sampling Distribu9on of X 5 4/25/11 O FR M FO BE RE O FR M FO BE RE = 0.33 = 0.30 = 0.33 = 0.30 Random Sample Random Sample X FR OM BE FO RE FR OM BE FO RE = 0.33 = 0.30 = 0.33 = 0.30 X 6 4/25/11 O FR M FO BE RE O FR M FO BE RE = 0.33 = 0.30 Sampling Distribu9on of the Mean Characteris9cs of the Sampling Distribu9on of X n = 2 Sampling Distribu9on of the Mean n = 5 Sampling Distribu9on of the Mean Sampling distribu9on has a mean = As sample size (n) increases, the variability of the sampling distribu9on decreases ! n n = 20 Sampling Distribu9on of the Mean n = 60 Sampling Distribu9on of the Mean The sampling distribu9on is normally distributed when popula9on is normal or samples are large, n > ~30 n = 120 FR OM BE FO RE Standard (Sampling) Error FR OM BE FO RE Standard Error Standard Devia9on of the Sampling Distribu9on of Sample Means ! !2 !X = = n n 7 4/25/11 O FR M FO BE RE = 100 = 15 O FR M FO BE RE ! X = 10.61 n = 2 = 0.33 = 0.30 Sampling Distribu9on of the Mean ! X = 0.212
Sampling Distribu9on of the Mean n = 2 ! X = 7.5 n = 4 ! X = 0.134 n = 5 ! X = 3.35 n = 20 Sampling Distribu9on of the Mean ! X = 0.067 n = 20 n = 60 ! X = 1.94 n = 60 Sampling Distribu9on of the Mean ! X = 0.039 n = 120 ! X = 1.37 Sampling Distribu9on of the Mean ! X = 0.027 n = 120 FR OM BE FO RE FR OM BE FO RE The Logic of Hypothesis Tes9ng Facebook 8 4/25/11
O FR M FO BE RE Popula9on All Individuals in the All Individuals USA using Facebook O FR M FO BE RE Popula9on All Individuals in the All Individuals USA using Facebook in the USA = 15 hours = 100 = 5 hours = 15 in the USA = 15 hours = 100 = 5 hours = 15 Random Sample n = 100 FR OM BE FO RE Popula9on All Individuals in the All Individuals USA using Facebook FR OM BE FO RE Popula9on All Individuals in the All Individuals USA using Facebook in the USA = 15 hours = 100 = 5 hours = 15 in the USA = 15 hours = 100 = 5 hours = 15 Random Sample n = 100 Treatment $ Random Sample n = 100 Treatment $ Sample Time on Facebook during sixth month for each person 9 4/25/11 O FR M FO BE RE Four Steps to Hypothesis Tes9ng Check Your Understanding Which hypothesis states that there is no effect? A B The Null Hypothesis The Alterna9ve Hypothesis 1. State a sta9s9cal hypothesis about a popula9on, usually about a popula9on parameter 2. Use the hypothesis to predict the characteris9cs samples from that popula9on should have; pick criteria to decide when samples do not support that hypothesis 3. Obtain a random sample of size n from the popula9on and compute a test sta9s9c 4. Compare obtained sample with the predic9on made by the sta9s9cal hypothesis. If sample is consistent, conclude hypothesis is reasonable; if sample is very inconsistent, conclude hypothesis is unreasonable Check Your Understanding Which hypothesis states that there is no effect? A B The Null Hypothesis The Alterna9ve Hypothesis FR OM BE FO RE Sta9s9cal Hypotheses Null Hypothesis (H0) the treatment does not have an effect Alterna9ve Hypothesis (H1) the treatment has an effect 10 4/25/11 O FR M FO BE RE Sta9s9cal Hypotheses Null Hypothesis (H0) treatment = without treatment Alterna9ve Hypothesis (H1) treatment without treatment O FR M FO BE RE Popula9on All Individuals in the All Individuals USA using Facebook in the USA = 15 hours = 100 = 5 hours = 15 Random Sample n = 100 Treatment $ Sample Time on Facebook during sixth month for each person FR OM BE FO RE Popula9on All Individuals in the All Individuals USA using Facebook FR OM BE FO RE Popula9on All Individuals in the All Individuals USA using Facebook in the USA = 15 hours = 100 = 5 hours = 15 in the USA = 15 hours = 100 = 5 hours = 15 Treatment $ Hypothe9cal Hypothe9cal Random Sample n = 100 Treatment $ Sample Time on Facebook during sixth month for each person Random Sample n = 100 Treatment $ Sample Time on Facebook during sixth month for each person 11 4/25/11 O FR M FO BE RE Popula9on All Individuals in the All Individuals USA using Facebook Popula9on Treatment $ All Individuals in the USA using Facebook O FR M FO BE RE Popula9on All Individuals in the All Individuals USA using Facebook Popula9on Treatment $ All Individuals in the USA using Facebook in the USA = 15 hours = 100 = 5 hours = 15 = ? hours = 5 hours in the USA = 15 hours = 100 = 5 hours = 15 = ? hours = 5 hours Hypothe9cal Hypothe9cal Random Sample n = 100 Treatment $ Sample Time on Facebook during sixth month for each person Random Sample n = 100 Treatment $ Sample Time on Facebook during sixth month for each person Random Sample n = 100 FR OM BE FO RE Popula9on All Individuals in the All Individuals USA using Facebook Popula9on All Individuals in the FR OM BE FO RE Popula9on All Individuals in the All Individuals USA using Facebook Popula9on All Individuals in the in the USA = 15 hours = 100 = 5 hours = 15 Treatment $ USA using Facebook = ? hours = 5 hours in the USA = 15 hours = 100 = 5 hours = 15 Treatment $ USA using Facebook = ? hours = 5 hours Hypothe9cal Hypothe9cal Random Sample n = 100 Treatment $ Sample Time on Facebook during sixth month for each person Random Sample n = 100 Random Sample n = 100 Treatment $ Random Sample n = 100 Sample Time on Facebook during sixth month for each person Sample Time on Facebook during sixth month for each person Sample Time on Facebook during sixth month for each person 12 4/25/11 O FR M FO BE RE Popula9on All Individuals in the All Individuals USA using Facebook Popula9on Treatment $ All Individuals in the USA using Facebook O FR M FO BE RE Sta9s9cal Hypotheses Null Hypothesis (H0) treatment = 15 Alterna9ve Hypothesis (H1) treatment 15 in the USA = 15 hours = 100 = 5 hours = 15 = 15 hours = 5 hours If H0 is true Hypothe9cal Random Sample n = 100 Treatment $ Sample Time on Facebook during sixth month for each person Random Sample n = 100 Sample Time on Facebook during sixth month for each person FR OM BE FO RE FR OM BE FO RE Four Steps to Hypothesis Tes9ng Four Steps to Hypothesis Tes9ng 1. State a sta9s9cal hypothesis about a popula9on, usually about a popula9on parameter 2. Use the hypothesis to predict the characteris9cs samples from that popula9on should have; pick criteria to decide when samples do not support that hypothesis 1. State a sta9s9cal hypothesis about a popula9on, usually about a popula9on parameter 2. Use the hypothesis to predict the characteris9cs samples from that popula9on should have; pick criteria to decide when samples do not support that hypothesis 3. Obtain a random sample of size n from the popula9on and compute a test sta9s9c 3. Obtain a random sample of size n from the popula9on and compute a test sta9s9c 4. Compare obtained sample with the predic9on made by the sta9s9cal hypothesis. If sample is consistent, conclude hypothesis is reasonable; if sample is very inconsistent, conclude hypothesis is unreasonable 4. Compare obtained sample with the predic9on made by the sta9s9cal hypothesis. If sample is consistent, conclude hypothesis is reasonable; if sample is very inconsistent, conclude hypothesis is unreasonable 13 4/25/11 O FR M FO BE RE Sta9s9cal Hypotheses Null Hypothesis (H0) treatment = 15 Alterna9ve Hypothesis (H1) treatment 15 O FR M FO BE RE Distribu9on of Sample Means X = 15
! X = 0.5 2.5 13.75 2 14 1.5 14.25 1 14.5 .5 14.75 15 .5 15.25 1 15.5 1.5 15.75 2 16 2.5 16.25 FR OM BE FO RE Distribu9on of Sample Means X = 15
! X = 0.5 FR OM BE FO RE Alpha Level, The probability value that is used to define which sample outcomes are considered very unlikely if the null hypothesis is true Low Probability Samples if H0 is True High Probability Samples if H0 is True 1.5 14.25 1 14.5 .5 14.75 15 .5 15.25 1 15.5 1.5 15.75 Low Probability Samples if H0 is True 2.5 13.75 2 14 2 16 2.5 16.25 Which samples do not support H0 14 4/25/11 Check Your Understanding Suppose you took a sample and got a mean that was among the least likely 10% of sample means. Would you find that convincing evidence that sampling error wasn't the cause of your sample mean being different from the popula9on mean? Check Your Understanding Suppose you took a sample and got a mean that was among the least likely 10% of sample means. Would you find that convincing evidence that sampling error wasn't the cause of your sample mean being different from the popula9on mean? A B Yes, I would find that convincing evidence to reject the "chance explana9on" No, I would not find that convincing evidence to reject the "chance explana9on" A B Yes, I would find that convincing evidence to reject the "chance explana9on" No, I would not find that convincing evidence to reject the "chance explana9on" FR OM BE FO RE Alpha Level, (most common) FR OM BE FO RE Distribu9on of Sample Means X = 15
! X = 0.5 ! = 0.05 2.5% High Probability Samples if H0 is True 2 14 1.5 14.25 1 14.5 .5 14.75 15 .5 15.25 1 15.5 1.5 15.75 2 16 2.5% 2.5 13.75 2.5 16.25 15 4/25/11 O FR M FO BE RE Cri9cal Region The region of the sampling distribu9on that contains the sample outcomes that are considered very unlikely if H0 is true O FR M FO BE RE FR OM BE FO RE Distribu9on of Sample Means X = 15
! X = 0.5 FR OM BE FO RE Four Steps to Hypothesis Tes9ng 1. State a sta9s9cal hypothesis about a popula9on, usually about a popula9on parameter 2. Use the hypothesis to predict the characteris9cs samples from that popula9on should have; pick criteria to decide when samples do not support that hypothesis 2.5% High Probability Samples if H0 is True 2 14 1.5 14.25 1 14.5 .5 14.75 15 .5 15.25 1 15.5 1.5 15.75 2 16 2.5% 2.5 13.75 2.5 16.25 3. Obtain a random sample of size n from the
popula9on and compute a test sta9s9c zcri9cal = 1.96 zcri9cal = +1.96 4. Compare obtained sample with the predic9on made by the sta9s9cal hypothesis. If sample is consistent, conclude hypothesis is reasonable; if sample is very inconsistent, conclude hypothesis is unreasonable 16 4/25/11 Four Steps to Hypothesis Tes9ng 1. State a sta9s9cal hypothesis about a popula9on, usually about a popula9on parameter Popula9on All Individuals in the All Individuals USA using Facebook Popula9on Treatment $ All Individuals in the USA using Facebook in the USA = 15 hours = 100 = 5 hours = 15 = ? hours = 5 hours Hypothe9cal 2. Use the hypothesis to predict the characteris9cs samples from that popula9on should have; pick criteria to decide when samples do not support that hypothesis Random Sample n = 100 Treatment $ Sample Time on Facebook during sixth month for each person Random Sample n = 100 3. Obtain a random sample of size n from the popula9on and compute a test sta9s9c 4. Compare obtained sample with the predic9on made by the sta9s9cal hypothesis. If sample is consistent, conclude hypothesis is reasonable; if sample is very inconsistent, conclude hypothesis is unreasonable Sample Time on Facebook during sixth month for each person Popula9on All Individuals in the All Individuals USA using Facebook Popula9on All Individuals in the Four Steps to Hypothesis Tes9ng 1. State a sta9s9cal hypothesis about a popula9on, usually about a popula9on parameter in the USA = 15 hours = 100 = 5 hours = 15 Treatment $ USA using Facebook = ? hours = 5 hours Hypothe9cal Random Sample n = 100 Treatment $ Sample Time on Facebook during sixth month for each person Random Sample n = 100 2. Use the hypothesis to predict the characteris9cs samples from that popula9on should have; pick criteria to decide when samples do not support that hypothesis Sample Sta9s9cs X = 16 s = 5.1 Sample Time on Facebook during sixth month for each person 3. Obtain a random sample of size n from the popula9on and compute a test sta9s9c 4. Compare obtained sample with the predic9on made by the sta9s9cal hypothesis. If sample is consistent, conclude hypothesis is reasonable; if sample is very inconsistent, conclude hypothesis is unreasonable 17 4/25/11 Four Steps to Hypothesis Tes9ng 1. State a sta9s9cal hypothesis about a popula9on, usually about a popula9on parameter Test Sta9s9c A test sta9s9c is a numerical summary of the degree to which a sample is unlike the samples predicted by the null hypothesis 2. Use the hypothesis to predict the characteris9cs samples from that popula9on should have; pick criteria to decide when samples do not support that hypothesis 3. Obtain a random sample of size n from the popula9on and compute a test sta9s9c 4. Compare obtained sample with the predic9on made by the sta9s9cal hypothesis. If sample is consistent, conclude hypothesis is reasonable; if sample is very inconsistent, conclude hypothesis is unreasonable ZTest Sta9s9c zX = X! !X = 15 x = 0.5 X = 16 zX = X ! "X 18 4/25/11 = 15 x = 0.5 X = 16 zX = X ! "X = 15 x = 0.5 X = 16 zX = X ! "X zX = 16 !15 0.5 zX = 16 !15 0.5 zX = 2 Four Steps to Hypothesis Tes9ng 1. State a sta9s9cal hypothesis about a popula9on, usually about a popula9on parameter Four Steps to Hypothesis Tes9ng 1. State a sta9s9cal hypothesis about a popula9on, usually about a popula9on parameter 2. Use the hypothesis to predict the characteris9cs samples from that popula9on should have; pick criteria to decide when samples do not support that hypothesis 2. Use the hypothesis to predict the characteris9cs samples from that popula9on should have; pick criteria to decide when samples do not support that hypothesis 3. Obtain a random sample of size n from the popula9on and compute a test sta9s9c 3. Obtain a random sample of size n from the popula9on and compute a test sta9s9c 4. Compare obtained sample with the predic9on made by the sta9s9cal hypothesis. If sample is consistent, conclude hypothesis is reasonable; if sample is very inconsistent, conclude hypothesis is unreasonable 4. Compare obtained sample with the predic9on made by the sta9s9cal hypothesis. If sample is consistent, conclude hypothesis is reasonable; if sample is very inconsistent, conclude hypothesis is unreasonable 19 4/25/11 Distribu9on of Sample Means X = 15
! X = 0.5 Distribu9on of Sample Means X = 15
! X = 0.5 2.5% High Probability Samples if H0 is True 2 14 1.5 14.25 1 14.5 .5 14.75 15 .5 15.25 1 15.5 1.5 15.75 2 16 2.5% 2.5% High Probability Samples if H0 is True 2 14 1.5 14.25 1 14.5 .5 14.75 15 .5 15.25 1 15.5 1.5 15.75 2 16 2.5% 2.5 13.75 2.5 16.25 2.5 13.75 2.5 16.25 zcri9cal = 1.96 zcri9cal = +1.96 zcri9cal = 1.96 zcri9cal = +1.96 Xobserved = 16 zx = +2 Distribu9on of Sample Means zX = 2
2.5% High Probability Samples if H0 is True 2 1.5 1 .5 .5 1 1.5 2 2.5% zX > zcritical
Reject Null Hypothesis Reject H0 2.5 2.5 zcri9cal = 1.96 zcri9cal = +1.96 zx = +2 20 4/25/11 Distribu9on of Sample Means X = 15
! X = 0.5 zX = 2 zX > zcritical
Reject Null Hypothesis Reject H0 2.5% High Probability Samples if H0 is True 2 14 1.5 14.25 1 14.5 .5 14.75 15 .5 15.25 1 15.5 1.5 15.75 2 16 2.5% 2.5 13.75 2.5 16.25 zcri9cal = 1.96 zcri9cal = +1.96 Xobserved = 16 zx = +2 Distribu9on of Sample Means X = 15
! X = 0.5 zX = X ! "X 2.5% High Probability Samples if H0 is True 2 14 1.5 14.25 1 14.5 .5 14.75 15 .5 15.25 1 15.5 1.5 15.75 2 16 2.5% zX > zcritical
Reject H0 zX < zcritical
Retain H0 or Fail to Reject H0 2.5 13.75 2.5 16.25 zcri9cal = 1.96 Xobserved = 14 zx = 2 zcri9cal = +1.96 21 4/25/11 zX = X ! "X zX = X ! "X zX > zcritical
Reject H0 zX < zcritical
Retain H0 or Fail to Reject H0 zX > zcritical
Reject H0 zX < zcritical
Retain H0 or Fail to Reject H0 zX = X ! "X zX = X ! "X zX > zcritical
Reject H0 zX < zcritical
Retain H0 or Fail to Reject H0 zX > zcritical
Reject H0 zX < zcritical
Retain H0 or Fail to Reject H0 22 4/25/11 Sta9s9cally Significant A result is said to be sta9s9cally significant if the result is very unlikely to occur when the null hypothesis is true; akin to saying the effect is real Conveying Results The effect of money on individuals' usage of Facebook was inves9gated. Money was found to sta9s9cally significantly increase 9me spent on Facebook, z = 2.0, p < 0.05. Conveying Results The effect of money on individuals' usage of Facebook was inves9gated. Money was found to sta9s9cally significantly increase 9me spent on Facebook, z = 2.0, p < 0.05. Observed value of the test sta9s9c Conveying Results The effect of money on individuals' usage of Facebook was inves9gated. Money was found to sta9s9cally significantly increase 9me spent on Facebook, z = 2.0, p < 0.05. Observed value of the test sta9s9c Likelihood of this outcome or more extreme 23 4/25/11 Conveying Results The effect of money on individuals' usage of Facebook was inves9gated. Money was found to sta9s9cally significantly increase 9me spent on Facebook, z = 2.0, p < 0.05. Observed value of the test sta9s9c Conveying Results The effect of money on individuals' usage of Facebook was inves9gated. Money was found to sta9s9cally significantly increase 9me spent on Facebook, z = 2.0, p < 0.05. Observed value of the test sta9s9c Outcome was in the "Cri9cal Region" Alpha Value Likelihood of this outcome or more extreme 24 4/25/11 Four Steps to Hypothesis Tes9ng 1. State a sta9s9cal hypothesis about a popula9on, usually about a popula9on parameter Four Steps to Hypothesis Tes9ng 1. State a H0 and H1 2. Use the hypothesis to predict the characteris9cs samples from that popula9on should have; pick criteria to decide when samples do not support that hypothesis 2. Determine criteria for rejec9ng the null hypothesis 3. Obtain a random sample of size n from the popula9on and compute a test sta9s9c. 3. Obtain a random sample of size n from the popula9on and compute a test sta9s9c 4. Compare obtained sample with the predic9on made by the sta9s9cal hypothesis. If sample is consistent, conclude hypothesis is reasonable; if sample is very inconsistent, conclude hypothesis is unreasonable 4. Made Decision: If value of test sta9s9c is more extreme than cri9cal values of test sta9s9c, reject H0; otherwise, fail to reject H0 ZTest zX = X ! "X zX = X ! "X zX > zcritical
Reject H0 zX < zcritical
Retain H0 or Fail to Reject H0 One Sample Test Requires knowledge of popula9on and 25 4/25/11 Distribu9on of Sample Means 2.5% High Probability Samples if H0 is True 2 1.5 1 .5 .5 1 1.5 2 2.5% 2.5 2.5 zcri9cal = 1.96 zcri9cal = +1.96 Possible Truths The Nature of Errors in Sta9s9cal Decision Theory There is No Effect H0 is True There is an Effect H1 is True 26 4/25/11 Popula9on All Individuals in the All Individuals USA using Facebook Popula9on Treatment $ All Individuals in the USA using Facebook in the USA = 15 hours = 100 = 5 hours = 15 = ? hours = 5 hours Truth Hypothe9cal Random Sample n = 100 Treatment $ Sample Time on Facebook during sixth month for each person Random Sample n = 100 There is No Effect H0 is True There is an Effect H1 is True Sample Time on Facebook during sixth month for each person Truth There is No Effect H0 is True There is an Effect H1 is True Truth There is No Effect H0 is True There is an Effect H1 is True Decisions Decisions Retain H0 Retain H0 27 4/25/11 Truth There is No Effect H0 is True There is an Effect H1 is True Truth There is No Effect H0 is True There is an Effect H1 is True Decisions Retain H0 CORRECT Retain H0 INCORRECT Decisions Retain H0 CORRECT Reject H0 Retain H0 INCORRECT Reject H0 Truth There is No Effect H0 is True There is an Effect H1 is True Truth There is No Effect H0 is True There is an Effect H1 is True Decisions Retain H0 CORRECT Reject H0 INCORRECT Retain H0 INCORRECT Reject H0 CORRECT Decisions Retain H0 CORRECT Reject H0 TYPE I ERROR Retain H0 INCORRECT Reject H0 CORRECT 28 4/25/11 Truth There is No Effect H0 is True There is an Effect H1 is True Type I Error A Type I error is when no effect is present, but a researcher rejects the null hypothesis "False Alarm" or "Alpha Error" Decisions Retain H0 CORRECT Reject H0 TYPE I ERROR Retain H0 TYPE II ERROR Reject H0 CORRECT Type II Error A Type II error is when a real effect is present, but a researcher fails to rejects the null hypothesis "Miss" or "Beta Error" Truth There is No Effect H0 is True There is an Effect H1 is True Decisions Retain H0 CORRECT Reject H0 TYPE I ERROR Retain H0 TYPE II ERROR Reject H0 CORRECT 29 4/25/11 Check Your Understanding If you rejected H0, which of the following errors could you have made? A B C Type I Error Type II Error Neither of the above Check Your Understanding If you rejected H0, which of the following errors could you have made? A B C Type I Error Type II Error Neither of the above Truth There is No Effect H0 is True There is an Effect H1 is True Smoke Detector Decisions Retain H0 CORRECT Reject H0 TYPE I ERROR Retain H0 TYPE II ERROR Reject H0 CORRECT 30 4/25/11 Truth There is No Fire H0 is True There is a Fire H1 is True Truth There is No EFire There is No ffect H0 is True There is ian Effect There s a Fire H1 is True Decisions Retain H0 CORRECT TYPE
I ERROR TYPE II ERROR Reject H0 CORRECT Decisions Retain H0 CORRECT TYPE I ERROR TYPE II ERROR Reject H0 CORRECT Truth There is No EFire There is No ffect H0 is True There is ian Effect There s a Fire H1 is True Truth There is No EFire There is No ffect H0 is True There is ian Effect There s a Fire H1 is True Decisions Retain H0 CORRECT TYPE I ERROR TYPE II ERROR Reject H0 CORRECT Decisions Retain H0 CORRECT TYPE I ERROR TYPE II ERROR Reject H0 CORRECT 31 4/25/11 Truth There is No EFire There is No ffect H0 is True There is ian Effect There s a Fire H1 is True Truth There is No EFire There is No ffect H0 is True There is ian Effect There s a Fire H1 is True Decisions Retain H0 CORRECT TYPE I ERROR TYPE II ERROR Reject H0 CORRECT Decisions Retain H0 CORRECT TYPE I ERROR TYPE II ERROR Reject H0 CORRECT Truth There is No EFire There is No ffect H0 is True There is ian Effect There s a Fire H1 is True Truth There is No EFire There is No ffect H0 is True There is ian Effect There s a Fire H1 is True Decisions Retain H0 CORRECT TYPE I ERROR TYPE II ERROR Reject H0 CORRECT Decisions Retain H0 CORRECT TYPE I ERROR TYPE II ERROR Reject H0 CORRECT 32 4/25/11 Distribu9on of Sample Means 2.5% High Probability Samples if H0 is True 2 1.5 1 .5 .5 1 1.5 2 2.5% 2.5 2.5 zcri9cal = 1.96 zcri9cal = +1.96 Distribu9on of Sample Means Truth There is No Effect H0 is True There is an Effect H1 is True 2.5% Decisions High Probability Samples if H0 is True 2 1.5 1 .5 .5 1 1.5 2 2.5% 2.5 2.5 Retain H0 CORRECT Reject H0 TYPE I ERROR Retain H0 TYPE II ERROR Reject H0 CORRECT zcri9cal = 1.96 zx = 0.4 zcri9cal = +1.96 33 4/25/11 Truth There is No Effect H0 is True There is an Effect H1 is True Decisions We NEVER "accept" the Null Hypothesis on the basis of sample data Retain H0 CORRECT Reject H0 TYPE I ERROR Retain H0 TYPE II ERROR Reject H0 CORRECT We NEVER "accept" the Null Hypothesis on the basis of sample data Never, never, never. Sir. Francis Bacon 1561  1626 David Hume 1711  1776 34 4/25/11 The Problem of Induc9on Popula9on Effect Popula9on Popula9on 35 4/25/11 Sample Sample Popula9on Popula9on Sample Sample Popula9on Popula9on 36 4/25/11 Sample Sample Popula9on Popula9on Sample Sample Popula9on Popula9on 37 4/25/11 Sample Sample Popula9on Popula9on Sample Sample Popula9on Popula9on 38 4/25/11 We NEVER "accept" the Null Hypothesis on the basis of sample data Never, never, never. We only "Retain H0" or "Fail to Reject H0" A lack of evidence for an effect is not good evidence for a lack of an effect Truth There is No Effect H0 is True There is an Effect H1 is True Decisions Retain H0 CORRECT Reject H0 TYPE I ERROR Retain H0 TYPE II ERROR Reject H0 CORRECT 39 4/25/11 Truth There is No Effect H0 is True There is an Effect H1 is True 2.5% Distribu9on of Sample Means Decisions Retain H0 CORRECT Reject H0 TYPE I ERROR Retain H0 TYPE II ERROR Reject H0 CORRECT High Probability Samples if H0 is True 2 1.5 1 .5 .5 1 1.5 2 2.5% 2.5 2.5 zcri9cal = 1.96 zcri9cal = +1.96 Check Your Understanding When performing a hypothesis test with = 0.05, what is the probability we will "False Alarm" (commit a Type I error) if the null hypothesis is actually true A B C D p = 1.0 p = p = 0 Unable to determine Check Your Understanding When performing a hypothesis test with = 0.05, what is the probability we will "False Alarm" (commit a Type I error) if the null hypothesis is actually true A B C D p = 1.0 p = p = 0 Unable to determine 40 4/25/11 Distribu9on of Sample Means Truth There is No Effect H0 is True There is an Effect H1 is True 2.5% Decisions High Probability Samples if H0 is True 2 1.5 1 .5 .5 1 1.5 2 2.5% 2.5 2.5 Retain H0 CORRECT Reject H0 TYPE I ERROR Retain H0 TYPE II ERROR Reject H0 CORRECT zcri9cal = 1.96 zcri9cal = +1.96 Truth There is No Effect H0 is True There is an Effect H1 is True Truth There is No Effect H0 is True There is an Effect H1 is True Decisions Retain H0 CORRECT Reject H0 TYPE I ERROR, p = Retain H0 TYPE II ERROR Reject H0 CORRECT Decisions Retain H0 CORRECT Reject H0 TYPE I ERROR, p = Retain H0 TYPE II ERROR Reject H0 CORRECT 41 4/25/11 Truth There is No Effect H0 is True There is an Effect H1 is True Truth There is No Effect H0 is True There is an Effect H1 is True Decisions Retain H0 CORRECT Reject H0 TYPE I ERROR, p = Retain H0 TYPE II ERROR, p = Reject H0 CORRECT Decisions Retain H0 CORRECT Reject H0 TYPE I ERROR, p = Retain H0 TYPE II ERROR, p = Reject H0 CORRECT For Next Time Review Chapter 8 Do Review Answers to Homework 4 Review Midterm 42 ...
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This note was uploaded on 01/10/2012 for the course PSYC PSYC 60 taught by Professor ? during the Winter '09 term at UCSD.
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