T-test in SPSS Hypothesis tests of proportions Confidence Intervals (End of chapter 6 material)
|
|
- Madeleine Beasley
- 7 years ago
- Views:
Transcription
1 T-test in SPSS Hypothesis tests of proportions Confidence Intervals (End of chapter 6 material)
2 Definition of p-value: The probability of getting evidence as strong as you did assuming that the null hypothesis is true. A smaller p-value means that it s less likely you would get a sample like this if the null hypothesis were true. A smaller p-value means stronger evidence against that null hypothesis.
3 Definition of alpha, the level of significance: The highest acceptable p-value that we will use to reject the null hypothesis. The default alpha is A smaller alpha means less of a chance of falsely rejecting the null. (Also called a Type I error) A smaller alpha means we want to be more certain about something before rejecting the null.
4 If the p-value is smaller than the alpha, we reject the null hypothesis. (Enough evidence to reject) If the p-value is larger than the null, we fail to reject the null hypothesis. (Not yet enough evidence to reject)
5 SPSS Example: Milk dataset. In the milk data set, good milk had a calcium level of 20 mg/l. Bad milk, for our cases, will have something other than 20. Step 1: Load the milk dataset. First we re going to try goodcalc4, which is a sample of 25 bottles.
6 Our null hypothesis is that the milk is good (calcium is 20mg/L) The alternative is that the milk has a different calcium value. We re comparing the mean of one sample to a specific value (20), so we ll go to Analyze Compare Means One-Sample T Test
7 Choose good sample, n=25, 3 rd. Move this variable to the right by dragging or using the move arrow. Then, change the test value to 20. (The hypothesized mean)
8 Click OK You ll get two tables. The first is a data summary like what we ve seen before.
9 The sample size is 25 The sample mean is The sample standard deviation is The standard error of the mean is (t-score = if we were doing this by hand.) The second table is the result of the t-test
10 Sig. (2-tailed) is the p-value for a two sided test. We re doing a two-sided test (not equal to 20), so this works. p-value =.275 >.050 (default level of significance) So we fail to reject the null.
11 Let s try some bad milk, as found in lowclac2, and this time let s say we don t care if the milk has too much calcium.
12 Another possibility is to include the upper area in the null hypothesis. The analysis is exactly the same. (Both ways acceptable)
13 (SPSS steps are the same, but with bad sample, n=25) SPSS gives us the two-sided significance, but we only want one side. By symmetry, we use half of two-sided p-value to get the one-sided value. p-value =.016 / 2 =.008 <.05.
14 We reject the null hypothesis. The milk is bad. Two-tailed means two-sided. The tails are terms for the ends of a distribution.
15 Having two tails isn t normal.
16 But in statistics, the Normal has two tails. Everything we ve done so far with means (z-scores, t-tests) we can do with proportions as well. The only difference is in the standard error. P is the sample proportion.
17 For proportions we always use the z-score (and not the t- table). is population proportion.
18 For proportions we always use the z-score (and not the t- table). Z is still the number of standard deviations about the mean.
19 Example: ICBC (Insurance Corporation of British Columbia) is concerned about people not wearing seatbelts in cars. If fewer than 90% of drivers are wearing seatbelts, ICBC will start a campaign to pick that number back up.
20 They surveyed 500 people (by hidden camera to prevent response bias) and find 461 wear seatbelts. First, get the sample proportion P, and its standard error. P = 461 / 500 = 0.922
21 Next, get the z-score. We want the chance of getting a sample of this proportion or less if the true proportion is.90. This area will include the mean, so we ll use area between and then add 50%. Total Area = 96.78%, or.9678
22 Why look at area less than z=1.85? The alternative hypothesis was that seatbeat usage is less than We found seatbeat usage was actually HIGHER than.900, so there should be very little evidence against the null. Area less than 1.85:.9678 P-value is.9678 >.05 (default level of significance), So we fail to reject the null. Real life terms: No seatbeat intervention is necessary.
23 Always wear your seatbelt, you never know who s on the road.
24 Confidence intervals From our sample, the proportion of people using their seatbelts was P = It would be dishonest to say that the true proportion that uses seatbelts is = But that s our best guess from our sample, so it would be even more dishonest to say it s any other value either.
25 Instead of a single value, it would be a lot more honest to give an interval that captured most of that uncertainty of the value and say We re 95% confident that the true parameter (mean, proportion, whatever) is in this interval. The interval we gave would be the 95% confidence interval. (90%, 99% or other values are possible, but 95% is default, just like 5% significance.)
26 The standard confidence interval is centered about the sample proportion. means plus or minus. To get the upper end of the interval, use the plus. To get the lower end of the interval, use the minus.
27 is the true proportion and P is the sample proportion as before.
28 is the standard error. In this case of the proportion.
29 Z* Stands for the critical z-score. For a 95% interval, it s whatever z-score would put 95% in the middle. (Or 2.5% on either side)
30 Two ways to find z*. 1. Look for the appropriate area beyond in the z-table. 2. Look at the bottom of the t-table for the appropriate significance at df. (One-tailed) For 95%, the area beyond is 2.5%. Both ways will give you a critical z-score z* = 1.96.
31 In the case the seatbelts, the 95% confidence interval would be:
32 =.922 (1.96)(.0119).922 (1.96)(.0119) = = (1.96)(.0119) = =.945 The 95% confidence interval is (.899 to.945) Or , 19 times out of 20.
33 Subtle note: This doesn t mean there s 95% chance that the true proportion is in the interval (.899 to.945). is a fixed value, it s either in there or it isn t. We ve set an interval that has a 95% chance to contain the parameter.
34 Each blue vertical line is a confidence interval. The red dotted line horizontally across them represents the parameter value. Most blue lines cross the red line (include the parameter), but not all of them.
35 Confidence interval: Milk example. Find the 95% confidence interval of the calcium level in the good milk. From SPSS, we know the sample mean is and that the standard error of the mean is 1.082
36 The milk example uses a t* critical, because we re using the t- distribution. In t-table: One-tailed,.025 significance, df=24, the critical value is: (.050 sig. in two-tailed gives the same value)
37 We re 95% confidence that the true calcium level is between (2.064)(1.082) = = (2.064)(1.082) = = is between and Since the hypothesized value of 20 is within the confidence interval, 20 is a plausible value for the parameter. Just as before, we fail to reject the null hypothesis.
38 We can use the confidence intervals to do two-sided hypothesis tests as well. By-hand confidence interval rule: If the confidence interval contains the value given in the null hypothesis, we fail to reject. Otherwise, reject to contains 20, so we fail to reject
39 In SPSS, doing a one-sample t-test will automatically give you a confidence interval as well (defaults to 95%). The values given in SPSS are in relation to means = means = 21.02
40 SPSS does this because then the reject/fail to reject rule is simplified a bit: If the confidence interval includes zero, we fail to reject. Otherwise, reject. (-3.44 to 1.02 contains zero, so we fail to reject)
41 Final point: The confidence interval only works for two-sided tests. Why? The interval cuts off at both ends. It has a lower limit and an upper limit. That means if the sample value is too far above or too far below the null hypothesis value, it will be rejected. By definition that s a two-sided test.
42 On Monday, we do two-sample t-tests (start of chapter 7). Assignment 3 coming tonight or on the weekend.
THE FIRST SET OF EXAMPLES USE SUMMARY DATA... EXAMPLE 7.2, PAGE 227 DESCRIBES A PROBLEM AND A HYPOTHESIS TEST IS PERFORMED IN EXAMPLE 7.
THERE ARE TWO WAYS TO DO HYPOTHESIS TESTING WITH STATCRUNCH: WITH SUMMARY DATA (AS IN EXAMPLE 7.17, PAGE 236, IN ROSNER); WITH THE ORIGINAL DATA (AS IN EXAMPLE 8.5, PAGE 301 IN ROSNER THAT USES DATA FROM
More informationTwo Related Samples t Test
Two Related Samples t Test In this example 1 students saw five pictures of attractive people and five pictures of unattractive people. For each picture, the students rated the friendliness of the person
More informationOdds ratio, Odds ratio test for independence, chi-squared statistic.
Odds ratio, Odds ratio test for independence, chi-squared statistic. Announcements: Assignment 5 is live on webpage. Due Wed Aug 1 at 4:30pm. (9 days, 1 hour, 58.5 minutes ) Final exam is Aug 9. Review
More informationHypothesis testing - Steps
Hypothesis testing - Steps Steps to do a two-tailed test of the hypothesis that β 1 0: 1. Set up the hypotheses: H 0 : β 1 = 0 H a : β 1 0. 2. Compute the test statistic: t = b 1 0 Std. error of b 1 =
More informationt Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon
t-tests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com
More informationLAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.
More informationIndependent t- Test (Comparing Two Means)
Independent t- Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent t-test when to use the independent t-test the use of SPSS to complete an independent
More informationChapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing
Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing 8-3 Testing a Claim About a Proportion 8-5 Testing a Claim About a Mean: s Not Known 8-6 Testing
More informationSection 7.1. Introduction to Hypothesis Testing. Schrodinger s cat quantum mechanics thought experiment (1935)
Section 7.1 Introduction to Hypothesis Testing Schrodinger s cat quantum mechanics thought experiment (1935) Statistical Hypotheses A statistical hypothesis is a claim about a population. Null hypothesis
More informationChapter 2 Probability Topics SPSS T tests
Chapter 2 Probability Topics SPSS T tests Data file used: gss.sav In the lecture about chapter 2, only the One-Sample T test has been explained. In this handout, we also give the SPSS methods to perform
More informationC. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters.
Sample Multiple Choice Questions for the material since Midterm 2. Sample questions from Midterms and 2 are also representative of questions that may appear on the final exam.. A randomly selected sample
More informationAn SPSS companion book. Basic Practice of Statistics
An SPSS companion book to Basic Practice of Statistics SPSS is owned by IBM. 6 th Edition. Basic Practice of Statistics 6 th Edition by David S. Moore, William I. Notz, Michael A. Flinger. Published by
More informationChapter Study Guide. Chapter 11 Confidence Intervals and Hypothesis Testing for Means
OPRE504 Chapter Study Guide Chapter 11 Confidence Intervals and Hypothesis Testing for Means I. Calculate Probability for A Sample Mean When Population σ Is Known 1. First of all, we need to find out the
More informationIntroduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses
Introduction to Hypothesis Testing 1 Hypothesis Testing A hypothesis test is a statistical procedure that uses sample data to evaluate a hypothesis about a population Hypothesis is stated in terms of the
More informationTwo-sample hypothesis testing, II 9.07 3/16/2004
Two-sample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For two-sample tests of the difference in mean, things get a little confusing, here,
More informationTwo-sample t-tests. - Independent samples - Pooled standard devation - The equal variance assumption
Two-sample t-tests. - Independent samples - Pooled standard devation - The equal variance assumption Last time, we used the mean of one sample to test against the hypothesis that the true mean was a particular
More informationLesson 1: Comparison of Population Means Part c: Comparison of Two- Means
Lesson : Comparison of Population Means Part c: Comparison of Two- Means Welcome to lesson c. This third lesson of lesson will discuss hypothesis testing for two independent means. Steps in Hypothesis
More informationOpgaven Onderzoeksmethoden, Onderdeel Statistiek
Opgaven Onderzoeksmethoden, Onderdeel Statistiek 1. What is the measurement scale of the following variables? a Shoe size b Religion c Car brand d Score in a tennis game e Number of work hours per week
More informationTesting a claim about a population mean
Introductory Statistics Lectures Testing a claim about a population mean One sample hypothesis test of the mean Department of Mathematics Pima Community College Redistribution of this material is prohibited
More informationHYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION
HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate
More informationHYPOTHESIS TESTING WITH SPSS:
HYPOTHESIS TESTING WITH SPSS: A NON-STATISTICIAN S GUIDE & TUTORIAL by Dr. Jim Mirabella SPSS 14.0 screenshots reprinted with permission from SPSS Inc. Published June 2006 Copyright Dr. Jim Mirabella CHAPTER
More informationAn Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS
The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10- TWO-SAMPLE TESTS Practice
More informationHypothesis testing. c 2014, Jeffrey S. Simonoff 1
Hypothesis testing So far, we ve talked about inference from the point of estimation. We ve tried to answer questions like What is a good estimate for a typical value? or How much variability is there
More informationHow To Test For Significance On A Data Set
Non-Parametric Univariate Tests: 1 Sample Sign Test 1 1 SAMPLE SIGN TEST A non-parametric equivalent of the 1 SAMPLE T-TEST. ASSUMPTIONS: Data is non-normally distributed, even after log transforming.
More informationMind on Statistics. Chapter 12
Mind on Statistics Chapter 12 Sections 12.1 Questions 1 to 6: For each statement, determine if the statement is a typical null hypothesis (H 0 ) or alternative hypothesis (H a ). 1. There is no difference
More informationThe Dummy s Guide to Data Analysis Using SPSS
The Dummy s Guide to Data Analysis Using SPSS Mathematics 57 Scripps College Amy Gamble April, 2001 Amy Gamble 4/30/01 All Rights Rerserved TABLE OF CONTENTS PAGE Helpful Hints for All Tests...1 Tests
More informationLesson 9 Hypothesis Testing
Lesson 9 Hypothesis Testing Outline Logic for Hypothesis Testing Critical Value Alpha (α) -level.05 -level.01 One-Tail versus Two-Tail Tests -critical values for both alpha levels Logic for Hypothesis
More informationGood luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:
Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours
More informationUnit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
More informationHYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More informationIntroduction to Hypothesis Testing
I. Terms, Concepts. Introduction to Hypothesis Testing A. In general, we do not know the true value of population parameters - they must be estimated. However, we do have hypotheses about what the true
More informationKSTAT MINI-MANUAL. Decision Sciences 434 Kellogg Graduate School of Management
KSTAT MINI-MANUAL Decision Sciences 434 Kellogg Graduate School of Management Kstat is a set of macros added to Excel and it will enable you to do the statistics required for this course very easily. To
More informationPsychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck!
Psychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck! Name: 1. The basic idea behind hypothesis testing: A. is important only if you want to compare two populations. B. depends on
More informationIndependent samples t-test. Dr. Tom Pierce Radford University
Independent samples t-test Dr. Tom Pierce Radford University The logic behind drawing causal conclusions from experiments The sampling distribution of the difference between means The standard error of
More information6: Introduction to Hypothesis Testing
6: Introduction to Hypothesis Testing Significance testing is used to help make a judgment about a claim by addressing the question, Can the observed difference be attributed to chance? We break up significance
More informationAnalysis of Variance ANOVA
Analysis of Variance ANOVA Overview We ve used the t -test to compare the means from two independent groups. Now we ve come to the final topic of the course: how to compare means from more than two populations.
More informationTwo-Sample T-Tests Assuming Equal Variance (Enter Means)
Chapter 4 Two-Sample T-Tests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when the variances of
More informationCHAPTER 14 NONPARAMETRIC TESTS
CHAPTER 14 NONPARAMETRIC TESTS Everything that we have done up until now in statistics has relied heavily on one major fact: that our data is normally distributed. We have been able to make inferences
More informationStat 411/511 THE RANDOMIZATION TEST. Charlotte Wickham. stat511.cwick.co.nz. Oct 16 2015
Stat 411/511 THE RANDOMIZATION TEST Oct 16 2015 Charlotte Wickham stat511.cwick.co.nz Today Review randomization model Conduct randomization test What about CIs? Using a t-distribution as an approximation
More informationComparing Two Groups. Standard Error of ȳ 1 ȳ 2. Setting. Two Independent Samples
Comparing Two Groups Chapter 7 describes two ways to compare two populations on the basis of independent samples: a confidence interval for the difference in population means and a hypothesis test. The
More informationGeneral Method: Difference of Means. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n 1, n 2 ) 1.
General Method: Difference of Means 1. Calculate x 1, x 2, SE 1, SE 2. 2. Combined SE = SE1 2 + SE2 2. ASSUMES INDEPENDENT SAMPLES. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n
More informationHYPOTHESIS TESTING: POWER OF THE TEST
HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9-step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,
More information1 Hypothesis Testing. H 0 : population parameter = hypothesized value:
1 Hypothesis Testing In Statistics, a hypothesis proposes a model for the world. Then we look at the data. If the data are consistent with that model, we have no reason to disbelieve the hypothesis. Data
More informationExperimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test
Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely
More informationIntroduction. Hypothesis Testing. Hypothesis Testing. Significance Testing
Introduction Hypothesis Testing Mark Lunt Arthritis Research UK Centre for Ecellence in Epidemiology University of Manchester 13/10/2015 We saw last week that we can never know the population parameters
More informationUsing Microsoft Excel to Analyze Data from the Disk Diffusion Assay
Using Microsoft Excel to Analyze Data from the Disk Diffusion Assay Entering and Formatting Data Open Excel. Set up the spreadsheet page (Sheet 1) so that anyone who reads it will understand the page (Figure
More information7. Comparing Means Using t-tests.
7. Comparing Means Using t-tests. Objectives Calculate one sample t-tests Calculate paired samples t-tests Calculate independent samples t-tests Graphically represent mean differences In this chapter,
More informationUsing Microsoft Excel to Analyze Data
Entering and Formatting Data Using Microsoft Excel to Analyze Data Open Excel. Set up the spreadsheet page (Sheet 1) so that anyone who reads it will understand the page. For the comparison of pipets:
More informationTesting for differences I exercises with SPSS
Testing for differences I exercises with SPSS Introduction The exercises presented here are all about the t-test and its non-parametric equivalents in their various forms. In SPSS, all these tests can
More information22. HYPOTHESIS TESTING
22. HYPOTHESIS TESTING Often, we need to make decisions based on incomplete information. Do the data support some belief ( hypothesis ) about the value of a population parameter? Is OJ Simpson guilty?
More informationChapter 26: Tests of Significance
Chapter 26: Tests of Significance Procedure: 1. State the null and alternative in words and in terms of a box model. 2. Find the test statistic: z = observed EV. SE 3. Calculate the P-value: The area under
More informationChapter 2. Hypothesis testing in one population
Chapter 2. Hypothesis testing in one population Contents Introduction, the null and alternative hypotheses Hypothesis testing process Type I and Type II errors, power Test statistic, level of significance
More informationDDBA 8438: Introduction to Hypothesis Testing Video Podcast Transcript
DDBA 8438: Introduction to Hypothesis Testing Video Podcast Transcript JENNIFER ANN MORROW: Welcome to "Introduction to Hypothesis Testing." My name is Dr. Jennifer Ann Morrow. In today's demonstration,
More informationClass 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationHYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More informationStudy Guide for the Final Exam
Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make
More informationChapter 5 Analysis of variance SPSS Analysis of variance
Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means One-way ANOVA To test the null hypothesis that several population means are equal,
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationChapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion
Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion Learning Objectives Upon successful completion of Chapter 8, you will be able to: Understand terms. State the null and alternative
More informationData Analysis Tools. Tools for Summarizing Data
Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool
More informationWISE Power Tutorial All Exercises
ame Date Class WISE Power Tutorial All Exercises Power: The B.E.A.. Mnemonic Four interrelated features of power can be summarized using BEA B Beta Error (Power = 1 Beta Error): Beta error (or Type II
More informationTwo-Sample T-Tests Allowing Unequal Variance (Enter Difference)
Chapter 45 Two-Sample T-Tests Allowing Unequal Variance (Enter Difference) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when no assumption
More informationWeek 4: Standard Error and Confidence Intervals
Health Sciences M.Sc. Programme Applied Biostatistics Week 4: Standard Error and Confidence Intervals Sampling Most research data come from subjects we think of as samples drawn from a larger population.
More informationChapter 7 Section 7.1: Inference for the Mean of a Population
Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used
More information3.4 Statistical inference for 2 populations based on two samples
3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted
More informationComparing Means in Two Populations
Comparing Means in Two Populations Overview The previous section discussed hypothesis testing when sampling from a single population (either a single mean or two means from the same population). Now we
More informationSPSS Explore procedure
SPSS Explore procedure One useful function in SPSS is the Explore procedure, which will produce histograms, boxplots, stem-and-leaf plots and extensive descriptive statistics. To run the Explore procedure,
More informationFormula for linear models. Prediction, extrapolation, significance test against zero slope.
Formula for linear models. Prediction, extrapolation, significance test against zero slope. Last time, we looked the linear regression formula. It s the line that fits the data best. The Pearson correlation
More informationSCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES
SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR
More information1.5 Oneway Analysis of Variance
Statistics: Rosie Cornish. 200. 1.5 Oneway Analysis of Variance 1 Introduction Oneway analysis of variance (ANOVA) is used to compare several means. This method is often used in scientific or medical experiments
More informationChapter 9. Two-Sample Tests. Effect Sizes and Power Paired t Test Calculation
Chapter 9 Two-Sample Tests Paired t Test (Correlated Groups t Test) Effect Sizes and Power Paired t Test Calculation Summary Independent t Test Chapter 9 Homework Power and Two-Sample Tests: Paired Versus
More informationPearson's Correlation Tests
Chapter 800 Pearson's Correlation Tests Introduction The correlation coefficient, ρ (rho), is a popular statistic for describing the strength of the relationship between two variables. The correlation
More informationName: Date: Use the following to answer questions 3-4:
Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin
More informationIntroduction to Hypothesis Testing OPRE 6301
Introduction to Hypothesis Testing OPRE 6301 Motivation... The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about
More informationQUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS
QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS This booklet contains lecture notes for the nonparametric work in the QM course. This booklet may be online at http://users.ox.ac.uk/~grafen/qmnotes/index.html.
More informationTutorial 5: Hypothesis Testing
Tutorial 5: Hypothesis Testing Rob Nicholls nicholls@mrc-lmb.cam.ac.uk MRC LMB Statistics Course 2014 Contents 1 Introduction................................ 1 2 Testing distributional assumptions....................
More informationHypothesis Test for Mean Using Given Data (Standard Deviation Known-z-test)
Hypothesis Test for Mean Using Given Data (Standard Deviation Known-z-test) A hypothesis test is conducted when trying to find out if a claim is true or not. And if the claim is true, is it significant.
More information1 Why is multiple testing a problem?
Spring 2008 - Stat C141/ Bioeng C141 - Statistics for Bioinformatics Course Website: http://www.stat.berkeley.edu/users/hhuang/141c-2008.html Section Website: http://www.stat.berkeley.edu/users/mgoldman
More informationDescribing Populations Statistically: The Mean, Variance, and Standard Deviation
Describing Populations Statistically: The Mean, Variance, and Standard Deviation BIOLOGICAL VARIATION One aspect of biology that holds true for almost all species is that not every individual is exactly
More informationLesson 7 Z-Scores and Probability
Lesson 7 Z-Scores and Probability Outline Introduction Areas Under the Normal Curve Using the Z-table Converting Z-score to area -area less than z/area greater than z/area between two z-values Converting
More informationA full analysis example Multiple correlations Partial correlations
A full analysis example Multiple correlations Partial correlations New Dataset: Confidence This is a dataset taken of the confidence scales of 41 employees some years ago using 4 facets of confidence (Physical,
More informationSimple Regression Theory II 2010 Samuel L. Baker
SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the
More informationSPSS/Excel Workshop 3 Summer Semester, 2010
SPSS/Excel Workshop 3 Summer Semester, 2010 In Assignment 3 of STATS 10x you may want to use Excel to perform some calculations in Questions 1 and 2 such as: finding P-values finding t-multipliers and/or
More informationThis chapter discusses some of the basic concepts in inferential statistics.
Research Skills for Psychology Majors: Everything You Need to Know to Get Started Inferential Statistics: Basic Concepts This chapter discusses some of the basic concepts in inferential statistics. Details
More informationTesting Group Differences using T-tests, ANOVA, and Nonparametric Measures
Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 35487-0348 Phone:
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationComparison of frequentist and Bayesian inference. Class 20, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Comparison of frequentist and Bayesian inference. Class 20, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom 1 Learning Goals 1. Be able to explain the difference between the p-value and a posterior
More informationHypothesis Testing. Reminder of Inferential Statistics. Hypothesis Testing: Introduction
Hypothesis Testing PSY 360 Introduction to Statistics for the Behavioral Sciences Reminder of Inferential Statistics All inferential statistics have the following in common: Use of some descriptive statistic
More informationRegression Analysis: A Complete Example
Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty
More informationNCSS Statistical Software
Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, two-sample t-tests, the z-test, the
More informationTests for One Proportion
Chapter 100 Tests for One Proportion Introduction The One-Sample Proportion Test is used to assess whether a population proportion (P1) is significantly different from a hypothesized value (P0). This is
More informationLecture Notes Module 1
Lecture Notes Module 1 Study Populations A study population is a clearly defined collection of people, animals, plants, or objects. In psychological research, a study population usually consists of a specific
More informationWe are often interested in the relationship between two variables. Do people with more years of full-time education earn higher salaries?
Statistics: Correlation Richard Buxton. 2008. 1 Introduction We are often interested in the relationship between two variables. Do people with more years of full-time education earn higher salaries? Do
More informationPaired T-Test. Chapter 208. Introduction. Technical Details. Research Questions
Chapter 208 Introduction This procedure provides several reports for making inference about the difference between two population means based on a paired sample. These reports include confidence intervals
More informationPoint Biserial Correlation Tests
Chapter 807 Point Biserial Correlation Tests Introduction The point biserial correlation coefficient (ρ in this chapter) is the product-moment correlation calculated between a continuous random variable
More informationIntroduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing.
Introduction to Hypothesis Testing CHAPTER 8 LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 Identify the four steps of hypothesis testing. 2 Define null hypothesis, alternative
More informationStatistics 2014 Scoring Guidelines
AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home
More informationp ˆ (sample mean and sample
Chapter 6: Confidence Intervals and Hypothesis Testing When analyzing data, we can t just accept the sample mean or sample proportion as the official mean or proportion. When we estimate the statistics
More informationHypothesis Testing: Two Means, Paired Data, Two Proportions
Chapter 10 Hypothesis Testing: Two Means, Paired Data, Two Proportions 10.1 Hypothesis Testing: Two Population Means and Two Population Proportions 1 10.1.1 Student Learning Objectives By the end of this
More information