Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Chapter 8 Hypothesis Tests Chapter Table of Contents Introduction One-Sample t-test Paired t-test Two-Sample Test for Proportions Two-Sample Test for Variances Discussion of Other Tests References...178

2 156 Chapter 8. Hypothesis Tests

3 Chapter 8 Hypothesis Tests Introduction Hypothesis tests are frequently performed for one and two samples. For one sample, you are often interested in whether a population characteristic such as the mean is equivalent to a certain value. For two samples, you may be interested in whether the true means are different. When you have paired data, you may be interested in whether the mean difference is zero. Statistical hypothesis tests depend on a statistic designed to measure the degree of evidence for various alternative hypotheses. You compute the value of the statistic for your sample. If the value is improbable under the hypothesis you want to test, then you reject the hypothesis. Figure 8.1. Hypothesis Tests Menu

4 158 Chapter 8. Hypothesis Tests The Analyst Application enables you to perform hypothesis tests for means, proportions, and variances for either one or two samples. The examples in this chapter demonstrate how you can use the Analyst Application to perform a one-sample t-test, a paired t-test, a two-sample test for proportions, and a two-sample test for variances. Additionally, the section Discussion of Other Tests on page 177 provides information on other hypothesis tests you can perform with the Analyst Application. One-Sample t-test The One-Sample t-test task enables you to test whether the mean of a variable is less than, greater than, or equal to a specific value. The observed mean of the variable is compared to this value. The data set analyzed in the following example, Bthdth92, is taken from the 1995 Statistical Abstract of the United States, and it contains measures of the birth rate and infant mortality rate for 1992 in the United States. Information is provided for the 50 states and the District of Columbia, grouped by region. Suppose you want to determine whether the average infant mortality rate in the United States is equal to a specific value. Note that the one-sample t-test is appropriate in this situation because the standard deviation of the population from which the data arise is unknown. When you know the standard deviation of the population, use the One-Sample Z-Test for a Mean task (see the section Discussion of Other Tests on page 177 for more information). Open the Bthdth92 Data Set The data are provided in the Analyst Sample Library. To access this Analyst sample data set, follow these steps: 1. Select Tools! Sample Data ::: 2. Select Bthdth Click OK to create the sample data set in your Sasuser directory. 4. Select File! Open By SAS Name :::

5 One-Sample t-test Select Sasuser from the list of Libraries. 6. Select Bthdth92 from the list of members. 7. Click OK to bring the Bthdth92 data set into the data table. Request a One-Sample t-test To test whether the average infant mortality rate is equal to 8, follow these steps: 1. Select Statistics! Hypothesis Tests! One-Sample t-test for a Mean ::: 2. Select death as the variable to be analyzed. 3. Enter 8 in the box labeled Null: Mean = and press Enter. Your alternative hypothesis can be that the mean is less than, greater than, or not equal to a specified value. In this example, the alternative hypothesis is that the mean of the variable death is not equal to 8. In Figure 8.2, the one-sample t-test dialog defines the null and alternative hypotheses and specifies death as the variable to be tested. Figure 8.2. One-Sample t-test Dialog The default one-sample t-test task includes sample statistics for the variable death and the hypothesis test results.

6 160 Chapter 8. Hypothesis Tests Compute a Confidence Interval for the Mean To produce a confidence interval for the mean in addition to the hypothesis test, follow these steps: 1. ClickontheTests button in the main dialog. 2. Select Interval to request a two-sided confidence interval for the mean. You can choose either a one-sided or a two-sided confidence interval for the mean. The selections Lower bound and Upper bound specify one-sided confidence bounds. The default confidence level is 95%. You can click on the down arrow to select another confidence level, or you can enter a confidence level in the box. 3. Click OK to return to the main dialog. Figure 8.3 displays the selection of a 95% two-sided confidence interval for the mean. Note that you can also request a retrospective power analysis of the test in the Power Analysis tab. Figure 8.3. One-Sample t-test: Tests Dialog

7 One-Sample t-test 161 Request a t Distribution Plot To request a t distribution plot in addition to the hypothesis test, follow these steps: 1. ClickonthePlots button in the main dialog. 2. Select t distribution plot. 3. Click OK to return to the main dialog. Figure 8.4 displays the Plots dialog with t distribution plot selected. Figure 8.4. One-Sample t-test: Plots Dialog Click OK in the main dialog to perform the analysis. Review the Results The results of the hypothesis test are displayed in Figure 8.5. The output includes the Sample Statistics table for the variable death, the hypothesis test results, and the 95% confidence interval for the mean. The mean of the variable death is 8:61, which is greater than the specified test value of 8.

8 162 Chapter 8. Hypothesis Tests Figure 8.5. One-Sample t-test: Output The t statistic of 2:102 and the associated p-value (0:0406) provide evidence at the =0:05 level that the average infant mortality rate is not equal to 8. The confidence interval indicates that you can be 95% confident that the true mean of the variable lies within the interval [8:03; 9:20]. The requested t distribution plot is displayed in Figure 8.6. The plot depicts the calculated t statistic superimposed on a t distribution density function with 50 degrees of freedom.

9 One-Sample t-test 163 Figure 8.6. One-Sample t-test: t Distribution Plot Because this analysis requests a two-tailed test, two critical regions are shaded, one in each of the left and right tails. The alpha level for the test is 0:05; thus, each region represents 2.5% of the area under the curve. In a one-tailed test at the =0:05 level, the critical region appears in one tail only, and it represents 5% of the area under the curve. Here, the t statistic falls in the shaded region. Thus, the null hypothesis is rejected.

10 164 Chapter 8. Hypothesis Tests Paired t-test The Paired t-test enables you to determine whether the means of paired samples are equal. The term paired means that there is a correspondence between observations from each population. For example, the birth and death data analyzed in the preceding section are considered to be paired data because, in each observation, the variables birth and death correspond to the same state. Suppose that you want to determine whether the means for the birth rate and the infant mortality rate are equal. Analyst provides the Two-Sample Paired t-test for Means task, which tests the equality of means of two paired samples. The two samples in this example are the birth rate (birth) and the infant mortality rate (death) for each state. Open the Bthdth92 Data Set The data are provided in the Analyst Sample Library. To access this Analyst sample data set, follow these steps: 1. Select Tools! Sample Data ::: 2. Select Bthdth Click OK to create the sample data set in your Sasuser directory. 4. Select File! Open By SAS Name ::: 5. Select Sasuser from the list of Libraries. 6. Select Bthdth92 from the list of members. 7. Click OK to bring the Bthdth92 data set into the data table.

11 Paired t-test 165 Request a Paired t-test To perform this analysis, follow these steps: 1. Select Statistics! Hypothesis Tests! Two-Sample Paired t-test for Means ::: 2. Select the variable birth as the Group 1 variable. 3. Select the variable death as the Group 2 variable. The test of interest is whether the difference of the means is zero. This is the default value in Analyst, although you can specify other values as well. You can choose one of three alternative hypotheses. The default is that the difference between the means is not equal to the specified difference, which is the two-sided alternative. The one-sided alternatives are that the difference is greater than, or less than, the difference specified in the null hypothesis. Figure 8.7. Paired t-test Dialog In Figure 8.7, the null hypothesis specifies that the means of the variables birth and death are equal (or, equivalently, that the difference between the means is 0). The alternative hypothesis is that the two means are not equal.

12 166 Chapter 8. Hypothesis Tests Request Plots To specify a box-and-whisker plot and a means plot in addition to the hypothesis test, follow these steps: 1. ClickonthePlots button in the main dialog. 2. Select Box-&-whisker plot. 3. Select Means plot. 4. Click OK. Figure 8.8 displays the Plots dialog with Box-&-whisker plot and Means plot selected. Figure 8.8. Paired t-test: Plots Dialog Click OK in the main dialog to perform the analysis.

13 Paired t-test 167 Review the Results The results of the analysis, displayed in Figure 8.9, contain the mean, standard deviation, and standard error of the mean for both variables. The Hypothesis Test table provides the observed t statistic, the degrees of freedom, and the associated p-value of the test. Figure 8.9. Paired t-test: Results In Figure 8.9, the Sample Statistics table shows that the mean of the variable birth is larger than that of the variable death. In the Hypothesis Test table, the t statistic (19:926) and associated p- value (< 0:0001) indicate that the difference between the two means is statistically very significant. Figure 8.10 displays the side-by-side box plots of birth and death. Observations that fall beyond the whiskers are individually identified with a square symbol.

14 168 Chapter 8. Hypothesis Tests Figure Paired t-test: Box-and-Whisker Plot The means and standard error plot displayed in Figure 8.11 provides another view of the two variables. The means plot depicts an interval centered on the sample mean for each variable. The vertical line interval extends two standard deviations on either side of the mean.

15 Two-Sample Test for Proportions 169 Figure Paired t-test: Means Plot Two-Sample Test for Proportions In the Two-Sample Test for Proportions task, you can determine whether two probabilities are the same. The data analyzed in this example are taken from a study measuring the accuracy of two computer programs. Each program searches the World Wide Web and returns a list of web pages that meet a particular set of specified criteria. The data set Search contains two samples in which each observation is either yes or no. A response of yes indicates that the program returns the desired page at the top of the list of potential pages; a value of no indicates that this is not

16 170 Chapter 8. Hypothesis Tests the case. The data set contains the results of 535 searches using an older search program and 409 searches using a new program. The variables containing the results for the old and new programs are named oldfind and newfind, respectively. Suppose that you want to determine whether the probability of a correct search by the new algorithm is higher than that for the old algorithm. That is, you want to determine whether you can reject the null hypothesis that the two probabilities are equal in favor of the alternative that the new probability is larger. The values for analysis are contained in the two variables oldfind and newfind. Open the Search Data Set The data are provided in the Analyst Sample Library. To access this Analyst sample data set, follow these steps: 1. Select Tools! Sample Data ::: 2. Select Search. 3. Click OK to create the sample data set in your Sasuser directory. 4. Select File! Open By SAS Name ::: 5. Select Sasuser from the list of Libraries. 6. Select Search from the list of members. 7. Click OK to bring the Search data set into the data table. Request a Two-Sample Test for Proportions To perform the analysis, follow these steps: 1. Select Statistics! Hypothesis Tests! Two-Sample Test for Proportions ::: 2. Select Two variables in the box labeled Groups are in. 3. Select the variable newfind as the Group 1 variable. 4. Select the variable oldfind as the Group 2 variable. 5. Select the Level of Interest by clicking on the down arrow and selecting yes to test whether the two groups have the same proportions of success. 6. Specify the Alternative hypothesis by selecting Prop 1 - Prop 2 > 0.

17 Two-Sample Test for Proportions 171 Note that, if your data are arranged so that the values for the two groups are contained in a single variable, you can define the dependent and group variables by selecting One variable in the box labeled Groups are in. Figure 8.12 displays the Two-Sample Test for Proportions dialog. Figure Two-Sample Test for Proportions Dialog In Figure 8.12, the null hypothesis specifies that the proportions of success for the algorithms are equal (or, equivalently, that the difference between the proportions is 0). The alternative hypothesis is that the probability of a correct search by the new algorithm is higher than that for the old algorithm. Click OK in the main dialog to perform the analysis. Review the Results The results of the hypothesis test are displayed in Figure 8.13.

18 172 Chapter 8. Hypothesis Tests Figure Two-Sample Test for Proportions: Results The Sample Statistics table lists the frequency of yes and no responses for each variable. The Hypothesis Test table displays the null and alternative hypotheses and the results of the test. The observed proportion of yes responses is 0:8631 for the newfind variable, and 0:8093 for the oldfind variable. The Z statistic of 2:19 and associated p-value of 0:0142 indicate that the proportion of successful searches is significantly larger for the new search algorithm. Two-Sample Test for Variances In the Two-Sample Test for Variances task, you can test whether two variables have different variances, or, if you have a single variable that contains values for two groups, you can determine whether the variance differs between the groups. The data set analyzed in this example, Gpa, contains test scores for 224 students. The data include the students grade point averages (the variable gpa), high school scores in mathematics, science, and English (the variables hsm, hss, andhse, respectively), and SAT math and verbal scores (the variables satm and satv, respectively).

19 Two-Sample Test for Variances 173 Suppose that you want to examine the difference in grade point averages between males and females. You can use the two-sample test for variances to test whether the variance of the grade point average differs between males and females. Open the Gpa Data Set The data are provided in the Analyst Sample Library. To access this Analyst sample data set, follow these steps: 1. Select Tools! Sample Data ::: 2. Select GPA. 3. Click OK to create the sample data set in your Sasuser directory. 4. Select File! Open By SAS Name ::: 5. Select Sasuser from the list of Libraries. 6. Select Gpa from the list of members. 7. Click OK to bring the Gpa data set into the data table. Request a Two-Sample Test for Variances To perform the hypothesis test, follow these steps: 1. Select Statistics! Hypothesis Tests! Two-Sample Test for Variances ::: 2. Ensure that One variable is selected in the box labeled Groups are in. 3. Select the variable gpa as the Dependent variable. 4. Select the variable sex as the Group variable. If your data are arranged so that the values for both groups are contained in two variables, you can define the two groups by checking the Two variables selection in the box labeled Groups are in. The null hypothesis for the test is that the two variances are equal (or, equivalently, that their ratio is equal to 1). You can specify the type of alternative hypothesis. The three choices are that Variance 1

20 174 Chapter 8. Hypothesis Tests is not equal to, is greater than, or is less than Variance 2. In Figure 8.14, the alternative hypothesis states that the two variances are not equal, which is the two-sided alternative hypothesis. Figure Two-Sample Test for Variances Dialog Request a Box-&-Whisker Plot To request a box-and-whisker plot in addition to the hypothesis test, follow these steps: 1. ClickonthePlots button. 2. Select Box-&-whisker plot. 3. Click OK. Figure 8.15 displays the Plots dialog with Box-&-whisker plot selected. Note that the plot is constructed to have a mean of zero.

21 Two-Sample Test for Variances 175 Figure Two-Sample Test for Variances: Plots Dialog Click OK in the Two-Sample Test for Variances dialog to perform the hypothesis test. Review the Results Figure 8.16 displays the results of the hypothesis test. The output contains the results of the hypothesis test, including summary statistics, the F statistic, and the associated p-value. Figure Two-Sample Test for Variances: Output The Sample Statistics table displays the variance of the variable gpa for both females (0:6509) and males(0:5311). The Hypoth-

22 176 Chapter 8. Hypothesis Tests esis Test table displays the test statistics: the F value is 1:23 and the resulting p-value is 0:3222. Thus, the data give no evidence for rejecting the hypothesis of equal variances. Figure 8.17 displays the box-and-whisker plot. Observations that fall beyond the whiskers are identified with a square symbol. Figure Two-Sample Test for Variances: Box-and-whisker Plot The box-and-whisker plot displays the amount of spread and the range for the two variables. The two groups do not appear to be appreciably different.

23 Discussion of Other Tests 177 Discussion of Other Tests The following descriptions provide an overview of other hypothesis tests available in the Analyst Application. One-Sample Z-Test for a Mean In the One-Sample Z-Test for a Mean task, you can test whether the mean of a population is equal to the value you specify in the null hypothesis. This test is appropriate when the population standard deviation or variance is known, and your data are either normally distributed or you have a large number of observations. Generally, a sample size of at least 30 is considered to be sufficient. The default output from the test includes summary statistics for the selected variable, the Z statistic, and the associated p-value. One-Sample Test for a Proportion In the One-Sample Test for a Proportion task, you can test whether the proportion of a population giving a certain response is equal to the proportion you specify in the null hypothesis. The default output from this test provides a frequency table of responses versus the analysis variable, the observed proportion, the Z statistic, and the associated p-value. One-Sample Test for a Variance In the One-Sample Test for a Variance task, you can test whether the variance of a population is equal to the value you specify in the null hypothesis. The default output from this test includes summary statistics for the selected variable, the chi-square statistic, and the associated p-value. Two-Sample t-test for Means In the Two-Sample t-test for Means task, you can test whether the means of two populations are equal or, optionally, whether they differ by a specified amount. Two-sample data arise when two independent samples are observed, possibly with different sample sizes. Note that, if the two samples are not independent, the two-sample t-test is inappropriate and you should use instead the Two-Sample

24 178 Chapter 8. Hypothesis Tests Paired t-test for Means task (see the section Paired t-test beginning on page 164 for more information). The default output from the test includes summary statistics for the two samples, two t statistics, and the associated p-values. The first t statistic assumes the population variances of the two groups are equal; the second statistic is an approximate t statistic and should be used when the population variances of the two groups are potentially unequal. References SAS Institute Inc. (1999), SAS/STAT User s Guide, Version 7-1, Cary, NC: SAS Institute Inc. Schlotzhauer, Sandra D. and Littell, Ramon C. (1991), SAS System for Elementary Statistical Analysis, Second Edition, Cary, NC: SAS Institute Inc. U.S. Bureau of the Census (1995), Statistical Abstract of the United States, Washington, D.C.

25 The correct bibliographic citation for this manual is as follows: SAS Institute Inc., The Analyst Application, First Edition, Cary, NC: SAS Institute Inc., pp. The Analyst Application, First Edition Copyright 1999 SAS Institute Inc., Cary, NC, USA. ISBN All rights reserved. Printed in the United States of America. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, by any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS Institute, Inc. U.S. Government Restricted Rights Notice. Use, duplication, or disclosure of the software by the government is subject to restrictions as set forth in FAR Commercial Computer Software-Restricted Rights (June 1987). SAS Institute Inc., SAS Campus Drive, Cary, North Carolina st printing, October 1999 SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. indicates USA registration. IBM, ACF/VTAM, AIX, APPN, MVS/ESA, OS/2, OS/390, VM/ESA, and VTAM are registered trademarks or trademarks of International Business Machines Corporation. indicates USA registration. Other brand and product names are registered trademarks or trademarks of their respective companies. The Institute is a private company devoted to the support and further development of its software and related services.

Chapter 12 Sample Size and Power Calculations Chapter Table of Contents Introduction...253 Hypothesis Testing...255 Confidence Intervals...260 Equivalence Tests...264 One-Way ANOVA...269 Power Computation

Chapter 32 Histograms and Bar Charts Chapter Table of Contents VARIABLES...470 METHOD...471 OUTPUT...472 REFERENCES...474 467 Part 3. Introduction 468 Chapter 32 Histograms and Bar Charts Bar charts are

Chapter 35 Scatter Plots Chapter Table of Contents VARIABLES...496 METHOD...496 OUTPUT...497 493 Part 3. Introduction 494 Chapter 35 Scatter Plots A scatter plot is a graphic representation of the relationship

Chapter 2 The Data Table Chapter Table of Contents Introduction... 21 Bringing in Data... 22 OpeningLocalFiles... 22 OpeningSASFiles... 27 UsingtheQueryWindow... 28 Modifying Tables... 31 Viewing and Editing

### t 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

### Two-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

### 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

### 9-3.4 Likelihood ratio test. Neyman-Pearson lemma

9-3.4 Likelihood ratio test Neyman-Pearson lemma 9-1 Hypothesis Testing 9-1.1 Statistical Hypotheses Statistical hypothesis testing and confidence interval estimation of parameters are the fundamental

### Two-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

### Testing Hypotheses using SPSS

Is the mean hourly rate of male workers \$2.00? T-Test One-Sample Statistics Std. Error N Mean Std. Deviation Mean 2997 2.0522 6.6282.2 One-Sample Test Test Value = 2 95% Confidence Interval Mean of the

### LAB 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.

### Chapter 7 Appendix. Inference for Distributions with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83/-84 Calculators

Chapter 7 Appendix Inference for Distributions with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83/-84 Calculators Inference for the Mean of a Population Excel t Confidence Interval for Mean Confidence

### An 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

### Two-Sample T-Test from Means and SD s

Chapter 07 Two-Sample T-Test from Means and SD s Introduction This procedure computes the two-sample t-test and several other two-sample tests directly from the mean, standard deviation, and sample size.

### SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS)

SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS) State of the course address: The Final exam is Aug 9, 3:30pm 6:30pm in B9201 in the Burnaby Campus. (One

### Name: 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

### Good 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

### OS/2: TELNET Access Method

259 CHAPTER 18 OS/2: TELNET Access Method SAS Support for TELNET on OS/2 259 SAS/CONNECT 259 System and Software Requirements for SAS/CONNECT 259 Local Host Tasks 260 Configuring Local and Remote Host

### Business Statistics. Lecture 8: More Hypothesis Testing

Business Statistics Lecture 8: More Hypothesis Testing 1 Goals for this Lecture Review of t-tests Additional hypothesis tests Two-sample tests Paired tests 2 The Basic Idea of Hypothesis Testing Start

### Chapter 8 Introduction to Hypothesis Testing

Chapter 8 Student Lecture Notes 8-1 Chapter 8 Introduction to Hypothesis Testing Fall 26 Fundamentals of Business Statistics 1 Chapter Goals After completing this chapter, you should be able to: Formulate

### T-test in SPSS Hypothesis tests of proportions Confidence Intervals (End of chapter 6 material)

T-test in SPSS Hypothesis tests of proportions Confidence Intervals (End of chapter 6 material) Definition of p-value: The probability of getting evidence as strong as you did assuming that the null hypothesis

### 3.4 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

### SAS / INSIGHT. ShortCourse Handout

SAS / INSIGHT ShortCourse Handout February 2005 Copyright 2005 Heide Mansouri, Technology Support, Texas Tech University. ALL RIGHTS RESERVED. Members of Texas Tech University or Texas Tech Health Sciences

### Hypothesis Testing. Male Female

Hypothesis Testing Below is a sample data set that we will be using for today s exercise. It lists the heights for 10 men and 1 women collected at Truman State University. The data will be entered in the

### Two 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

### Hypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam

Hypothesis Testing 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Hypothesis Testing... 3 3. Hypothesis Tests Concerning the Mean... 10 4. Hypothesis Tests

### Hypothesis Testing hypothesis testing approach formulation of the test statistic

Hypothesis Testing For the next few lectures, we re going to look at various test statistics that are formulated to allow us to test hypotheses in a variety of contexts: In all cases, the hypothesis testing

### UNIX Operating Environment

97 CHAPTER 14 UNIX Operating Environment Specifying File Attributes for UNIX 97 Determining the SAS Release Used to Create a Member 97 Creating a Transport File on Tape 98 Copying the Transport File from

### SPSS Guide: Tests of Differences

SPSS Guide: Tests of Differences I put this together to give you a step-by-step guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar

### Confidence Intervals for One Standard Deviation Using Standard Deviation

Chapter 640 Confidence Intervals for One Standard Deviation Using Standard Deviation Introduction This routine calculates the sample size necessary to achieve a specified interval width or distance from

### Point-Biserial and Biserial Correlations

Chapter 302 Point-Biserial and Biserial Correlations Introduction This procedure calculates estimates, confidence intervals, and hypothesis tests for both the point-biserial and the biserial correlations.

### Pearson'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

### Guide for SPSS for Windows

Guide for SPSS for Windows Index Table Open an existing data file Open a new data sheet Enter or change data value Name a variable Label variables and data values Enter a categorical data Delete a record

### NCSS 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

### Chapter Additional: Standard Deviation and Chi- Square

Chapter Additional: Standard Deviation and Chi- Square Chapter Outline: 6.4 Confidence Intervals for the Standard Deviation 7.5 Hypothesis testing for Standard Deviation Section 6.4 Objectives Interpret

### Chapter 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,

### General Procedure for Hypothesis Test. Five types of statistical analysis. 1. Formulate H 1 and H 0. General Procedure for Hypothesis Test

Five types of statistical analysis General Procedure for Hypothesis Test Descriptive Inferential Differences Associative Predictive What are the characteristics of the respondents? What are the characteristics

### 1 SAMPLE SIGN TEST. Non-Parametric Univariate Tests: 1 Sample Sign Test 1. A non-parametric equivalent of the 1 SAMPLE T-TEST.

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.

### Independent 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

### Point 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

### Chapter 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

### Chapter Five: Paired Samples Methods 1/38

Chapter Five: Paired Samples Methods 1/38 5.1 Introduction 2/38 Introduction Paired data arise with some frequency in a variety of research contexts. Patients might have a particular type of laser surgery

### Confidence Intervals for the Difference Between Two Means

Chapter 47 Confidence Intervals for the Difference Between Two Means Introduction This procedure calculates the sample size necessary to achieve a specified distance from the difference in sample means

### Introduction to Hypothesis Testing. Point estimation and confidence intervals are useful statistical inference procedures.

Introduction to Hypothesis Testing Point estimation and confidence intervals are useful statistical inference procedures. Another type of inference is used frequently used concerns tests of hypotheses.

### HYPOTHESIS 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

### Comparing Two or more than Two Groups

CRJ 716 Using Computers in Social Research Comparing Two or more than Two Groups Comparing Means, Conducting T-Tests and ANOVA Agron Kaci John Jay College Chapter 9/1: Comparing Two or more than Two Groups

### Hypothesis Testing or How to Decide to Decide Edpsy 580

Hypothesis Testing or How to Decide to Decide Edpsy 580 Carolyn J. Anderson Department of Educational Psychology University of Illinois at Urbana-Champaign Hypothesis Testing or How to Decide to Decide

### HYPOTHESIS 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,

### Chapter 11-12 1 Review

Chapter 11-12 Review Name 1. In formulating hypotheses for a statistical test of significance, the null hypothesis is often a statement of no effect or no difference. the probability of observing the data

### Statistical Significance and Bivariate Tests

Statistical Significance and Bivariate Tests BUS 735: Business Decision Making and Research 1 1.1 Goals Goals Specific goals: Re-familiarize ourselves with basic statistics ideas: sampling distributions,

### Part 1 Running a Hypothesis Test in Rcmdr

Math 17, Section 2 Spring 2011 Lab 7 Name SOLUTIONS Goal: To gain experience with hypothesis tests for a proportion Part 1 Running a Hypothesis Test in Rcmdr The goal of this part of the lab is to become

### This tutorial explains how to perform one sample, two sample, and paired t tests in Excel.

1 This tutorial explains how to perform one sample, two sample, and paired t tests in Excel. One Sample T test One sample t tests test whether the population mean underlying a sample set of numbers is

### SPSS: Descriptive and Inferential Statistics. For Windows

For Windows August 2012 Table of Contents Section 1: Summarizing Data...3 1.1 Descriptive Statistics...3 Section 2: Inferential Statistics... 10 2.1 Chi-Square Test... 10 2.2 T tests... 11 2.3 Correlation...

### Statistics and research

Statistics and research Usaneya Perngparn Chitlada Areesantichai Drug Dependence Research Center (WHOCC for Research and Training in Drug Dependence) College of Public Health Sciences Chulolongkorn University,

### Chapter 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

### Unit 29 Chi-Square Goodness-of-Fit Test

Unit 29 Chi-Square Goodness-of-Fit Test Objectives: To perform the chi-square hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni

### Data 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

### BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420

BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420 1. Which of the following will increase the value of the power in a statistical test

### HYPOTHESIS 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

### Use Excel to Analyse Data. Use Excel to Analyse Data

Introduction This workbook accompanies the computer skills training workshop. The trainer will demonstrate each skill and refer you to the relevant page at the appropriate time. This workbook can also

### Lesson 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

### CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY

CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY The hypothesis testing statistics detailed thus far in this text have all been designed to allow comparison of the means of two or more samples

### Chapter 16 Appendix. Nonparametric Tests with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83-/84 Calculators

The Wilcoxon Rank Sum Test Chapter 16 Appendix Nonparametric Tests with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83-/84 Calculators These nonparametric tests make no assumption about Normality.

### Confidence Intervals for Cp

Chapter 296 Confidence Intervals for Cp Introduction This routine calculates the sample size needed to obtain a specified width of a Cp confidence interval at a stated confidence level. Cp is a process

### The alternative hypothesis,, is the statement that the parameter value somehow differs from that claimed by the null hypothesis. : 0.5 :>0.5 :<0.

Section 8.2-8.5 Null and Alternative Hypotheses... The null hypothesis,, is a statement that the value of a population parameter is equal to some claimed value. :=0.5 The alternative hypothesis,, is the

### Inferential Statistics

Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

### Box plots & t-tests. Example

Box plots & t-tests Box Plots Box plots are a graphical representation of your sample (easy to visualize descriptive statistics); they are also known as box-and-whisker diagrams. Any data that you can

### Introduction to Hypothesis Testing. Copyright 2014 Pearson Education, Inc. 9-1

Introduction to Hypothesis Testing 9-1 Learning Outcomes Outcome 1. Formulate null and alternative hypotheses for applications involving a single population mean or proportion. Outcome 2. Know what Type

### A Quick Guide to Confidence Intervals and Hypotheses Tests Using the TI-Calc AP Statistics

Example: Confidence Intervals for One Proportion In January 2007, Consumer Reports conducted a study of bacteria in frozen chicken sold in the US. They purchased a random selection of 525 packages of frozen

### Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1

Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1 Calculate counts, means, and standard deviations Produce

### KSTAT 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

### Testing: is my coin fair?

Testing: is my coin fair? Formally: we want to make some inference about P(head) Try it: toss coin several times (say 7 times) Assume that it is fair ( P(head)= ), and see if this assumption is compatible

### E205 Final: Version B

Name: Class: Date: E205 Final: Version B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of a local nightclub has recently surveyed a random

### How to Conduct a Hypothesis Test

How to Conduct a Hypothesis Test The idea of hypothesis testing is relatively straightforward. In various studies we observe certain events. We must ask, is the event due to chance alone, or is there some

### CHAPTER 9 HYPOTHESIS TESTING

CHAPTER 9 HYPOTHESIS TESTING The TI-83 Plus and TI-84 Plus fully support hypothesis testing. Use the key, then highlight TESTS. The options used in Chapter 9 are given on the two screens. TESTING A SINGLE

### Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation

Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.

### Null Hypothesis H 0. The null hypothesis (denoted by H 0

Hypothesis test In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing a claim about a property

### Opgaven 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

### Hypothesis Testing. Hypothesis Testing CS 700

Hypothesis Testing CS 700 1 Hypothesis Testing! Purpose: make inferences about a population parameter by analyzing differences between observed sample statistics and the results one expects to obtain if

### Chapter 8. Hypothesis Testing

Chapter 8 Hypothesis Testing Hypothesis In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing

### Statistiek I. t-tests. John Nerbonne. CLCG, Rijksuniversiteit Groningen. John Nerbonne 1/35

Statistiek I t-tests John Nerbonne CLCG, Rijksuniversiteit Groningen http://wwwletrugnl/nerbonne/teach/statistiek-i/ John Nerbonne 1/35 t-tests To test an average or pair of averages when σ is known, we

### Chapter 25 Specifying Forecasting Models

Chapter 25 Specifying Forecasting Models Chapter Table of Contents SERIES DIAGNOSTICS...1281 MODELS TO FIT WINDOW...1283 AUTOMATIC MODEL SELECTION...1285 SMOOTHING MODEL SPECIFICATION WINDOW...1287 ARIMA

### MCQ TESTING OF HYPOTHESIS

MCQ TESTING OF HYPOTHESIS MCQ 13.1 A statement about a population developed for the purpose of testing is called: (a) Hypothesis (b) Hypothesis testing (c) Level of significance (d) Test-statistic MCQ

### Outline of Topics. Statistical Methods I. Types of Data. Descriptive Statistics

Statistical Methods I Tamekia L. Jones, Ph.D. (tjones@cog.ufl.edu) Research Assistant Professor Children s Oncology Group Statistics & Data Center Department of Biostatistics Colleges of Medicine and Public

### Hypothesis 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.

### Statistical foundations of machine learning

Machine learning p. 1/45 Statistical foundations of machine learning INFO-F-422 Gianluca Bontempi Département d Informatique Boulevard de Triomphe - CP 212 http://www.ulb.ac.be/di Machine learning p. 2/45

### NCSS 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

### EXST SAS Lab Lab #9: Two-sample t-tests

EXST700X Lab Spring 014 EXST SAS Lab Lab #9: Two-sample t-tests Objectives 1. Input a CSV file (data set #1) and do a one-tailed two-sample t-test. Input a TXT file (data set #) and do a two-tailed two-sample

### Multiple One-Sample or Paired T-Tests

Chapter 610 Multiple One-Sample or Paired T-Tests Introduction This chapter describes how to estimate power and sample size (number of arrays) for paired and one sample highthroughput studies using the.

### 9.1 SAS. SQL Query Window. User s Guide

SAS 9.1 SQL Query Window User s Guide The correct bibliographic citation for this manual is as follows: SAS Institute Inc. 2004. SAS 9.1 SQL Query Window User s Guide. Cary, NC: SAS Institute Inc. SAS

### User Installation Guide for SAS 9.1 Foundation for 64-bit Microsoft Windows

User Installation Guide for SAS 9.1 Foundation for 64-bit Microsoft Windows Installation Instructions Where to Begin SAS Setup Wizard Repair or Remove SAS Software Glossary Where to Begin Most people who

### C. 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

Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology Step-by-Step - Excel Microsoft Excel is a spreadsheet software application

### c. The factor is the type of TV program that was watched. The treatment is the embedded commercials in the TV programs.

STAT E-150 - Statistical Methods Assignment 9 Solutions Exercises 12.8, 12.13, 12.75 For each test: Include appropriate graphs to see that the conditions are met. Use Tukey's Honestly Significant Difference

### Tests for Two Proportions

Chapter 200 Tests for Two Proportions Introduction This module computes power and sample size for hypothesis tests of the difference, ratio, or odds ratio of two independent proportions. The test statistics