The Chi-Square Test. STAT E-50 Introduction to Statistics
|
|
- Junior Daniels
- 1 years ago
- Views:
Transcription
1 STAT -50 Introduction to Statistics The Chi-Square Test The Chi-square test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed frequencies with expected frequencies. In a hypothesis test, the expected frequencies are those we would expect if the null hypothesis our test is true. O The formula is where O represents the observed frequency and represents the expected frequency. The value df depends on the type test you are performing. The Chi-Square Distribution The χ distribution is nonnegative not symmetrical; it is skewed to the right distributed to form a family distributions, with a separate distribution for each different degrees freedom. The Chi-Square Test for Goodness Fit The goodness--fit test compares the distribution observed outcomes for a single categorical variable to the expected outcomes predicted by a probability model. This test involves one sample, and one variable. Assumptions and Conditions: Be sure that the data is counts, or frequencies Independence assumption Sample size assumption xpected cell frequency condition: each expected frequency is at least The Chi-square test is one-sided 0 (df, α) Automobile insurance is much more expensive for teenage than for older. To justify this cost difference, insurance companies claim that the younger are much more likely to be involved in costly. To test this claim, a researcher obtains information about registered from the Department Motor Vehicles and selects a sample 300 accident reports from the police department. The DMV reports the age registered in each age category as reported below. The accident reports is also shown. Does this data indicate that occur with the same distribution as the ages the? H 0 : H a : 5 6 1
2 Automobile insurance is much more expensive for teenage than for older. To justify this cost difference, insurance companies claim that the younger are much more likely to be involved in costly. To test this claim, a researcher obtains information about registered from the Department Motor Vehicles and selects a sample 300 accident reports from the police department. The DMV reports the age registered in each age category as reported below. The accident reports is also shown. Does this data indicate that occur with the same distribution as the ages the? H 0 : The distribution the ages involved in is the same as the distribution the ages registered. H a : The distribution the ages involved in is not the same as the distribution the ages registered. xpected cell frequency condition Under or over (this is the data) expected O - (O - ) (O - ) 7 8 xpected cell frequency condition xpected cell frequency condition Under or over n = Note: Σ observed = Σ expected expected O - (O - ) (O - ) Under or over n = Note: Σ observed = Σ expected expected O - (O - ) (O - ) 9 10 xpected cell frequency condition xpected cell frequency condition Under or over n = Note: Σ observed = Σ expected expected O - (O - ) (O - ) Under or over n = Note: Σ observed = Σ expected expected O - (O - ) (O - ) 11 1
3 xpected cell frequency condition - each expected frequency 5 Under or over n = Note: Σ observed = Σ expected expected O - (O - ) (O - ) 13 expected O - (O - ) (O - ) Under or over Specify the sampling distribution model and the test you will use. O, with df = k-1 = df = 14 expected O - (O - ) (O - ) Under or over Note: Σ(O - ) = 0 Specify the sampling distribution model and the test you will use. expected O - (O - ) (O - ) Under or over Note: Σ(O - ) = 0 Specify the sampling distribution model and the test you will use. O, with df = k-1 O, with df = k-1 = df = = df = expected O - (O - ) (O - ) Under or over expected O - (O - ) (O - ) Under or over Specify the sampling distribution model and the test you will use. Since the conditions are met, we will use a Chi-square model with degrees freedom, and do a Chi-square goodness--fit test. O, with df = k-1 = df = 17 O, with df = k-1 = df = 3-1 = P-value: 18 3
4 = df = 3-1 = P-value: P <.005 Statistical conclusion: Conclusion in context: expected O - (O - ) (O - ) Under or over expected O - (O - ) (O - ) Under or over = df = 3-1 = Using SPSS for a Goodness Fit Test If you have the expected proportions: 1. Create a numeric variable with a width 1 and no decimal places for the categories. Code the values this variable as follows: In the Values column, click on the box with the three dots: P-value: P <.005 Statistical conclusion: Since the p-value is small, reject the null hypothesis. Conclusion in context: The data indicates that the distribution ages involved in is not the same as the distribution ages the in the population. 1 You will then see the Value Labels dialog box. Since there are three categories ages, enter the values 1,, and 3 as coding variables: Then click on Add and you will see the results: nter the value "1" and code it as "under 0". (You do not have to use quotation marks; they will be added by SPSS.) 3 4 4
5 Continue adding all categories, one at a time, and then click on OK. You will see the results in the Values column in Variable View Create a numeric variable with no decimal places for the observed frequencies. You can then enter the observed frequency for that category. Then, for each category, enter the coded value: Repeat this until all observed frequencies have been entered: As you enter each value you will see a drop-down box. If you click on it, you can choose from the list labels. However, if you just move to the next column, you will see the category name associated with the coded value Weight the cases using the observed frequencies. 4. Now select > Analyze > Nonparametric Tests > Legacy Dialogs > Chi-Square
6 5. Select the variable with the observed frequencies as the Test Variable In the xpected Values box, select Values: 6. nter the expected s (as decimals) one at a time, and click on Add until all have been entered: nter the expected s (as decimals) one at a time, and click on Add until all have been entered: 7. After the last value has been entered, click on OK. You should see a table showing the observed and expected frequencies and a table with the results the Chi-square test: count Observed N xpected N Residual Test Statistics count Chi-Square a df Asymp. Sig..001 a. 0 cells (.0%) have expected frequencies less than 5. The minimum expected cell frequency is These results show that χ = 13.76, and p =.001 (Note that you also have the option to choose All categories equal if that is appropriate.) The Chi-Square Test for Homogeneity In a test for homogeneity, we compare observed distributions for several groups to see if there are differences among the respective populations. The central issue is whether the category proportions are the same for all the populations. The test involves several samples but only one variable. The article Relationship Health Behaviors to Alcohol and Cigarette Use by College Students (J. College Student Development (199)) included data on drinking behavior for independently chosen random samples male and female students similar to the data shown below. Does there appear to be a gender difference with respect to drinking behavior? None 140 ( ) 186 ( ) Low (1-7) 478 ( ) 661 ( ) Moderate (8-4) 300 ( ) 173 ( ) High (5 or more) 63 ( ) 16 ( )
7 The Chi-Square Test for Homogeneity Assumptions and Conditions: Be sure that the data is counts, or frequencies Independence assumption If you want to generalize from the data to a population. Sample size assumption xpected cell frequency condition ach expected frequency is at least 5 The article Relationship Health Behaviors to Alcohol and Cigarette Use by College Students (J. College Student Development (199)) included data on drinking behavior for independently chosen random samples male and female students similar to the data shown below. Does there appear to be a gender difference with respect to drinking behavior? H 0 : H a : xpected cell frequency condition The article Relationship Health Behaviors to Alcohol and Cigarette Use by College Students (J. College Student Development (199)) included data on drinking behavior for independently chosen random samples male and female students similar to the data shown below. Does there appear to be a gender difference with respect to drinking behavior? H 0 : The proportions the four drinking levels are the same for males and for females H a : The proportions the four drinking levels are not the same for males and for females xpected cell frequency condition: (row total)(column total) n 39 Specify the sampling distribution model and the test you will use. df = (R - 1)(C - 1) None 140 ( ) 186 ( ) Low (1-7) 478 ( ) 661 ( ) Moderate (8-4) 300 ( ) 173 ( ) High (5 or more) 63 ( ) 16 ( ) 40 None 140 ( ) 186 ( ) Low (1-7) 478 ( ) 661 ( ) Moderate (8-4) 300 ( ) 173 ( ) High (5 or more) 63 ( ) 16 ( ) None 140 ( ) 186 ( ) Low (1-7) 478 ( ) 661 ( ) Moderate (8-4) 300 ( ) 173 ( ) High (5 or more) 63 ( ) 16 ( ) Specify the sampling distribution model and the test you will use. df = (R - 1)(C - 1) = (4-1)( - 1) = (3)(1) = 3 Fill in the row and column totals. The conditions are met, so we will use a Chi-square model with 3 degrees freedom, and do a Chi-square test homogeneity
8 None 140 ( ) 186 ( ) 36 Low (1-7) 478 ( ) 661 ( ) 1139 Moderate (8-4) 300 ( ) 173 ( ) 473 High (5 or more) 63 ( ) 16 ( ) None 140 ( ) 186 ( ) 36 Low (1-7) 478 ( ) 661 ( ) 1139 Moderate (8-4) 300 ( ) 173 ( ) 473 High (5 or more) 63 ( ) 16 ( ) Calculate the expected frequencies for each cell, using (row total)(column total) = n Calculate the expected frequencies for each cell, using (row total)(column total) = n None 140 ( ) 186 ( ) 36 Low (1-7) 478 ( ) 661 ( ) 1139 Moderate (8-4) 300 ( ) 173 ( ) 473 High (5 or more) 63 ( ) 16 ( ) Calculate the expected frequencies for each cell, using (row total)(column total) = n O None 140 ( ) 186 ( ) 36 Low (1-7) 478 ( ) 661 ( ) 1139 Moderate (8-4) 300 ( ) 173 ( 4.95 ) 473 High (5 or more) 63 ( 38.4 ) 16 ( ) O.17 + None 140 ( ) 186 ( ) 36 Low (1-7) 478 ( ) 661 ( ) 1139 Moderate (8-4) 300 ( ) 173 ( 4.95 ) 473 High (5 or more) 63 ( 38.4 ) 16 ( ) O None 140 ( ) 186 ( ) 36 Low (1-7) 478 ( ) 661 ( ) 1139 Moderate (8-4) 300 ( ) 173 ( 4.95 ) 473 High (5 or more) 63 ( 38.4 ) 16 ( )
9 O None 140 ( ) 186 ( ) 36 Low (1-7) 478 ( ) 661 ( ) 1139 Moderate (8-4) 300 ( ) 173 ( 4.95 ) 473 High (5 or more) 63 ( 38.4 ) 16 ( ) O = None 140 ( ) 186 ( ) 36 Low (1-7) 478 ( ) 661 ( ) 1139 Moderate (8-4) 300 ( ) 173 ( 4.95 ) 473 High (5 or more) 63 ( 38.4 ) 16 ( ) O None 140 ( ) 186 ( ) 36 Low (1-7) 478 ( ) 661 ( ) 1139 Moderate (8-4) 300 ( ) 173 ( 4.95 ) 473 High (5 or more) 63 ( 38.4 ) 16 ( ) = The article Relationship Health Behaviors to Alcohol and Cigarette Use by College Students (J. College Student Development (199)) included data on drinking behavior for independently chosen random samples male and female students similar to the data shown below. Does there appear to be a gender difference with respect to drinking behavior? H 0 : The proportions the four drinking levels are the same for males and females H a : The proportions the four drinking levels are not the same for males and females = df = 3 P-value: p <.005 Statistical conclusion: Conclusion in context: The article Relationship Health Behaviors to Alcohol and Cigarette Use by College Students (J. College Student Development (199)) included data on drinking behavior for independently chosen random samples male and female students similar to the data shown below. Does there appear to be a gender difference with respect to drinking behavior? H 0 : The proportions the four drinking levels are the same for males and females H a : The proportions the four drinking levels are not the same for males and females = df = 3 P-value: p <.005 Statistical conclusion: p is small, so the null hypothesis is rejected Conclusion in context: The data does indicate a gender difference with respect to drinking behavior
10 Using SPSS for a Test for Homogeneity 1. Create a string variable for each the categories, and a numeric variable for the observed frequencies. Be sure to make the columns wide enough ("columns" in Variable View). 3. Select > Analyze > Descriptive Statistics > Crosstabs Select one variable as the row variable and the other as the column variable. Click on Statistics and then on Chi-square. Then enter the values these two variables:. Weight the cases using the observed frequencies. (> Data > Weight Cases ) Click on the Cells button, and select Observed and xpected in the Cell Display window. Then click on Continue. Your output should include a table showing the observed and expected frequencies: Click on Display clustered bar charts to produce the graph shown in the results. Click on Continue and then click on OK. gender * level Crosstabulation level high low moderate none gender female Count xpected Count male Count xpected Count Count xpected Count and a table with the results your Chi-square test: Here is the graph that represents the results: Chi-Square Tests Value df Asymp. Sig. (- sided) Pearson Chi-Square a Likelihood Ratio N Valid Cases 017 a. 0 cells (.0%) have expected count less than 5. The minimum expected count is These results show that χ = 96.56, and p =
11 The Chi-Square Test for Independence In a test for independence, we investigate association between two categorical variables in a single population. There is one sample, but there are two variables. Assumptions and Conditions: If you want to generalize from the data to a population. xpected cell frequency condition 61 The table shown below was constructed using data in the article Television Viewing and Physical Fitness in Adults (Research Quarterly for xercise and Sport (1990)). The author hoped to determine whether time spent watching television is associated with cardiovascular fitness. Subjects were asked about their television viewing time (per day, rounded to the nearest hour) and were classified as physically fit if they scored in the excellent or very good category on a step test. H o : H a : 0 35 ( ) 147 ( ) ( ) 69 ( ) ( ) ( ) 5 or more 4 ( ) 34 ( ) 6 The table shown below was constructed using data in the article Television Viewing and Physical Fitness in Adults (Research Quarterly for xercise and Sport (1990)). The author hoped to determine whether time spent watching television is associated with cardiovascular fitness. Subjects were asked about their television viewing time (per day, rounded to the nearest hour) and were classified as physically fit if they scored in the excellent or very good category on a step test. xpected cell frequency condition 0 35 ( ) 147 ( ) ( ) 69 ( ) ( ) ( ) 5 or more 4 ( ) 34 ( ) H o : Fitness and TV viewing are independent H a : Fitness and TV viewing are not independent ( ) 147 ( ) ( ) 69 ( ) ( ) ( ) 5 or more 4 ( ) 34 ( ) Specify the sampling distribution model and the test you will use ( ) 147 ( ) ( ) 69 ( ) ( ) ( ) 5 or more 4 ( ) 34 ( ) Find the row and column totals. df = (R - 1)(C - 1) = (4-1)( - 1) = (3)(1) = 3 Since the conditions are met, we will use a Chi-square model with 3 degrees freedom, and do a Chi-square test for independence
12 0 35 ( ) 147 ( ) ( ) 69 ( ) ( ) ( ) 50 5 or more 4 ( ) 34 ( ) ( 5.48 ) 147 ( ) ( 10.0 ) 69 ( ) ( ) ( ) 50 5 or more 4 ( 5.3 ) 34 ( ) (row total)(column total) = n (row total)(column total) = n ( 5.48 ) 147 ( ) ( 10.0 ) 69 ( ) ( ) ( ) 50 5 or more 4 ( 5.3 ) 34 ( 3.68 ) ( 5.48 ) 147 ( ) ( 10.0 ) 69 ( ) ( ) ( ) 50 5 or more 4 ( 5.3 ) 34 ( 3.68 ) (row total)(column total) = n O ( 5.48 ) 147 ( ) ( 10.0 ) 69 ( ) ( ) ( ) 50 5 or more 4 ( 5.3 ) 34 ( 3.68 ) ( 5.48 ) 147 ( ) ( 10.0 ) 69 ( ) ( ) ( ) 50 5 or more 4 ( 5.3 ) 34 ( 3.68 ) O O =
13 6.161 df = ( 5.48 ) 147 ( ) ( 10.0 ) 69 ( ) ( ) ( ) 50 5 or more 4 ( 5.3 ) 34 ( 3.68 ) P-value: df = ( 5.48 ) 147 ( ) ( 10.0 ) 69 ( ) ( ) ( ) 50 5 or more 4 ( 5.3 ) 34 ( 3.68 ) df = ( 5.48 ) 147 ( ) ( 10.0 ) 69 ( ) ( ) ( ) 50 5 or more 4 ( 5.3 ) 34 ( 3.68 ) P-value: p >.10 Statistical conclusion: Conclusion in context: 75 P-value: p >.10 Statistical conclusion: Since the p-value is large, we cannot reject the null hypothesis. Conclusion in context: There is not enough evidence to conclude that time spent watching television is associated with cardiovascular fitness. 76 Using SPSS for a Test for Independence Then enter the frequencies as before: Follow the instructions for a Chi-Square test for homogeneity. You may define two string variables for the categories and one numeric variable for the counts, or you may choose to use coding for one or either the variables representing the categories
14 Weight the cases by counts, and then use > Analyze > Descriptive Statistics > Crosstabs SPSS output: Select one variable as the row variable and the other as the column variable. TVGroup * Fitness Crosstabulation Fitness Fit Not Fit Click on Statistics and then on Chi-square. Click on the Cells button, and select Observed and xpected in the Cell Display window. Click on Display clustered bar charts to produce the graph shown in the results. Then click on Continue and on OK. TVGroup 0 Count xpected Count Count xpected Count Count 8 50 xpected Count or more Count xpected Count Count xpected Count SPSS output: Here is the graph that supports these results: Chi-Square Tests Value df Asymp. Sig. (- sided) Pearson Chi-Square a Likelihood Ratio N Valid Cases 100 a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.3. These results show that χ = and p = A health pressional selected a random sample 100 patients from each four major hospital emergency rooms to see if the major reasons for emergency room visits (accident, illegal activity, illness, other) are the same in all four hospitals. This is an example a. A goodness--fit test b. A test for homogeneity c. A test for independence 1. A health pressional selected a random sample 100 patients from each four major hospital emergency rooms to see if the major reasons for emergency room visits (accident, illegal activity, illness, other) are the same in all four hospitals. This is an example a. A goodness--fit test b. A test for homogeneity c. A test for independence
15 . An urban economist wants to determine whether the region the United States a resident lives in is related to his level education. He randomly selects 1800 US residents and asks them to report their level education and the region the US in which they live. The economist is using a. A goodness--fit test b. A test for homogeneity c. A test for independence. An urban economist wants to determine whether the region the United States a resident lives in is related to his level education. He randomly selects 1800 US residents and asks them to report their level education and the region the US in which they live. The economist is using a. A goodness--fit test b. A test for homogeneity c. A test for independence As part a class project, a student asked a random sample students about their preferred st drink: Pepsi, Coke, or 7-Up, to determine whether these three drinks were equally preferred by students. 3. As part a class project, a student asked a random sample students about their preferred st drink: Pepsi, Coke, or 7-Up, to determine whether these three drinks were equally preferred by students. The student should use a. A goodness--fit test b. A test for homogeneity c. A test for independence The student should use a. A goodness--fit test b. A test for homogeneity c. A test for independence
Module 9: Nonparametric Tests. The Applied Research Center
Module 9: Nonparametric Tests The Applied Research Center Module 9 Overview } Nonparametric Tests } Parametric vs. Nonparametric Tests } Restrictions of Nonparametric Tests } One-Sample Chi-Square Test
Directions for Chi-Square for One and for Two Variables Datasets: One_way_chi_square.sav and Two_way_Chi_square.sav. One-way Chi-square
Directions for Chi-Square for One and for Two Variables Datasets: One_way_chi_square.sav and Two_way_Chi_square.sav One-way Chi-square 1. Open the dataset containing the already grouped frequency of student
Chi-Square Analysis (Ch.8) Purpose. Purpose. Examples
Chi-Square Analysis (Ch.8) Chi-square test of association (contingency) x tables rxc tables Post-hoc Interpretation Running SPSS Windows CROSSTABS Chi-square test of goodness of fit Purpose Chi-square
13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations.
13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations. Data is organized in a two way table Explanatory variable (Treatments)
SPSS Workbook 3 Chi-squared & Correlation
TEESSIDE UNIVERSITY SCHOOL OF HEALTH & SOCIAL CARE SPSS Workbook 3 Chi-squared & Correlation Research, Audit and data RMH 2023-N Module Leader:Sylvia Storey Phone:016420384969 s.storey@tees.ac.uk 1 SPSS
SPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)
Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer
Chapter 11. Chapter 11 Overview. Chapter 11 Objectives 11/24/2015. Other Chi-Square Tests
11/4/015 Chapter 11 Overview Chapter 11 Introduction 11-1 Test for Goodness of Fit 11- Tests Using Contingency Tables Other Chi-Square Tests McGraw-Hill, Bluman, 7th ed., Chapter 11 1 Bluman, Chapter 11
The Chi-Square Goodness-of-Fit Test, Equal Proportions
Chapter 11 Chi-Square Tests 1 Chi-Square Tests Chapter 11 The Chi-Square Goodness-of-Fit Test, Equal Proportions A hospital wants to know if the proportion of births are the same for each day of the week.
General Guidelines about SPSS. Steps needed to enter the data in the SPSS
General Guidelines about SPSS The entered data has to be numbers and not letters. For example, in the Gender section, we can not write Male and Female in the answers, however, we must give them a code.
Is it statistically significant? The chi-square test
UAS Conference Series 2013/14 Is it statistically significant? The chi-square test Dr Gosia Turner Student Data Management and Analysis 14 September 2010 Page 1 Why chi-square? Tests whether two categorical
Chapter 11: Chi-square (χ 2 )
Chapter 11: Chi-square (χ 2 ) *This chapter corresponds with Chapter 16 in your text ( What to do when you re not normal ). What it is: Chi-square is a nonparametric statistic. This means that it can be
An introduction to IBM SPSS Statistics
An introduction to IBM SPSS Statistics Contents 1 Introduction... 1 2 Entering your data... 2 3 Preparing your data for analysis... 10 4 Exploring your data: univariate analysis... 14 5 Generating descriptive
Chi Square Test. PASSS Research Question 4: Chi Square Test
Chi Square Test Is there a statistically significant relationship between a student s Year 11 truancy and his or her enrolment in full time education after secondary school? A chi-square test is a statistical
Chi Square Goodness of Fit & Two-way Tables (Create) MATH NSPIRED
Overview In this activity, you will look at a setting that involves categorical data and determine which is the appropriate chi-square test to use. You will input data into a list or matrix and conduct
Chi square. Response Vowel in Response Choice # of Observed # of Expected Choices Responses Responses
Chi square Chi-square uses categorical data. It looks at how many things fall into different categories, and calculates whether the probability of obtaining those count is significantly different from
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
The Chi Square Test. Diana Mindrila, Ph.D. Phoebe Balentyne, M.Ed. Based on Chapter 23 of The Basic Practice of Statistics (6 th ed.
The Chi Square Test Diana Mindrila, Ph.D. Phoebe Balentyne, M.Ed. Based on Chapter 23 of The Basic Practice of Statistics (6 th ed.) Concepts: Two-Way Tables The Problem of Multiple Comparisons Expected
Nonparametric Tests. Chi-Square Test for Independence
DDBA 8438: Nonparametric Statistics: The Chi-Square Test Video Podcast Transcript JENNIFER ANN MORROW: Welcome to "Nonparametric Statistics: The Chi-Square Test." My name is Dr. Jennifer Ann Morrow. In
We know from STAT.1030 that the relevant test statistic for equality of proportions is:
2. Chi 2 -tests for equality of proportions Introduction: Two Samples Consider comparing the sample proportions p 1 and p 2 in independent random samples of size n 1 and n 2 out of two populations which
Chi-Square Test (χ 2 )
Chi Square Tests Chi-Square Test (χ 2 ) Nonparametric test for nominal independent variables These variables, also called "attribute variables" or "categorical variables," classify observations into a
Bivariate Statistics Session 2: Measuring Associations Chi-Square Test
Bivariate Statistics Session 2: Measuring Associations Chi-Square Test Features Of The Chi-Square Statistic The chi-square test is non-parametric. That is, it makes no assumptions about the distribution
1. Chi-Squared Tests
1. Chi-Squared Tests We'll now look at how to test statistical hypotheses concerning nominal data, and specifically when nominal data are summarized as tables of frequencies. The tests we will considered
Chi-Square Tests and the F-Distribution. Goodness of Fit Multinomial Experiments. Chapter 10
Chapter 0 Chi-Square Tests and the F-Distribution 0 Goodness of Fit Multinomial xperiments A multinomial experiment is a probability experiment consisting of a fixed number of trials in which there are
Hypothesis Testing for a Proportion
Math 122 Intro to Stats Chapter 6 Semester II, 2015-16 Inference for Categorical Data Hypothesis Testing for a Proportion In a survey, 1864 out of 2246 randomly selected adults said texting while driving
Main Effects and Interactions
Main Effects & Interactions page 1 Main Effects and Interactions So far, we ve talked about studies in which there is just one independent variable, such as violence of television program. You might randomly
SPSS Bivariate Statistics
SPSS Bivariate Statistics Social Science Research Lab American University, Washington, D.C. Web. www.american.edu/provost/ctrl/pclabs.cfm Tel. x3862 Email. SSRL@American.edu Course Objectives In this tutorial
Using SPSS to perform Chi-Square tests:
Using SPSS to perform Chi-Square tests: Graham Hole, January 2006: page 1: Using SPSS to perform Chi-Square tests: This handout explains how to perform the two types of Chi-Square test that were discussed
Simple Linear Regression in SPSS STAT 314
Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year s sales records in Virginia Beach, Virginia. The following data were obtained,
SPSS: Expected frequencies, chi-squared test. In-depth example: Age groups and radio choices. Dealing with small frequencies.
SPSS: Expected frequencies, chi-squared test. In-depth example: Age groups and radio choices. Dealing with small frequencies. Quick Example: Handedness and Careers Last time we tested whether one nominal
CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS
CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS CHI-SQUARE TESTS OF INDEPENDENCE (SECTION 11.1 OF UNDERSTANDABLE STATISTICS) In chi-square tests of independence we use the hypotheses. H0: The variables are independent
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
Chi Square Analysis. When do we use chi square?
Chi Square Analysis When do we use chi square? More often than not in psychological research, we find ourselves collecting scores from participants. These data are usually continuous measures, and might
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
SPSS TUTORIAL & EXERCISE BOOK
UNIVERSITY OF MISKOLC Faculty of Economics Institute of Business Information and Methods Department of Business Statistics and Economic Forecasting PETRA PETROVICS SPSS TUTORIAL & EXERCISE BOOK FOR BUSINESS
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
6 Comparison of differences between 2 groups: Student s T-test, Mann-Whitney U-Test, Paired Samples T-test and Wilcoxon Test
6 Comparison of differences between 2 groups: Student s T-test, Mann-Whitney U-Test, Paired Samples T-test and Wilcoxon Test Having finally arrived at the bottom of our decision tree, we are now going
Chapter 23. Inferences for Regression
Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily
MATH 10: Elementary Statistics and Probability Chapter 11: The Chi-Square Distribution
MATH 10: Elementary Statistics and Probability Chapter 11: The Chi-Square Distribution Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of slides,
Analysis of categorical data: Course quiz instructions for SPSS
Analysis of categorical data: Course quiz instructions for SPSS The dataset Please download the Online sales dataset from the Download pod in the Course quiz resources screen. The filename is smr_bus_acd_clo_quiz_online_250.xls.
How to Make APA Format Tables Using Microsoft Word
How to Make APA Format Tables Using Microsoft Word 1 I. Tables vs. Figures - See APA Publication Manual p. 147-175 for additional details - Tables consist of words and numbers where spatial relationships
EPS 625 INTERMEDIATE STATISTICS FRIEDMAN TEST
EPS 625 INTERMEDIATE STATISTICS The Friedman test is an extension of the Wilcoxon test. The Wilcoxon test can be applied to repeated-measures data if participants are assessed on two occasions or conditions
Chi-square test Testing for independeny The r x c contingency tables square test
Chi-square test Testing for independeny The r x c contingency tables square test 1 The chi-square distribution HUSRB/0901/1/088 Teaching Mathematics and Statistics in Sciences: Modeling and Computer-aided
Lab #7: Chi-Square. In case you re curious, the study was published in Here s the reference:
Psychology 210 Lab #7: Chi-Square As usual, log in and launch SPSS and open up a data file. The data set of the day is called michigankids.sav and is located on the class web page. Open it up and we ll
Simple Linear Regression One Binary Categorical Independent Variable
Simple Linear Regression Does sex influence mean GCSE score? In order to answer the question posed above, we want to run a linear regression of sgcseptsnew against sgender, which is a binary categorical
Chi-square test: Germination data Dan Flynn
Chi-square test: Germination data Dan Flynn This lab examines whether the germination rates of lettuce seeds differed across the herb treatments. The Chi-square test is one of the standard methods for
IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA
CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA Summer 2013, Version 2.0 Table of Contents Introduction...2 Downloading the
IBM SPSS Statistics 23 Part 4: Chi-Square and ANOVA
IBM SPSS Statistics 23 Part 4: Chi-Square and ANOVA Winter 2016, Version 1 Table of Contents Introduction... 2 Downloading the Data Files... 2 Chi-Square... 2 Chi-Square Test for Goodness-of-Fit... 2 With
Bivariate Analysis. Comparisons of proportions: Chi Square Test (X 2 test) Variable 1. Variable 2 2 LEVELS >2 LEVELS CONTINUOUS
Bivariate Analysis Variable 1 2 LEVELS >2 LEVELS CONTINUOUS Variable 2 2 LEVELS X 2 chi square test >2 LEVELS X 2 chi square test CONTINUOUS t-test X 2 chi square test X 2 chi square test ANOVA (F-test)
Chapter 13. Chi-Square. Crosstabs and Nonparametric Tests. Specifically, we demonstrate procedures for running two separate
1 Chapter 13 Chi-Square This section covers the steps for running and interpreting chi-square analyses using the SPSS Crosstabs and Nonparametric Tests. Specifically, we demonstrate procedures for running
Odds 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
IBM SPSS Statistics for Beginners for Windows
ISS, NEWCASTLE UNIVERSITY IBM SPSS Statistics for Beginners for Windows A Training Manual for Beginners Dr. S. T. Kometa A Training Manual for Beginners Contents 1 Aims and Objectives... 3 1.1 Learning
MATH Chapter 23 April 15 and 17, 2013 page 1 of 8 CHAPTER 23: COMPARING TWO CATEGORICAL VARIABLES THE CHI-SQUARE TEST
MATH 1342. Chapter 23 April 15 and 17, 2013 page 1 of 8 CHAPTER 23: COMPARING TWO CATEGORICAL VARIABLES THE CHI-SQUARE TEST Relationships: Categorical Variables Chapter 21: compare proportions of successes
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.
χ 2 = (O i E i ) 2 E i
Chapter 24 Two-Way Tables and the Chi-Square Test We look at two-way tables to determine association of paired qualitative data. We look at marginal distributions, conditional distributions and bar graphs.
Frequency Tables. Chapter 500. Introduction. Frequency Tables. Types of Categorical Variables. Data Structure. Missing Values
Chapter 500 Introduction This procedure produces tables of frequency counts and percentages for categorical and continuous variables. This procedure serves as a summary reporting tool and is often used
11. Chi Square. Go to Data/Weight Cases and select Freq as the weights. Select Analyze/Nonparametric Tests/Chi Square.
11. Chi Square Objectives Calculate goodness of fit Chi Square Calculate Chi Square for contingency tables Calculate effect size Save data entry time by weighting cases A Chi Square is used to analyze
Example 11-3, pg. 495 The Chi-Square Goodness-of-Fit Test
132 Chapter 11 Chi-Square Tests Chi-Square Tests Chapter 11 Section 11.2 Example 11-3, pg. 495 The Chi-Square Goodness-of-Fit Test A bank manager wanted to investigate if the percentage of people who use
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...
This 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
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
Simulating Chi-Square Test Using Excel
Simulating Chi-Square Test Using Excel Leslie Chandrakantha John Jay College of Criminal Justice of CUNY Mathematics and Computer Science Department 524 West 59 th Street, New York, NY 10019 lchandra@jjay.cuny.edu
Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
A Guide for a Selection of SPSS Functions
A Guide for a Selection of SPSS Functions IBM SPSS Statistics 19 Compiled by Beth Gaedy, Math Specialist, Viterbo University - 2012 Using documents prepared by Drs. Sheldon Lee, Marcus Saegrove, Jennifer
Technology Step-by-Step Using StatCrunch
Technology Step-by-Step Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate
Allelopathic Effects on Root and Shoot Growth: One-Way Analysis of Variance (ANOVA) in SPSS. Dan Flynn
Allelopathic Effects on Root and Shoot Growth: One-Way Analysis of Variance (ANOVA) in SPSS Dan Flynn Just as t-tests are useful for asking whether the means of two groups are different, analysis of variance
Chapter 23. Two Categorical Variables: The Chi-Square Test
Chapter 23. Two Categorical Variables: The Chi-Square Test 1 Chapter 23. Two Categorical Variables: The Chi-Square Test Two-Way Tables Note. We quickly review two-way tables with an example. Example. Exercise
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.
Chapter 21 Section D
Chapter 21 Section D Statistical Tests for Ordinal Data The rank-sum test. You can perform the rank-sum test in SPSS by selecting 2 Independent Samples from the Analyze/ Nonparametric Tests menu. The first
The Goodness-of-Fit Test
on the Lecture 49 Section 14.3 Hampden-Sydney College Tue, Apr 21, 2009 Outline 1 on the 2 3 on the 4 5 Hypotheses on the (Steps 1 and 2) (1) H 0 : H 1 : H 0 is false. (2) α = 0.05. p 1 = 0.24 p 2 = 0.20
UNDERSTANDING THE INDEPENDENT-SAMPLES t TEST
UNDERSTANDING The independent-samples t test evaluates the difference between the means of two independent or unrelated groups. That is, we evaluate whether the means for two independent groups are significantly
IBM SPSS Statistics 20 Part 1: Descriptive Statistics
CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES IBM SPSS Statistics 20 Part 1: Descriptive Statistics Summer 2013, Version 2.0 Table of Contents Introduction...2 Downloading the
PASS Sample Size Software
Chapter 250 Introduction The Chi-square test is often used to test whether sets of frequencies or proportions follow certain patterns. The two most common instances are tests of goodness of fit using multinomial
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
People like to clump things into categories. Virtually every research
05-Elliott-4987.qxd 7/18/2006 5:26 PM Page 113 5 Analysis of Categorical Data People like to clump things into categories. Virtually every research project categorizes some of its observations into neat,
Introduction to Statistics with SPSS (15.0) Version 2.3 (public)
Babraham Bioinformatics Introduction to Statistics with SPSS (15.0) Version 2.3 (public) Introduction to Statistics with SPSS 2 Table of contents Introduction... 3 Chapter 1: Opening SPSS for the first
Using SPSS, Chapter 2: Descriptive Statistics
1 Using SPSS, Chapter 2: Descriptive Statistics Chapters 2.1 & 2.2 Descriptive Statistics 2 Mean, Standard Deviation, Variance, Range, Minimum, Maximum 2 Mean, Median, Mode, Standard Deviation, Variance,
4. Descriptive Statistics: Measures of Variability and Central Tendency
4. Descriptive Statistics: Measures of Variability and Central Tendency Objectives Calculate descriptive for continuous and categorical data Edit output tables Although measures of central tendency and
3. Analysis of Qualitative Data
3. Analysis of Qualitative Data Inferential Stats, CEC at RUPP Poch Bunnak, Ph.D. Content 1. Hypothesis tests about a population proportion: Binomial test 2. Chi-square testt for goodness offitfit 3. Chi-square
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
Understanding and Interpreting the Chi-square Statistic (x 2 ) Rose Ann DiMaria, PhD, RN WVU-School of Nursing Charleston Division
Understanding and Interpreting the Chi-square Statistic (x 2 ) Rose Ann DiMaria, PhD, RN WVU-School of Nursing Charleston Division Inferential statistics Make judgments about accuracy of given sample in
Two Categorical Variables: The Chi Square Test
CHAPTER 22 Two Categorical Variables: The Chi Square Test Two Way Tables We can use Excel to create a two way table from our data that we place in columns in the spreadsheet. Our example uses the data
Having a coin come up heads or tails is a variable on a nominal scale. Heads is a different category from tails.
Chi-square Goodness of Fit Test The chi-square test is designed to test differences whether one frequency is different from another frequency. The chi-square test is designed for use with data on a nominal
Chi-Square Test. Contingency Tables. Contingency Tables. Chi-Square Test for Independence. Chi-Square Tests for Goodnessof-Fit
Chi-Square Tests 15 Chapter Chi-Square Test for Independence Chi-Square Tests for Goodness Uniform Goodness- Poisson Goodness- Goodness Test ECDF Tests (Optional) McGraw-Hill/Irwin Copyright 2009 by The
Handout 7: Understanding Relationships Between Two Categorical Variables
In this handout, we will continue to discuss ways to investigate the relationship between two categorical variables. Recall that a categorical variable takes on a value that is the name of a category or
Chi-Square Tests TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson
Math Objectives Students will recognize that chi-squared tests are for counts of categorical data. Students will identify the appropriate chi-squared test to use for a given situation: 2 Goodness of Fit
Exploring Relationships using SPSS inferential statistics (Part II) Dwayne Devonish
Exploring Relationships using SPSS inferential statistics (Part II) Dwayne Devonish Reminder: Types of Variables Categorical Variables Based on qualitative type variables. Gender, Ethnicity, religious
11 Correlations and Chi square test
11 Correlations and Chi square test We are now approaching the final statistical tests that you will learn in this course, Correlations and the Chi square test. Correlations Correlations are used to look
Using SPSS version 14 Joel Elliott, Jennifer Burnaford, Stacey Weiss
Using SPSS version 14 Joel Elliott, Jennifer Burnaford, Stacey Weiss SPSS is a program that is very easy to learn and is also very powerful. This manual is designed to introduce you to the program however,
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
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly
Two Correlated Proportions (McNemar Test)
Chapter 50 Two Correlated Proportions (Mcemar Test) Introduction This procedure computes confidence intervals and hypothesis tests for the comparison of the marginal frequencies of two factors (each with
Formula. obs. exp) exp
Chi-Square Test A fundamental problem is genetics is determining whether the experimentally determined data fits the results expected from theory (i.e. Mendel s laws as expressed in the Punnett square).
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,
12.2 CONTINGENCY TABLE p-value
12.2 Contingency Table p-value 143 12.2 CONTINGENCY TABLE p-value Example 12.2 (adapted from Keller, p. 503) A cola company sells four types of cola in North America. To see if the same marketing approach
Variables and Data A variable contains data about anything we measure. For example; age or gender of the participants or their score on a test.
The Analysis of Research Data The design of any project will determine what sort of statistical tests you should perform on your data and how successful the data analysis will be. For example if you decide
SPSS/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
Projects Involving Statistics (& SPSS)
Projects Involving Statistics (& SPSS) Academic Skills Advice Starting a project which involves using statistics can feel confusing as there seems to be many different things you can do (charts, graphs,
SPSS Workbook 4 T-tests
TEESSIDE UNIVERSITY SCHOOL OF HEALTH & SOCIAL CARE SPSS Workbook 4 T-tests Research, Audit and data RMH 2023-N Module Leader:Sylvia Storey Phone:016420384969 s.storey@tees.ac.uk SPSS Workbook 4 Differences
Chapter 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
CHI SQUARE DISTRIBUTION
CI SQUARE DISTRIBUTION 1 Introduction to the Chi Square Test of Independence This test is used to analyse the relationship between two sets of discrete data. Contingency tables are used to examine the