Unit 10 lesson 1
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This document discusses repeated measures ANOVA, which is an extension of one-way ANOVA used when multiple measurements are taken on the same subjects. It explains how repeated measures ANOVA partitions the variation due to individual differences and occasions, rather than treating all scores independently. The assumptions and process of conducting repeated measures ANOVA using SPSS are outlined, including checking for sphericity and applying corrections if it is not met. Polynomial trends that can be tested with repeated measures ANOVA are also introduced.
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Tugasan kumpulan anova
ANOVA is a statistical technique used to compare the means of three or more groups. It can test if population means are equal or if some are different. The document outlines the steps in ANOVA including describing data, stating hypotheses, calculating test statistics, and making conclusions. It also discusses one-way and two-way ANOVA designs, comparing means between multiple groups while controlling for Type I error, and the calculations involved including sums of squares, degrees of freedom, and F-ratios.
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The document discusses analysis of variance (ANOVA) which is used to compare the means of three or more groups. It explains that ANOVA avoids the problems of multiple t-tests by providing an omnibus test of differences between groups. The key steps of ANOVA are outlined, including partitioning variation between and within groups to calculate an F-ratio. A large F value indicates more difference between groups than expected by chance alone.
Analysis of variance
This document provides an introduction to analysis of variance (ANOVA). It defines key terms like factors, levels, and independent/quasi-independent variables. It explains the advantages of ANOVA over t-tests in comparing more than two treatment conditions. Examples are given of one-way ANOVA to compare a single factor with repeated measures and independent measures designs. Two-way ANOVA is introduced for studying the interaction between two factors. Mauchly's test and the assumption of sphericity are also discussed.
ANOVA - BI FACTORIAL ANOVA (2- WAY ANOVA)
A two-way ANOVA analyzes the influence of two independent variables on a single dependent variable. It tests for main effects of each independent variable as well as interactions between the variables. The independent variables are categorical and the dependent variable is measured on an ordinal or ratio scale. It compares sums of squares and mean squares to determine if the means of observations grouped by each factor differ significantly. An example tests the effect of gender and age on test scores, with gender, age as independent variables and test score as the dependent variable.
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This document provides an overview of analysis of variance (ANOVA) techniques. It discusses one-way and two-way ANOVA, including their assumptions, calculations, and applications. For example, it explains how to set up a two-way ANOVA table and calculate values like sums of squares, degrees of freedom, mean squares, and F values. It also gives an example of using one-way ANOVA to analyze differences in crop yields between four plots of land.
Analysis of variance (ANOVA)
This document provides an overview of analysis of variance (ANOVA). It begins by defining ANOVA and its historical background. It then discusses the basic concepts and assumptions of ANOVA, including comparing group means rather than variances. The document outlines why ANOVA is preferable to multiple t-tests and describes the different types of ANOVA designs including one-way, repeated measures, factorial, and mixed. It provides examples of main effects and interactions. Finally, it demonstrates how to perform one-way and factorial ANOVAs in SPSS and discusses post-hoc tests.
Anova copy
This document provides an introduction to analysis of variance (ANOVA), including what it is, why it is used instead of independent t-tests, the concepts of factors and levels, types of ANOVA (one-way, two-way, etc.), and the basic steps to compute a one-way ANOVA. It discusses assumptions of ANOVA, how to calculate mean square between and mean square error, how to interpret the F-ratio, and formulas used in the ANOVA table. Post-hoc tests are also introduced.
In Anova
ANOVA is a statistical technique used to determine whether the means of groups are statistically different from each other. It can be used to establish cause-and-effect relationships with a certain degree of certainty. There are different types of ANOVA for different study designs. The basic parts of an ANOVA include sums of squares, degrees of freedom, mean squares, and the F-statistic. ANOVA can be performed in Excel using the data analysis tool. An example shows how ANOVA was used to analyze measurement data from multiple inspectors.
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Tugasan kumpulan anova
ANOVA is a statistical technique used to compare the means of three or more groups. It can test if population means are equal or if some are different. The document outlines the steps in ANOVA including describing data, stating hypotheses, calculating test statistics, and making conclusions. It also discusses one-way and two-way ANOVA designs, comparing means between multiple groups while controlling for Type I error, and the calculations involved including sums of squares, degrees of freedom, and F-ratios.
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The document discusses analysis of variance (ANOVA) which is used to compare the means of three or more groups. It explains that ANOVA avoids the problems of multiple t-tests by providing an omnibus test of differences between groups. The key steps of ANOVA are outlined, including partitioning variation between and within groups to calculate an F-ratio. A large F value indicates more difference between groups than expected by chance alone.
Analysis of variance
This document provides an introduction to analysis of variance (ANOVA). It defines key terms like factors, levels, and independent/quasi-independent variables. It explains the advantages of ANOVA over t-tests in comparing more than two treatment conditions. Examples are given of one-way ANOVA to compare a single factor with repeated measures and independent measures designs. Two-way ANOVA is introduced for studying the interaction between two factors. Mauchly's test and the assumption of sphericity are also discussed.
ANOVA - BI FACTORIAL ANOVA (2- WAY ANOVA)
A two-way ANOVA analyzes the influence of two independent variables on a single dependent variable. It tests for main effects of each independent variable as well as interactions between the variables. The independent variables are categorical and the dependent variable is measured on an ordinal or ratio scale. It compares sums of squares and mean squares to determine if the means of observations grouped by each factor differ significantly. An example tests the effect of gender and age on test scores, with gender, age as independent variables and test score as the dependent variable.
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This document provides an overview of analysis of variance (ANOVA) techniques. It discusses one-way and two-way ANOVA, including their assumptions, calculations, and applications. For example, it explains how to set up a two-way ANOVA table and calculate values like sums of squares, degrees of freedom, mean squares, and F values. It also gives an example of using one-way ANOVA to analyze differences in crop yields between four plots of land.
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This document provides an overview of analysis of variance (ANOVA). It begins by defining ANOVA and its historical background. It then discusses the basic concepts and assumptions of ANOVA, including comparing group means rather than variances. The document outlines why ANOVA is preferable to multiple t-tests and describes the different types of ANOVA designs including one-way, repeated measures, factorial, and mixed. It provides examples of main effects and interactions. Finally, it demonstrates how to perform one-way and factorial ANOVAs in SPSS and discusses post-hoc tests.
Anova copy
This document provides an introduction to analysis of variance (ANOVA), including what it is, why it is used instead of independent t-tests, the concepts of factors and levels, types of ANOVA (one-way, two-way, etc.), and the basic steps to compute a one-way ANOVA. It discusses assumptions of ANOVA, how to calculate mean square between and mean square error, how to interpret the F-ratio, and formulas used in the ANOVA table. Post-hoc tests are also introduced.
In Anova
ANOVA is a statistical technique used to determine whether the means of groups are statistically different from each other. It can be used to establish cause-and-effect relationships with a certain degree of certainty. There are different types of ANOVA for different study designs. The basic parts of an ANOVA include sums of squares, degrees of freedom, mean squares, and the F-statistic. ANOVA can be performed in Excel using the data analysis tool. An example shows how ANOVA was used to analyze measurement data from multiple inspectors.
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This document provides an overview of one-way ANOVA, including its assumptions, steps, and an example. One-way ANOVA tests whether the means of three or more independent groups are significantly different. It compares the variance between sample means to the variance within samples using an F-statistic. If the F-statistic exceeds a critical value, then at least one group mean is significantly different from the others. Post-hoc tests may then be used to determine specifically which group means differ. The example calculates statistics to compare the analgesic effects of three drugs and finds no significant difference between the group means.
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ANOVA, ANCOVA, MANOVA, and MANCOVA are statistical analyses used to test differences between groups.
ANOVA tests for differences between 2 or more means and partitions variances into sums of squares between and within groups. ANCOVA controls for additional factors, called covariates, to reduce error and increase power.
MANOVA assesses the effect of independent variables on multiple dependent variables simultaneously, accounting for correlation between variables. It tests for overall differences using a multivariate F value. Univariate follow-ups can then examine differences on each individual dependent variable.
MANCOVA extends MANOVA to include controlling for covariates, allowing evaluation of changes in dependent variables while accounting for additional continuous factors measured at different
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This document discusses one-way analysis of variance (ANOVA), which allows for comparison of three or more means. It explains that ANOVA is needed when comparing more than two means, as multiple t-tests could lead to complications. The document also outlines the assumptions that must be met to use one-way ANOVA and describes the outputs generated, including descriptive statistics, an ANOVA table showing if group means are statistically significantly different, and a multiple comparisons table indicating which specific groups differ. An example is provided of a manager using one-way ANOVA to compare the productivity of employees who took beginner, intermediate, or advanced spreadsheet training courses.
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ANOVA (analysis of variance) is used to determine if different treatment groups differ significantly on some measure. It compares the variance between groups to the variance within groups. If the between-group variance is large relative to the within-group variance, it suggests the treatment had an effect. The analysis calculates an F-ratio, with larger values indicating it is less likely the groups differ due to chance. Researchers use statistical tables to determine the probability (p-value) that the F-ratio occurred by chance if there was actually no effect.
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This document provides an overview of common statistical tests used to analyze data, including the t-test, ANOVA, and ANCOVA. It describes the assumptions, test statistics, and SAS code for each test. The t-test is used to compare two population means or determine if two sets of data are significantly different. ANOVA examines differences among group means and can be one-way or two-way. ANCOVA combines aspects of ANOVA and regression by including categorical and continuous predictors to examine the influence of independent variables on a dependent variable while controlling for a covariate.
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One-way analysis of variance (ANOVA) tests allow you to determine if one given factor, such as drug treatment,
has a significant effect on gene expression behavior across any of the groups under study. A significant p-value
resulting from a 1-way ANOVA test would indicate that a gene is differentially expressed in at least one of the
groups analyzed. If there are more than two groups being analyzed, however, the 1-way ANOVA does not
specifically indicate which pair of groups exhibits statistical differences. Post Hoc tests can be applied in this
specific situation to determine which specific pair/pairs are differentially expressed. This document will provide
the necessary information for you to perform these analyses within GeneSpring.
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This document provides an overview of one-way ANOVA, including its assumptions, steps, and an example. One-way ANOVA tests whether the means of three or more independent groups are significantly different. It compares the variance between sample means to the variance within samples using an F-statistic. If the F-statistic exceeds a critical value, then at least one group mean is significantly different from the others. Post-hoc tests may then be used to determine specifically which group means differ. The example calculates statistics to compare the analgesic effects of three drugs and finds no significant difference between the group means.
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ANOVA tests for differences between 2 or more means and partitions variances into sums of squares between and within groups. ANCOVA controls for additional factors, called covariates, to reduce error and increase power.
MANOVA assesses the effect of independent variables on multiple dependent variables simultaneously, accounting for correlation between variables. It tests for overall differences using a multivariate F value. Univariate follow-ups can then examine differences on each individual dependent variable.
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ANOVA, or analysis of variance, is a statistical technique used to compare the means of two or more groups. It extends the t-test to be used when there are more than two groups. ANOVA tests the hypothesis that the means of all groups are equal. One-way ANOVA compares the means of a single independent variable divided into multiple groups. Two-way ANOVA models a dependent variable as a function of two independent variables and their interaction.
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This document discusses one-way analysis of variance (ANOVA), which allows for comparison of three or more means. It explains that ANOVA is needed when comparing more than two means, as multiple t-tests could lead to complications. The document also outlines the assumptions that must be met to use one-way ANOVA and describes the outputs generated, including descriptive statistics, an ANOVA table showing if group means are statistically significantly different, and a multiple comparisons table indicating which specific groups differ. An example is provided of a manager using one-way ANOVA to compare the productivity of employees who took beginner, intermediate, or advanced spreadsheet training courses.
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ANOVA (analysis of variance) is used to determine if different treatment groups differ significantly on some measure. It compares the variance between groups to the variance within groups. If the between-group variance is large relative to the within-group variance, it suggests the treatment had an effect. The analysis calculates an F-ratio, with larger values indicating it is less likely the groups differ due to chance. Researchers use statistical tables to determine the probability (p-value) that the F-ratio occurred by chance if there was actually no effect.
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This document provides an overview of analysis of variance (ANOVA) and how to conduct various ANOVA tests in SPSS. It defines ANOVA, discusses assumptions and types of ANOVA (one-way, factorial, repeated measures, mixed models), and provides step-by-step instructions for running one-way, factorial, repeated measures, and mixed models ANOVA in SPSS. It also briefly covers non-parametric equivalents and their SPSS procedures. Key points include how to check assumptions, interpret outputs including p-values and post-hoc tests, and choosing appropriate post-hoc tests and corrections based on assumption checks.
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One-way analysis of variance (ANOVA) tests allow you to determine if one given factor, such as drug treatment,
has a significant effect on gene expression behavior across any of the groups under study. A significant p-value
resulting from a 1-way ANOVA test would indicate that a gene is differentially expressed in at least one of the
groups analyzed. If there are more than two groups being analyzed, however, the 1-way ANOVA does not
specifically indicate which pair of groups exhibits statistical differences. Post Hoc tests can be applied in this
specific situation to determine which specific pair/pairs are differentially expressed. This document will provide
the necessary information for you to perform these analyses within GeneSpring.
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It is very difficult to distinguish the differences between ANOVA and regression. This is because both terms have more similarities than differences. It can be said that ANOVA and regression are the two sides of the same coin.
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One-way ANOVA compares the means of three or more independent groups and is used to determine if there are any statistically significant differences between the means. Two-way ANOVA compares the means of two independent variables and can examine interactions between them. MANOVA compares the means of multiple dependent variables. Researchers use ANOVA to examine questions about potential differences between groups based on one or more independent variables.
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Chapter 11 Chi-Square Tests and ANOVA 359 Chapter .docx
Chapter 11: Chi-Square Tests and ANOVA
359
Chapter 11: Chi-Square and ANOVA Tests
This chapter presents material on three more hypothesis tests. One is used to determine
significant relationship between two qualitative variables, the second is used to determine
if the sample data has a particular distribution, and the last is used to determine
significant relationships between means of 3 or more samples.
Section 11.1: Chi-Square Test for Independence
Remember, qualitative data is where you collect data on individuals that are categories or
names. Then you would count how many of the individuals had particular qualities. An
example is that there is a theory that there is a relationship between breastfeeding and
autism. To determine if there is a relationship, researchers could collect the time period
that a mother breastfed her child and if that child was diagnosed with autism. Then you
would have a table containing this information. Now you want to know if each cell is
independent of each other cell. Remember, independence says that one event does not
affect another event. Here it means that having autism is independent of being breastfed.
What you really want is to see if they are not independent. In other words, does one
affect the other? If you were to do a hypothesis test, this is your alternative hypothesis
and the null hypothesis is that they are independent. There is a hypothesis test for this
and it is called the Chi-Square Test for Independence. Technically it should be called
the Chi-Square Test for Dependence, but for historical reasons it is known as the test for
independence. Just as with previous hypothesis tests, all the steps are the same except for
the assumptions and the test statistic.
Hypothesis Test for Chi-Square Test
1. State the null and alternative hypotheses and the level of significance
Ho : the two variables are independent (this means that the one variable is not
affected by the other)
HA : the two variables are dependent (this means that the one variable is affected
by the other)
Also, state your α level here.
2. State and check the assumptions for the hypothesis test
a. A random sample is taken.
b. Expected frequencies for each cell are greater than or equal to 5 (The expected
frequencies, E, will be calculated later, and this assumption means E ≥ 5 ).
3. Find the test statistic and p-value
Finding the test statistic involves several steps. First the data is collected and
counted, and then it is organized into a table (in a table each entry is called a cell).
These values are known as the observed frequencies, which the symbol for an
observed frequency is O. Each table is made up of rows and columns. Then each
row is totaled to give a row total and each column is totaled to give a column
total.
Chapter 11: Chi-Squared Tests and ANOVA
360
The null hypothesis is that the variables are independent. Using the multiplication.
ANOVA.ppt
The document discusses analysis of variance (ANOVA) and experimental design. It explains that ANOVA allows testing the hypothesis of equality of multiple population means simultaneously, rather than conducting multiple pairwise t-tests. It describes the components of an ANOVA table including sources of variation (treatments, error), degrees of freedom, sums of squares, and mean squares. An example compares the yields of three potato varieties in a completely randomized design and demonstrates forming the ANOVA table to analyze the data.
RUNNING HEAD ONE WAY ANOVA1ONE WAY ANOVA .docx
RUNNING HEAD: ONE WAY ANOVA 1
ONE WAY ANOVA 8
One-Way ANOVA
Stacy Hernandez
PSY7620
Dr. Lorie Fernandez
Capella University
Data Analysis and Application (DAA)
The one way ANOVA is used to determine whether there are any significant differences between the means of two or more independent groups. In this sample, the file grades.sav is used with section (independent variable) and quiz3 (dependent variable).
Data File Description
1. The one way ANOVA is used to determine whether there are any significant differences between the means of two or more independent groups.
2. In this sample, the file grades.sav is used with section (independent variable) and quiz3 (dependent variable).
3. The sample size (N) is 105.
Testing Assumptions
The dependent variable, quiz3, is measured at the interval or ratio level (meaning continuous). The dependent variable (quiz3) in this case, is therefore continuous since it ranges from one to 10. The independent variable (section) should consist of two or more categorical independent groups. In this case, the independent variable (section), has three groups, therefore it meets this assumption. There should be independence of observation, meaning that there is no relationship between the observations in each group or between the groups themselves. There should be no significant outliers, although there are single data points within the data that do not follow a normal pattern. Therefore, the outliers found will a negative effect on the one-way ANOVA, reducing the validity of the results.
Note the above boxplot indicates outliers in section two, with the id of 21.
The dependent variable (quiz3) should approximately have a normal distribution for each category of the independent variable (section). The null hypothesis is that the data is of a normal distribution, that the mean (average value of the dependent variable) is the same for all groups.
Ho – the observed distribution fits the normal distribution.
The alternative hypothesis is that the data does not have a normal distribution; the average is not the same for all groups.
Ha – the observed distribution does not fit the normal distribution.
It is observed that the data is not normally distributed. Most sections have quiz3 values between five and nine note this is a visual estimate. Note that the largest group also has the largest value of quiz3. The statistics from the histogram of quiz3 reveal that the Mean is 8.05; the Standard Deviation is 2.322, with a total number N of 105.
Descriptive Statistics
N
Minimum
Maximum
Mean
Std. Deviation
Skewness
Kurtosis
Statistic
Statistic
Statistic
Statistic
Statistic
Statistic
Std. Error
Statistic
Std. Error
quiz3
105
0
10
8.05
2.322
-1.177
.236
.805
.467
section
105
1
3
2.00
.797
.000
.236
-1.419
.467
Valid N
105
When looking at skewness, for a perfectly normal and symmetrical distribution, it has a value of zero (Warner, 20 ...
Anova.ppt
Analysis of variance (ANOVA) is a statistical technique used to compare the means of three or more groups. It compares the variance between groups with the variance within groups to determine if the population means are significantly different. The key assumptions of ANOVA are independence, normality, and homogeneity of variances. A one-way ANOVA involves one independent variable with multiple levels or groups, and compares the group means to the overall mean to calculate an F-ratio statistic. If the F-ratio exceeds a critical value, then the null hypothesis that the group means are equal can be rejected.
oneway.ppt
The document provides an overview of one-way analysis of variance (ANOVA). It explains that one-way ANOVA tests whether the means of three or more groups are equal. An example compares exam scores of students in different rows of a classroom. The ANOVA calculation yields a p-value of 0.009, below the significance level of 0.05. This allows rejecting the null hypothesis that all row means are equal, indicating at least one row mean differs from the others.
Anova n metaanalysis
ANOVA and meta-analysis are statistical techniques used to analyze data from multiple groups or studies. ANOVA allows researchers to determine if variability between groups is statistically significant or due to chance. It compares the means of three or more independent groups and tests the hypothesis that their means are equal. Meta-analysis systematically combines results from independent studies on a topic to obtain an overall estimate of effect. It involves identifying relevant studies, determining their eligibility, abstracting their data, and statistically analyzing the data to summarize results. Both techniques provide a more robust analysis than examining individual studies alone.
non para.doc
This document discusses non-parametric tests and how to use them to compare groups when assumptions of parametric tests are violated. It explains that non-parametric tests like the Wilcoxon and Kruskal-Wallis tests can be used when samples are small or data is not normally distributed. The Kruskal-Wallis test allows comparison of more than two groups by ranking all data and comparing mean ranks between groups. An example compares student grades under different teaching methods using both Kruskal-Wallis and ANOVA tests.
Stat sample test ch 12
1. Analysis of variance (ANOVA) is a statistical technique used to test whether the means of three or more groups are equal. It analyzes the variations between and within groups.
2. ANOVA requires assumptions of normality, equal variances, independence, and random sampling. It uses sum of squares, mean squares and the F-test statistic to determine if group means are significantly different.
3. If the p-value is less than the significance level (often 0.05), the null hypothesis of equal group means is rejected, indicating at least one group mean is significantly different from the others.
Correlation: Bivariate Data and Scatter Plot
This document discusses bivariate data and scatter plots. Bivariate data involves collecting values of two variables from the same population. A scatter plot can show the relationship between two quantitative variables by plotting their ordered pairs. The direction and strength of the pattern in a scatter plot indicates whether the variables have a positive, negative, or no correlation. The correlation coefficient (r) measures the strength of the linear relationship between variables on a scale from -1 to 1.
Stat2013
The document provides information about performing chi-square tests and choosing appropriate statistical tests. It discusses key concepts like the null hypothesis, degrees of freedom, and expected versus observed values. Examples are provided to illustrate chi-square tests for goodness of fit and comparison of proportions. The document also compares parametric and non-parametric tests, providing examples of when each would be used.
Directions The purpose of Project 8 is to prepare you for the final.docx
Directions: The purpose of Project 8 is to prepare you for the final, comprehensive exam and is set up EXACTLY the same. Questions 1 and 2 are not graded in this exercise, but are on the final. Be sure to answer them still so you can receive feedback. Once done with these, move into the calculation questions.
Be advised that you will need to decide which type of test to use in most of the problems. Please write out all pertinent information for each of the 4 steps of hypothesis testing. For the calculations, you only need to provide the values of all statistics for that test. There is no need to show work.
List the four Steps of the Hypothesis test:
Step 1 –
Step 2 –
Step 3 –
Step 4 –
This semester we have discussed the following statistical analyses.
Z-test
One-Sample
t
-test
Independent Groups
t
-test
Repeated Measures
t
-test
One-Way ANOVA
Repeated Measures ANOVA
Correlation
When do you use them? Please type your answer in the Test Used column.
ơ is given
µ is given
Groups Compared
Test Used
No
No
Looks at the same group at 2 different times or across two different conditions
Yes
Yes
Sample against population
Examines the degree to which two variables relate to one another
No
No
Looks at the same group at 2 or more times or across 2 or more conditions
No
No
Examines mean differences between two different groups
No
Yes
Sample against population
No
No
Examines mean differences between 2 or more groups
1. A researcher for a cereal company wanted to demonstrate the health benefits of eating oatmeal. A sample of 9 volunteers was obtained and each participant ate a fixed diet without any oatmeal for 30 days. At the end of the 30-day period, cholesterol was measured for each individual. Then the participants began a second 30-day period in which they repeated exactly the same diet except that they added 2 cups of oatmeal each day. After the second 30-day period, cholesterol levels were measured again and the researcher recorded the difference between the two scores for each participant. For this sample, cholesterol scores average M = 16 points lower with the oatmeal diet with SS = 538 for the difference scores.
10 points
·
Are the data sufficient to indicate a significant change in cholesterol level? Use a two-tailed test with α = .01.
·
Compute r
2
to measure the size of the treatment effect.
2. One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specifically, birds with smaller brain, relative to their body size, are not simply smart enough to find food during the winter and must migrate to warmer climates where food is easily available. Birds with bigger brains, on the other hand, are more creative and can find food even when the weather turns harsh. Following are hypothetical data similar to the actual results. The numbers represent relative brain size for the individual birds in each sample.
10 points
Non-Migrating
S.
Week 3 Lecture 9 Effect Size When we reject the null h.docx
Week 3 Lecture 9
Effect Size
When we reject the null hypothesis with an ANOVA test, we have two questions that
arise. The first, which pair of means differs significantly, we have dealt with already. The
second question, similar to what we asked with the t-test null hypothesis rejection is; what
caused the rejection, the sample size or the variable interactions? This question is again
answered using an effect size measure.
Recall that the effect size measure shows how likely the variable interaction caused the
null hypothesis rejection. Large values lead us to say the variables caused the outcome, while
small values lead us to say the outcome has little to no practical significance as the sample size
was the most likely cause of the rejection of the null.
With the single factor ANOVA, the effect size measure is eta squared, and equals the
SS(between)/SS(total) (Tanner & Youssef-Morgan, 2013). For our salary example in Lecture 8,
eta squared equals 17686.02 (SS(between) / 18066 (SS(total) = 0.979 (rounded). Eta squared
effect size measures have different interpretation values than Cohen’s d (from the t-
test). According to Nandy (2012), a small eta squared effect size has a value of 0.01, a medium
of 0.06, and a large value of 0.14 or more. This means we have a large effect size, and the
variables of salary and grade interaction are the most likely cause of our rejecting the null
hypothesis rather than the sample size.
Side note: Eta squared can also be interpreted as the percent of “differences between
group scores that can be explained by the independent variable” (Tanner & Youssef-Morgan,
2013, p. 123). This is consistent with our saying the variable interactions caused the outcome.
Different Forms of ANOVA
Just as the t-test has several forms, so does the ANOVA test. Excel has three versions
available. While we will focus only on the single factor test, a brief description of the other two
versions will be presented.
ANOVA: Two factor without replication
The ANOVA – two factor without replication tests mean differences from two different
variables at the same time. If we are interested in knowing if the mean salary differs by grade
and also by gender, we can perform one two-factor test rather than two separate tests. As
mentioned in lecture two for this week, this is more efficient and maintains our desired alpha
significance level.
Excel Example. To test the mean salaries by grade and gender at the same time, we
would set up our hypothesis test as follows.
Step 1: Ho1: All salary means are equal across grades.
Ha1: At least one mean differs.
Ho2: All gender (male and female) means are equal.
Ha2: At least one mean differs.
Note that in this test, we need to have a hypothesis statement pair for each variable being
tested.
Step 2: ANOVA: Two sample without replication.
Step 3: Reject the null hypothesis if the p-value is < alpha = .05.
Step 4: Perform the test. W.
Similar to Unit 10 lesson 1 (20)
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Unit 10 lesson 1
- 1. Unit 10: Repeated Measures ANOVA Lesson 1: Further Applications of the ANOVA EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas Time Score Next Slide
- 2. Paired Samples t-test Occasion 3 12 11 12 15 16 14 Next Slide Occasion 2 9 8 7 8 9 8 Occasion 1 5 4 4 5 6 5 Person 1 Person 2 Person 3 Person 4 Person 5 Person 6 t-test t-test t-test
- 3. Repeated Measures ANOVA Where X ik is person i ’s score in group k T is the sum of all scores N is the total number of observations Next Slide NOTICE: No means!!!
- 4. Sum of Squares Total SS T = 54.667 Next Slide ANOVA Repeated Measures
- 6. Why Do RM? (cont). 1. The partitioning of the variation in the ANOVA needs to be adjusted so that we are using the correct df (and SS) to compute F-calc based on the corrected MS error . 2. We may or may not improve our chances of obtaining statistical significance. 3. Since we are partitioning out the variation due to individual differences from the residual variation (error), we will most likely note a larger eta-squared (this is an artificial eta-squared, however). Next Slide
- 7. Setting Up The Data Use the same example data for repeated measures as is in your book Mean test1 = 6.1 Mean test2 = 10.6 Mean test3 = 15.3 Next Slide
- 8. Using SPSS for Analysis Analyze General Linear Model Repeated Measures Next Slide
- 9. Analyzing the Data Next Slide
- 12. Reading the Results Next Slide Occasions Residual Individuals
- 13. The “Correct” Summary Table Next Slide
- 14. ANOVA vs. Repeated Measures Next Slide Data treated as a One-Way ANOVA with 3 levels 3 Repeated Measurements
- 15. Eta-squared in Repeated Measures Next Slide SS T SS Res SS O SS I In ANOVA: In Repeated Measures ANOVA:
- 16. The Final Summary Table Next Slide
- 17. Polynomial Trends Next Slide Linear Trend Quadratic Trend test1 test2 test3 Mean 6.1 10.6 15.3
- 18. Polynomial Trends (cont.) Next Slide Cubic Trend 5 data points Cubic Trend 4 data points
- 19. Unit 10: Repeated Measures ANOVA Lesson 1: Further Applications of the ANOVA EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas Time Score