Showing posts with label ANCOVA. Show all posts
Showing posts with label ANCOVA. Show all posts

Sunday, July 24, 2022

Post Hoc Tests and Data Analyses

 A post hoc test is a statistical test used to determine if a pair of values are significantly different from each other after the primary analysis has been completed.

The term post hoc is a Latin phrase meaning after the event.

A common use of post hoc tests is the comparison of group means after an F-test in an ANOVA has revealed significant differences among the groups. The reason to test for differences after an overall test like ANOVA is to reduce the risk of finding a significant difference by chance. That is, if researchers perform a large number of tests on a sample, they may find one or more tests significant by chance.

There are many post hoc tests. Following are some examples of tests that compare the means of two groups.

Bonferroni Test

This is a popular test. By dividing the significance level by the number of comparisons, the risk of finding a significant difference by chance is reduced. This procedure is called the Bonferroni Correction.

Tukey's Honest Significant Difference Test (HSD)

The Tukey HSD is a commonly used test, which adjusts for the number of comparisons.

Scheff├ęs Test

Scheff├ęs Test is similar to the Tukey HSD but it is slightly more conservative.

More post hoc tests

Additional post hoc tests are available. I will list them so you can recognize the test as one that evaluates a pair of means for significant differences after an overall test (such as an ANOVA).

Duncan's New Multiple Range Test (MRT)

Dunn's Multiple Comparison Test

Fisher's Least Significant Difference (LSD)

Holm-Bonferroni Procedure

Newman-Keuls

Rodger's Method

Dunnett's correction

Benjamin-Hochberg (BH) procedure

Cite this post

Sutton, G. (2022, July 24). Post hoc tests and data analyses. Assessment, Statistics, and Research. Retrieved from https://statistics.suttong.com/2022/07/post-hoc-tests-and-data-analyses.html 


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Thursday, January 14, 2021

Covariate

 

Covariate. A variable that is correlated with a dependent variable in a research study. When a covariate is identified and measured, the value of the dependent variable can be adjusted for the contribution of the covariate during data analysis.

Example: If researchers collect information on the variable age in a study about forgiveness and if age is related to forgiveness, then age can be treated as a covariate to identify how people scored on a forgiveness survey after the scores have been adjusted for age.

The word adjusted is a key word to look for in reading research that includes a covariate.

Procedures that include covariates are ANCOVA and MANCOVA.

Cite this post.

Sutton, G. W. (2021, January 14). Covariate. Statistics.  https://statistics.suttong.com/2021/01/covariate.html


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See my Books

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MANCOVA


 

MANCOVA (Multivariate Analysis of Covariance). A statistical procedure for analyzing results when there are one or more independent variables, two or more dependent variables, and one or more covariates.

Basic components of MANCOVA

Independent or grouping Variable = 1 or more

Dependent or criterion Variable = 2 or more

Covariates = 1 or more

Overall tests are used to determine significant effects or differences among the grouping variables.

An F test indicates significance overall and for specific effects or relationships.

A commonly reported measure of effect size is eta squared.

A p value reveals the probability of a significant relationship-- one that is not due to chance factors.


Applied Statistics Concepts for Counselors on AMAZON or GOOGLE






Creating Surveys on AMAZON    or   GOOGLE  Worldwide

Links to Connections

 

Checkout My Website   www.suttong.com

  

See my Books

 

  AMAZON       

 

  GOOGLE STORE

 

JOIN me on

 

   FACEBOOK   Geoff W. Sutton  

  

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Read many published articles:

 

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Tuesday, January 5, 2021

ANCOVA in Counseling & Behavioral Research

 


ANCOVA


ANCOVA is a procedure like ANOVA except researchers can study the effects of one or more independent variables on a dependent variable after adjusting for other variables, called covariates, which were not a primary focus of the study. The letter C in ANCOVA stands for covariate. There can be several covariates in a study. In testing for differences among groups experiencing different leadership styles, we could study the effects on employee satisfaction after adjusting for a covariate of years of employment. A key word in ANCOVA studies is adjusting. Analysts adjust the scores based on information about the covariate before testing for significant differences.


Basic features of an ANCOVA:


Independent or grouping Variable = 1 or more

Dependent or criterion Variable = 1

Covariates = 1 or more


An test indicates significance overall and for specific effects or relationships.

A commonly reported measure of effect size is eta squared.

value reveals the probability of a significant relationship-- one that is not due to chance factors.

Read more about ANCOVA in the following books.


Applied Statistics Concepts for Counselors on AMAZON or GOOGLE






Creating Surveys on AMAZON    or   GOOGLE  Worldwide










MORE about ANCOVA and COVARIANCE


Analysis of Covariance

Geoffrey W. Sutton, Ph.D.

            The analysis of covariance is a research strategy that is based upon a two or more groups design that yields at least interval data and could be analyzed using ANOVA. We use the term ANCOVA as an acronym. The letter C in the acronym represents a covariate. We usually refer to the covariate as a CV. A covariate is a variable that is significantly correlated with the dependent variable.

 In experimental research, the covariate helps reduce error variance and makes the F-test more sensitive to any main or interaction effects. The correlation between the covariate and the DV allows for the removal of the effects of a CV on a DV and represents a known source of systematic bias. 

In nonexperimental research, researchers can use the covariate to statistically remove the influence of a variable to help equate groups that could not be formed by random assignment or to better understand another relationships of interest. 

A third purpose is to examine group differences by controlling for the influence of a DV when there are several DVs in an analysis. This latter use is known as multivariate analysis of variance or, MANCOVA.

 You can use more than one CV in a research design or ANCOVA procedure. However, if there is a correlation greater than r =  .80 between two CVs, you should use only one of the CVs because they appear to be measuring a lot of the same variance.

  As with all statistical procedures, there are several assumptions to meet. The first three are basic assumptions for ANOVA and the next three are additional assumptions for ANCOVA.

1. All data are from random samples and independent of other data.

2. The scores on the DV are normally distributed in the population.

3. The distributions of scores on the DV have equal variances.

            Additional assumptions for ANCOVA

4. There is a linear relationship between the CV and the DV.

5. The slope for the regression line (for the CV) is the same in each group.

6. The CV has high reliability and was measured without error.

Research questions and hypotheses

 We generally use a key phrase to identify the CV in a research study. That key phrase can be controlling for or adjusted for. Here are some examples.

1. What is the difference between memory scores for people with right and left hemisphere stroke when adjusted for age?

2. What is the effect of a marriage enrichment program when controlling for years of marriage?

The research hypothesis states there is an effect or a difference when adjusting for the CV and the null hypothesis assumes the usual no difference, or no effect result, when adjusting for the CV.

Following is a hypothesis based on question number one.

H1: When adjusting for age, there is a significant difference between the means on verbal memory between patients who experience right and left hemisphere strokes.

H01: When adjusting for age, there is no significant difference between the means on verbal memory in the population between patients who experienced right and left hemisphere strokes (p < .05).

The research method with a CV

 We would follow usual procedures for delivering the IV (independent variable) or measuring a QIV (quasi-independent variable) along with the DVs. We would consider what variables might affect the DVs and collect data to measure those CVs. After all the data have been entered into our database, we would obtain the descriptive statistics. Next, make any adjustments to the data and calculate correlations between the measured variables. Those variables that were not the primary focus of the experiment or study will be entered as CVs in the ANOVA procedure if they are highly correlated with the DVs. We will perform the usual post hoc analyses, if applicable.

Results

When interpreting the results of an ANCOVA, we will refer to the adjusted means. SPSS reports the results of the analysis. In the Test of Between Subjects Effects table, SPSS reports the CV along with an F-test. If the CV made a significant contribution to the analysis, the p-value for the CV will be less than .05 (or your preferred level of significance). The output will also include adjusted and unadjusted means. When reporting the results, you should report both sets of means. In a small study, the means can be reported in a paragraph. In a larger study, the means should be placed in a table.

Example of ANCOVA reporting for a fictitious study.

IV = communication skills training vs. a no skills training control (2 groups)

DV = some measure of communication on a continuous scale

CV = years of employment-- a continuous scale

Workplace communication skills training for employees significantly improved positive statements when adjusted for years of employment, F(2,38) = 4.56, p = .03, eta2 = .42, Observed Power = .67.

 

Links to Connections

Checkout My Website   www.suttong.com

  

See my Books

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  GOOGLE STORE

 

FOLLOW me on

   FACEBOOK   Geoff W. Sutton  

  

   TWITTER  @Geoff.W.Sutton

 

   PINTEREST  www.pinterest.com/GeoffWSutton

 

Read published articles:

 

  Academia   Geoff W Sutton   

 

  ResearchGate   Geoffrey W Sutton 


Identity Salience Questionnaire (ISQ)

  Assessment name: Identity Salience Questionnaire (ISQ) Scale overview: The Identity Salience Questionnaire (ISQ) is a 6-item self-repor...