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Post-hoc tests tell the researcher which groups are different from each other. When you conduct an ANOVA, you are attempting to determine if there is a statistically significant difference among the groups. If you find that there is a difference, you will then need to examine where the group differences lay. At this point you could run post-hoc tests which are t tests examining mean differences between the groups.


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There are several multiple comparison tests that can be conducted that will control for Type I error rate, including the Bonferroni , Scheffe, Dunnet, and Tukey tests. The level of measurement of the variables and assumptions of the test play an important role in ANOVA. ANOVA assumes that the data is normally distributed. The ANOVA also assumes homogeneity of variance, which means that the variance among the groups should be approximately equal. ANOVA also assumes that the observations are independent of each other.

Researchers should keep in mind when planning any study to look out for extraneous or confounding variables.


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ANOVA has methods i. These assumptions can be tested using statistical software like Intellectus Statistics! Normality of the distribution of the scores can be tested using histograms, the values of skewness and kurtosis, or using tests such as Shapiro-Wilk or Kolmogorov-Smirnov. The assumption of independence can be determined from the design of the study. This is to say, that even if you violate the assumptions of homogeneity or normality, you can conduct the test and basically trust the findings. In general, with violations of homogeneity the analysis is considered robust if you have equal sized groups.

With violations of normality, continuing with the ANOVA is generally ok if you have a large sample size. Algina, J. Cardinal, R. ANOVA for the behavioural sciences researcher.

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Cortina, J. Davison, M. Psychometrika, 59 4 , Girden, E. ANOVA repeated measures. Iverson, G. Analysis of variance.

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Jackson, S. Klockars, A. Multiple comparisons. Levy, M. Testing for lack of fit in linear multiresponse models based on exact or near replicates. Communications in Statistics — Theory and Methods, 19 6 , Rutherford, A. Toothacker, L. Multiple comparisons procedures. Tsangari, H. Strategies and Tactics of Behavioral Research.

James M. Item Response Theory. Susan E.

ANOVA (Analysis of Variance)

Test Theory. Roderick P. Introduction to Psychometric Theory. Tenko Raykov. Steven K. Applied Longitudinal Data Analysis. Judith D. Andries van der Ark. Experimental Design and Statistics. Steve Miller. Andrew Rutherford. Invariant Measurement. George Engelhard Jr. Gregory R. Research Design and Statistical Analysis. Jerome L. Research Methods and Statistics in Psychology. S Alexander Haslam. Yaacov Petscher. Contemporary Psychometrics.

Albert Maydeu-Olivares. Applying Generalizability Theory using EduG. Jean Cardinet. Learning From Data. Arthur Glenberg. Terry E. Dr Duncan Cramer. Measurement, Design, and Analysis. Elazar J. Rasch Models for Measurement. David Andrich. Factor Analysis. Richard L. Modern Methods for Business Research. George A. An Introduction to Applied Multivariate Analysis. Multilevel Modeling. Steven P. Longitudinal Data Analysis. Jason Newsom. Structural Equation Modeling. Jichuan Wang. Introduction to Statistical Mediation Analysis. David MacKinnon.

Statistics 101: Understanding Covariance

Handbook of Research and Quantitative Methods in Psychology. Latent Class Analysis of Survey Error. Paul P. Detection Theory. Neil A. Using R With Multivariate Statistics. Randall E. Michael Quinn Patton. Intermediate Statistics. Keenan A. An Introduction to Qualitative Research. Uwe Flick. Research with Diverse Groups.


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