Abstract
In the previous chapter, you learned to compare the means of a numeric variable between two groups. But what if you want to compare a ratio or interval variable between more than two groups? If you are interested in comparing across more than two groups, you cannot run multiple t-tests because it increases the risk of a type I error (mistakenly concluding an intervention is effective or efficacious). In these instances, you will want to conduct a one-way analysis of variance (ANOVA). In this chapter, you will walk through how to conduct ANOVA and the appropriate post hoc tests by comparing frequencies of stop and searches conducted by the police between neighborhoods across different local authorities in London.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
DATA.POLICE.UK. (2019). Metropolitan Police Service, stop and search data set [Data file]. Retrieved March 30, 2020, from https://data.police.uk/data/.
Field, A., Miles, J., & Field, Z. (2012). Discovering statistics using R. Sage publications.
Ministry of Housing, Communities & Local Government (MHCLG). (2019). Indices of deprivation [Data file]. Retrieved March 30, 2020, from https://data.london.gov.uk/dataset/indices-of-deprivation.
Author information
Authors and Affiliations
Electronic Supplementary Material
Data 12.1
(CSV 351 kb)
Key Terms
- Bonferroni Correction
-
A post-hoc pairwise comparison of means that controls the type I error rate by dividing the selected α-level by the number of pairwise comparisons made.
- Data transformation
-
An adjustment of data to a different unit or scale (normally to deal with normality issues).
- Eta squared
-
The proportion of the total sum of squares that is accounted for by the between sum of squares. Eta squared is sometimes referred to as the percent of variance explained.
- F -distribution
-
A continuous probability distribution used as the null distribution in ANOVA.
- Kruskal-Wallis test
-
A nonparametric test of statistical significance for multiple groups, requiring at least an ordinal scale of measurement.
- Levene's test
-
A test of the equality of variances.
- Multiple comparisons problem
-
The problem associated with heightened chance of obtaining a false-positive (type I error) increase as the number of comparisons increase.
- One-way analysis of variance (ANOVA)
-
A parametric test of statistical significance that assesses whether differences in the means of several samples (groups) can lead the researcher to reject the null hypothesis that the means of the populations from which the samples are drawn are the same.
- Q-Q plot
-
Used to check for normality of data, plots the correlation between the sample and a normal distribution.
- Scheffé’s test
-
A multiple comparisons test that accounts for family-wise error rate by weighting the test statistic by the mean squared error, between-samples degrees of freedom, and group sizes.
- Tukey’s Honest Significant Difference (HSD)
-
A parametric test of statistical significance, adjusted for making pairwise comparisons. The HSD test defines the difference between the pairwise comparisons required to reject the null hypothesis.
- Welch’s ANOVA
-
ANOVA test for when the equality of variances assumption (homoscedasticity) is not met.
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Wooditch, A., Johnson, N.J., Solymosi, R., Medina Ariza, J., Langton, S. (2021). Analysis of Variance (ANOVA). In: A Beginner’s Guide to Statistics for Criminology and Criminal Justice Using R. Springer, Cham. https://doi.org/10.1007/978-3-030-50625-4_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-50625-4_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-50624-7
Online ISBN: 978-3-030-50625-4
eBook Packages: Law and CriminologyLaw and Criminology (R0)