2022 Introduction to Statistics in Research Mitchell 2nd ed

I N T R O T O R E S E A R C H : D A T A V I S U A L I Z A T I O N & C O M M O N S T A T T E S T S

Demonstrate One way ANOVA test The one-way ANOVA (Analysis of Variance) is an omnibus test statistic and cannot tell you which specific groups were statistically significantly different from each other, only that at least two groups were significantly different. The one-way ANOVA is a parametric test. It requires a post hoc test.

The average (mean) of THREE+ independent groups, interventions, or scores

Dependent Variable (outcome) Interval or ratio (i.e. continuous)

Independent Variable (Explanatory)

Usually three levels of variables

A one-way ANOVA uses one independent variable, while a two-way ANOVA uses two.

WHEN TO USE: Use an ANOVA when you have three or more categorical, independent groups. In the sample data, the categorical variables are North, South, East, and West region, but it could just as easily be ethnicity, professions, or physical activity. No participants should be in more than one group (independence of observations); otherwise, you a different test. TEST IT GRAPHICALLY: Use box plots or confidence interval plots. One of the main assumptions for a one-way ANOVA is that there should not be significant outliers. Outliers can have a negative effect on the one-way ANOVA and reduce the validity of the results.

Assumptions

Check it

Assumptions not met?

Residuals should be normally distributed

Test Graphically: Histogram, or Q-Q Plot

Use Kruskall-Wallis test (non- parametric)

(quantiles of the data versus quantiles of a distribution) Q- Q plot works well for small sample size Test numerically: Shapiro Wilk Levene’s test – default for SPSS Bartlett’s test (more sensitive to departures from normality)

Homogeneity of variance

Use Welch test (non- parametric) – Adjust for the differences in variance. For post hoc, use Games-Howell or Kruskall-Wallis

HYPOTHESIS:

There are a couple of ways to test the hypothesis. First review the null and alternative hypothesis.

Null Hypothesis

Alternative hypothesis

H o : µ 1 = … = µ k (all the population means are equal)

H a : Not µ 1 = … = µ k (at least one of the k population means differs from the others)

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