New Biostatistics PDF - Analysis of Variance (ANOVA)

StatisticalWorkshop Series 2023 Workshop 3: Analysis of Variance ( One – Way ANOVA) Dr. Arass J. Noori Goals Data Normality Statistics Scale of Variables Distributions Test selection...

StatisticalWorkshop Series 2023 Workshop 3: Analysis of Variance ( One – Way ANOVA) Dr. Arass J. Noori Goals Data Normality Statistics Scale of Variables Distributions Test selection ANOVA Sample size calculation Classification of Variables Interval Ratio  Scale of measures Scales  ANOVA ▪ Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ▪ In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means.  ▪ One-Way ANOVA ▪ Full Factorial ANOVA (also called two-way ANOVA) Types Why Does ANOVA work? Limitations of ANOVA? There is Difference, BUT which pair Effect size? Post Hoc Multiple comparisons One-Way ANOVA The one-way analysis of variance is also known as single-factor ANOVA or simple ANOVA. The one-way ANOVA is suitable for experiments with only one independent variable (factor) with two or more levels (dependent variable). A one-way ANOVA assumes: Independence: The value of the dependent variable for one observation is independent of the value of any other observations. Normalcy: The value of the dependent variable is normally distributed. Variance: The variance is comparable in different experiment groups. Continuous: The dependent variable is continuous and can be measured on a scale which can be subdivided. The null hypothesis (H0) is that all population means are equal, while the alternative hypothesis (H1) is that at least one mean differs.  One - Way Anova Test Requirements 1. More than 2 samples. 2. The population from which the samples are brought has a normal distribution. 3. An independent variable for two or more categorical independent classes. 4. Dependent variable must be continuous: Interval or Ratio 5. There needs to be homogeneity of variances. 1. Arrange data correctly. 2. Normality test for the dependent variable 3. Click Analyze > Compare Means > One-Way ANOVA... on the top menu Post hoc  Post hoc Bonferroni (more conservative) has more power when the number of comparisons is small, whereas Tukey is more powerful when testing large numbers of means.  ANOVA Test Result  A one-way ANOVA was performed to compare the effect of [independent variable] on [dependent variable]. A one-way ANOVA revealed that there [was or was not] a statistically significant Report difference in [dependent variable] between at least two groups (F(between groups df, within groups df) = [F-value], p = [p-value]). Tukey’s HSD Test for multiple comparisons found that the mean value of [dependent variable] was significantly different between [group name] and [group name] (p = [p-value], 95% C.I. = [lower, upper]). There was no statistically significant difference between [group name] and [group name] (p=[p-value]). A one-way ANOVA was performed to compare the effect of three different studying techniques on exam scores. A one-way ANOVA revealed that there was a statistically significant difference in mean exam score between at least two groups (F(2, 27) = [4.545], p = 0.02). Tukey’s HSD Test for multiple comparisons found that the mean value of exam score was significantly different between technique 1 and technique 2 (p = 0.024, 95% C.I. = [-14.48, -0.92]). There was no statistically significant difference in mean exam scores between technique 1 and technique 3 (p=0.883) or between technique 2 and technique 3 (p=0.067). Effect Size Eta-squared (η2) and partial eta-squared (ηp2) are effect sizes that express the amount of variance accounted for by one or more independent variables. Click Analyze > General Linear Model> Univariate... on the top menu Effect Size SSeffect 2280.15 SSerror 412.4 n2P 0.846837 84.6% 2.4 Click Analyze > General Linear Model> Univariate.......... >>>> Options > Estimates of effect size  G*Power If the effect size is NOT to be calculated, Sample size but based on Cohn’s suggestions: estimation for ANOVA But if the effect size is to be calculated: Q&A