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Comparison Wise Error Rate

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the simple question posed by an analysis of variance - do at least two treatment means differ? It may be that embedded in a group of experiment wise error rate treatments there is only one "control" treatment to which every other treatment experimentwise error rate should be compared, and comparisons among the non-control treatments may be uninteresting. One may also, after performing an analysis comparisonwise error rate of variance and rejecting the null hypothesis of equality of treatment means want to know exactly which treatments or groups of treatments differ. To answer these kinds of questions requires careful

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consideration of the hypotheses of interest both before and after an experiment is conducted, the Type I error rate selected for each hypothesis, the power of each hypothesis test, and the Type I error rate acceptable for the group of hypotheses as a whole. Comparisons or Contrasts If we let represent a treatment mean and ci a weight associated with the ith family wise error rate treatment mean then a comparison or contrast can be represented as: , where It can be seen that this contrast is a linear combination of treatment means (other contrasts such as quadratic and cubic are also possible). All of the following are possible comparisons: because they are weighted linear combinations of treatment means and the weights sum to zero. For example, previously we have performed comparisons between two treatment means using the t - statistic: with (n1 + n2) - 2 degrees of freedom. This statistic is a "contrast." The numerator of this expression follows the general form of the contrast outlined above with the weights c1 and c2 equal to 1 and -1, respectively: However, we also see that this contrast is divided by the pooled within cell or within group variation. So, a contrast is actually the ratio of a linear combination of weighted means to an estimate of the pooled within cell or error variation in the experiment: with degrees of freedom. For a non - directional null h

Descriptive Statistics Hypothesis Testing General Properties of Distributions Distributions Normal Distribution Sampling Distributions Binomial and Related Distributions Student's t Distribution Chi-square and F Distributions Other Key Distributions Testing for Normality family wise error rate post hoc and Symmetry ANOVA One-way ANOVA Factorial ANOVA ANOVA with Random or Nested Factors

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Design of Experiments ANOVA with Repeated Measures Analysis of Covariance (ANCOVA) Miscellaneous Correlation Reliability Non-parametric Tests Time Series Analysis

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Survival Analysis Handling Missing Data Regression Linear Regression Multiple Regression Logistic Regression Multinomial and Ordinal Logistic Regression Log-linear Regression Multivariate Descriptive Multivariate Statistics Multivariate Normal Distribution Hotelling’s T-square MANOVA Repeated Measures http://online.sfsu.edu/efc/classes/biol458/multcomp/multcomp.htm Tests Box’s Test Factor Analysis Cluster Analysis Appendix Mathematical Notation Excel Capabilities Matrices and Iterative Procedures Linear Algebra and Advanced Matrix Topics Other Mathematical Topics Statistics Tables Bibliography Author Citation Blogs Tools Real Statistics Functions Multivariate Functions Time Series Analysis Functions Missing Data Functions Data Analysis Tools Contact Us Experiment-wise error rate We could have conducted the analysis for Example 1 of http://www.real-statistics.com/one-way-analysis-of-variance-anova/experiment-wise-error-rate/ Basic Concepts for ANOVA by conducting multiple two sample tests. E.g. to decide whether or not to reject the following null hypothesis H0: μ1 = μ2 = μ3 We can use the following three separate null hypotheses: H0: μ1 = μ2 H0: μ2 = μ3 H0: μ1 = μ3 If any of these null hypotheses is rejected then the original null hypothesis is rejected. Note however that if you set α = .05 for each of the three sub-analyses then the overall alpha value is .14 since 1 – (1 – α)3 = 1 – (1 – .05)3 = 0.142525 (see Example 6 of Basic Probability Concepts). This means that the probability of rejecting the null hypothesis even when it is true (type I error) is 14.2525%. For k groups, you would need to run m = COMBIN(k, 2) such tests and so the resulting overall alpha would be 1 – (1 – α)m, a value which would get progressively higher as the number of samples increases. For example, if k = 6, then m = 15 and the probability of finding at least one significant t-test, purely by chance, even when the null hypothesis is true is over 50%. In fac

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