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The definitional equation of sample variance is = (¯), where the divisor is called the degrees of freedom (DF), the summation is called the sum of squares (SS), the result is called the mean square (MS) and the squared terms are deviations from the sample mean. ANOVA estimates 3 sample variances: a total variance based on all the observation ...
To determine an appropriate sample size n for estimating proportions, the equation below can be solved, where W represents the desired width of the confidence interval. The resulting sample size formula, is often applied with a conservative estimate of p (e.g., 0.5): = /
When there are only two means to compare, the t-test and the F-test are equivalent; the relation between ANOVA and t is given by F = t 2. An extension of one-way ANOVA is two-way analysis of variance that examines the influence of two different categorical independent variables on one dependent variable.
The formula for the one-way ANOVA F-test statistic is =, or =. The "explained variance", or "between-group variability" is = (¯ ¯) / where ¯ denotes the sample mean in the i-th group, is the number of observations in the i-th group, ¯ denotes the overall mean of the data, and denotes the number of groups.
Suppose that we take a sample of size n from each of k populations with the same normal distribution N(μ, σ 2) and suppose that ¯ is the smallest of these sample means and ¯ is the largest of these sample means, and suppose S 2 is the pooled sample variance from these samples. Then the following random variable has a Studentized range ...
In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of one parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size ...
To determine if there is a significant difference between two means with equal sample sizes, the Newman–Keuls method uses a formula that is identical to the one used in Tukey's range test, which calculates the q value by taking the difference between two sample means and dividing it by the standard error:
It can be used in calculating the sample size for a future study. When measuring differences between proportions, Cohen's h can be used in conjunction with hypothesis testing . A " statistically significant " difference between two proportions is understood to mean that, given the data, it is likely that there is a difference in the population ...