Statistics review 4: sample size calculations

Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...

One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:

One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...

The degree of freedom for a particular statistical calculation is the number of values that are free to vary. As a result, the minimum number of independent numbers can specify a particular statistic. The degrees of freedom differ greatly depending on known and uncalculated statistical components.
For example, suppose there are three unknown numbers whose mean is 10; although we can freely assign values to the first and second numbers, the value of the last number can not be arbitrarily...

The degree of freedom for a particular statistical calculation is the number of values that are free to vary. Thus, the minimum number of independent numbers can specify a particular statistic. The degrees of freedom differ greatly depending on known and uncalculated statistical components.
For example, suppose there are three unknown numbers whose mean is 10; although we can freely assign values to the first and second numbers, the value of the last number can not be arbitrarily assigned.

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...