"Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample."
Calculating the sample size needed for a particular study and estimating the power of a study.
Types of hypothesis tests: Understanding the different types of hypothesis tests (one-sided vs. two-sided, independent samples vs. paired samples) is important in determining the appropriate test to use when conducting power and sample size calculations.
Effect size: Effect size is the magnitude of a treatment effect or difference between two groups, and it is used to determine the minimum sample size needed to detect a statistically significant difference.
Power: Power is the probability of correctly rejecting a null hypothesis when the alternative hypothesis is true; it is influenced by sample size, effect size, and alpha level.
Alpha level: Alpha is the probability of making a Type I error (rejecting the null hypothesis when it is actually true), and it is typically set at 0.05.
Type II error: Type II error occurs when a null hypothesis is not rejected when it is actually false or when the calculated power is lower than the desired level of power.
Sample size determination: The process of determining the sample size required to achieve certain statistical power or precision of estimation.
Statistical significance: Statistical significance is a measure of the likelihood that a difference observed in a sample is not due to chance.
Confidence intervals: Confidence intervals provide a range of values within which the true population parameter is likely to fall.
Parametric vs. non-parametric tests: Parametric tests assume a certain distribution of data, while non-parametric tests make no assumptions about the distribution; understanding these differences is important in selecting the appropriate test for power and sample size calculations.
Correlation and regression: Understanding the principles of correlation and regression is important in determining the strength of a relationship between variables and how to account for them in power and sample size calculations.
One-sample t-test: Determines sample size and power for testing the mean of a single group against a known or hypothesized value.
Two-sample t-test: Determines sample size and power for testing the difference in means between two independent groups.
One-sample proportion test: Determines sample size and power for testing a single binomial proportion against a known or hypothesized value.
Two-sample proportion test: Determines sample size and power for testing the difference in binomial proportions between two independent groups.
Chi-squared test of independence: Determines sample size and power for testing the association between two categorical variables.
Continuous outcome regression: Determines sample size and power for regression models that aim to explain the relationship between a continuous outcome and various predictors.
Logistic regression: Determines sample size and power for the prediction models that aim to explain the relationship between a binary outcome and various predictors.
Survival analysis: Determines sample size and power for time-to-event data where the goal is to compare the survival curves between two groups.
Cluster randomized trials: Determine the required sample size and power for conducting a trial where the units of randomization are clusters, such as schools or clinics.
Non-inferiority trials: Determine the required sample size and power for testing whether a new intervention is not inferior to a standard intervention.
Equivalence trials: Determine the required sample size and power for testing whether a new intervention is equivalent to a standard intervention.
Correlation: Determine the required sample size and power for examining the correlation between two continuous variables.
ANOVA: Determine the required sample size and power for testing the differences in means among three or more independent groups.
ANCOVA: Determine the required sample size and power for testing the differences in means among three or more independent groups controlling for a covariate.
Meta-analysis: Determine the required sample size and power to pool data from multiple studies for a systematic review or meta-analysis.
"The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample."
"The sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power."
"In complicated studies, there may be several different sample sizes: for example, in a stratified survey there would be different sizes for each stratum."
"In a census, data is sought for an entire population, hence the intended sample size is equal to the population."
"In experimental design, where a study may be divided into different treatment groups, there may be different sample sizes for each group."
"Small samples, though sometimes unavoidable, can result in wide confidence intervals and risk of errors in statistical hypothesis testing."
"If a high precision is required (narrow confidence interval), this translates to a low target variance of the estimator."
"Using a target for the power of a statistical test to be applied once the sample is collected."
"Using a confidence level - the larger the required confidence level, the larger the sample size (given a constant precision requirement)."