02 CARDS Significance Effect Size Power

Statistical Power

The probability that a study will give a significant result if the research hypothesis is true.

Type I Error (α)

The probability of incorrectly rejecting a true null hypothesis.

Effect Size

A standardized measure of the size of the mean difference in terms of the standard deviation.

Power Formula

The power of a test is determined by subtracting the value of beta from 1 (Power = 1 - β).

Sample Size (n)

An important factor affecting statistical power; larger sample sizes generally increase power.

Cohen's d

A measure of effect size that expresses the difference between two population means in terms of standard deviation.

Significance Level (α)

The threshold for statistical significance, with higher α levels generally leading to greater power.

Power Analysis

A method to determine the sample size required to detect an effect of a given size with a desired degree of confidence.

One-tailed Test

A hypothesis test that focuses on one direction of the effect, increasing the power compared to a two-tailed test.

Standard Deviation (σ)

A measure of variability that indicates the average distance of data points from the mean.

Example of Statistical Power

In a clinical trial, achieving a power of 0.8 means there is an 80% chance of correctly rejecting the null hypothesis if the drug has a true effect.

Example of Type I Error (α)

A Type I error occurs if a researcher concludes that a new medication is effective when it actually has no effect.

Example of Effect Size

An effect size of 0.5 indicates a medium-sized effect, meaning the means of the two groups differ by 0.5 standard deviations.

Example of Power Analysis

Conducting a power analysis for a study that aims to test a new teaching method may determine that 100 students are needed to detect a significant difference.

Example of One-tailed Test

Testing whether a new teaching technique results in higher test scores than the traditional method is a one-tailed test focusing on one direction.

Example of Significance Level (α)

In a research study, setting α at 0.05 means researchers accept a 5% chance of committing a Type I error.

Example of Sample Size (n)

A study with a sample size of 200 participants provides more statistical power compared to a study with only 30 participants.

Example of Standard Deviation (σ)

If the test scores of a class have a standard deviation of 10, most scores fall within 10 points of the average score.

Example of Cohen's d

A Cohen's d of 0.8 in a study comparing two instructional methods indicates a large effect size, signifying a substantial difference between their outcomes.