stats mid 3

Power (in statistics)

The probability of detecting a real effect in a study.

Type I Error (α)

A false positive—rejecting a true null hypothesis.

Type II Error (β)

A false negative—not detecting a real effect.

Effect Size (d)

The difference between two population means expressed in terms of standard deviations.

Significance Level (α)

The threshold probability below which the null hypothesis is rejected.

Cohen's d

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

Sample Size (n)

The number of observations in a study that impacts the study's power.

Power Calculation

The method used to determine the sample size needed to achieve a desired level of power.

Cohen's Kappa

A measure of agreement used to assess the reliability of categorical items.

Post-Hoc Power

Power calculated after a study has been conducted, often considered misleading.

Noncentrality Parameter (δ)

A statistic used in power calculations to account for both effect size and sample size.

Assumption of Equal Variance

The assumption that the variances of two populations are equal when conducting certain statistical tests.

Meta-analysis

A statistical technique for combining results from multiple studies to arrive at a comprehensive conclusion.

Stereotype Threat

A situational predicament in which individuals are at risk of confirming negative stereotypes about their social group.

Resampling Methods

Techniques used to estimate the distribution of a statistic by repeatedly drawing samples from the data.

Harmonic Mean

A method for averaging that is appropriate when the means of two groups differ in sample size.

Type 1 error

rejecting the null hypothesis when it is actually true

what is a type 2 error

failing to reject the null hypothesis when it is actually false

what does a (alpha) represent in hypothesis testing?

the probability of making a type I error (rejecting Ho when it is true)

what does β (beta) represent in hypothesis testing?

The probability of making a type II error (not rejecting Ho when it is false)

what is statostical power

the probability of correctly rejecting Ho when it is false (1-β)

how does increasing sample size affect power?

it increases power by reducing variability and making it easier to detect a true effect

why is choosing the most powerful test important?

because it minimizes type II errors and increases the chance of detecting a true effect when it exists.

if a study fails to reject Ho but H1 is true, what can you conclude?

the study may not have had enough power to detect the difference

what happens to the power of the one-sample t-test when a increases

An increase in α (e.g., using α = .10 instead of α = .05) increases the power of the one-sample t-test. This is because increasing α makes it more likely that you will reject the null hypothesis, thereby making it easier to correctly reject a false null hypothesis, which increases power.

How does an increase in X̄ (sample mean) affect the power of the one-sample t test?

increases the power of the one-sample t-test because this change in the numerator of the test statistic increases the overall test statistic, making it more likely that you will reject the null hypothesis.

What is the effect of decreasing the denominator of the test statistic on power?

increases the power of the one-sample t-test because this change increases the overall test statistic, making it more likely you will reject the null hypothesis. This denominator decreases when either the sample size (N) increases or the population variance decreases.

Which factors can you influence when conducting a one-sample t test?

• As the person conducting the research, you can influence the following factors to increase power:

  • SX̄ (standard error of the mean)

  • α (Significance Level)

  • Sample size (N)

You cannot directly influence sX̄ (Standard Error), as it depends on the sample size and population variance.