Chapter 5-6 Stats

Distribution Of Means

The Distribution of means is the collection of sample means for all possible random samples of a particular size obtained from the population

Two Tailed Test Cutoffs

.05 = +- 1.96

.01 = +- 2.58

One Tailed Test Cutoffs

.05 = +- 1.64

.01 = +- 2.33

DOM Shape Assumption

If the population is normal = distribution of means is normal

Even if the original population is not normal, if N >= 30 then the DOM becomes approximately normal

DOM Mean Assumption

The mean of the DOM equals the mean of the population.

DOM Variance Assumption

The DOM has less variability than the original population because averaging scores out extreme values.

Center Limit Theorem

As the sample size increases, the DOM approaches a normal distribution regardless of the shape of the population

Standard Error

There will usually be a discrepancy between sample mean and the true population; because of this, this measures how much the sample means typically vary from the population

Confidence Interval (CI)

Used to get a sense of accuracy of an estimated population; range of all possible values for the true population base on sampling

Effect Size

The magnitude, or strength, of treatment - independent from the sample; Can be statistically significant without much practical power.

Statistical Power

Probability that the study will produce statistically significant results if the research hypothesis is true

Statistical Power Influences (Increase Power)

- Larger Sample Size

- Larger Effect Size

- Larger Alpha Level

- Less Variability (Smaller Standard Deviation)

Power: Larger Sample Size

This increases power because it decreases SE and makes it easier to detect real differences

Power: Larger Effect Size

This makes things easier to detect and hence increases the power

Power: Larger Alpha Size

Difference between .05 and .01 alpha.

Increasing this can make it easier to reject the null hypothesis; but increasing this puts you at risk for a Type 1 Error.

Power: Less Variability (Smaller Standard Deviation)

This increase power because treatment effects are easier to distinguish from random variation. Scores are more consistent.

Type 1 Error

Occurs when you reject a a true hypothesis: Think false alarm

Type 2 Error

Occurs when you fail to reject a false hypothesis; Think missed detection

Limits Of Hypothesis Testing

- Cannot prove the NH is true

- Statistical Difference does not mean practical significance

- Does not tell us why

- Affected by sample size

- Dependent on Alpha Level

- Errors can Occur (Type 1 & 2)

Confidence Interval 95%

+- 2.58

Confidence Interval 99%

+- 1.96

Effect Sizes Meanings

.20 = Small

.50 = Medium

.80 = Large