Overview of Inferential Statistics

Question 1

Central limit theorem makes three predictions about sampling distribution of means. What are they?

Answer 1

(a) The sampling distribution will increasingly approach a normal shape as the sample size increases, regardless of the shape of the population distribution of scores.
(b) The mean of the sampling distribution of means will be equal to the population mean.
(c) The standard deviation of the sampling distribution – which is referred to as the standard error of means – will be equal to the population standard deviation divided by the square root of the sample size.

Question 2

When a hypothesis is stated in a way that indicates that the independent variable does not have an effect on the dependent variable, it is called a _____.

When the hypothesis is stated in a way that indicates that the independent variable does have an effect on the dependent variable, it is called _____.

Answer 2

Null hypothesis; alternate hypothesis

The alternative hypothesis is usually most similar to the verbal hypothesis.

Question 3

What are the two possible correct decisions in regards to a null hypothesis?

Answer 3

Retains a true null hypothesis - any observed effects of IV on DV are due to sampling error or other factors.

Rejecting a false one - correctly concluding that the independent variable has had a significant effect on the dependent variable.

Question 4

In this type of decision error, the researcher has concluded that the independent variable has had a significant effect on the dependent variable, but the observed effect is actually due to sampling error or other factors

Answer 4

Type I error (AKA false positive)

Question 5

The probability of making a Type I error is know as _____.

Answer 5

Alpha (AKA the level of significance)

It is usually set at .05 or .01

Question 6

In this type of incorrect decision, a researcher retains a false null hypothesis. It is called ____.

Answer 6

Type II error.

Question 7

The probability of making a Type II error is know as _____.

Answer 7

Beta.

Beta is not set by the researcher, but can be reduced by increasing the statistical power.

Question 8

Statistical power (the ability to reject a false null hypothesis) is affected by four factors. They are…?

Answer 8

1. Size of alpha - larger alpha = more power
   (but it’s kept small to reduce probability of Type I error)
2. Size of the effect of the IV on the DV.
3. Sample size - MOAR SAMPLE = MOAR POWER!
4. Inferential statistical test chosen for analysis. Parametric tests (e.g., t-tests and analysis of variance) are more powerful than nonparamentric tests (e.g., chi-squared).