Essentials of Statistics for the Behavioral Sciences: Chapters 6-9

Question 1

Probability

Answer 1

For a situation in which several different outcomes are possible, the probability for any specific outcome is defined as a fraction or a proportion of all the possible outcomes. If the possible outcomes are identified as A, B, C, D, and so on, then probability of A = number of outcomes classified as A/ total number of possible outcomes

Question 2

Random Sample

Answer 2

This requires that each individual in the population has an equal chance of being selected. A second requirement, necessary for many statistical formulas, states that the probabilities must stay constant from one selection to the next if more than one individual is selected.

Question 3

Distribution of Sample Means

Answer 3

The collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population.

Question 4

Law of Large Numbers

Answer 4

The larger the sample size (n), the more probable it is that the sample mean will be close to the population mean.

Question 5

Sampling Distribution

Answer 5

A distribution of statistics obtained by selecting all the possible samples of a specific size from a population.

Question 6

Sampling Error

Answer 6

The natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.

Question 7

Standard Error of M

Answer 7

The standard deviation of the distribution of sample means, σM. The standard error provides a measure of how much distance is expected on average between a sample mean (M) and the population mean (μ).

Question 8

Alpha Level

Answer 8

The probability that the test will lead to a Type I error. That is, the alpha level determines the probability of obtaining sample data in the critical region even though the null hypothesis is true.

Question 9

Level of Significance

Answer 9

A probability value that is used to define the concept of “very unlikely” in a hypothesis test.

Question 10

Alternative Hypothesis (H1)

Answer 10

This states that there is a change, a difference, or a relationship for the general population. In the context of an experiment, H1 predicts that the independent variable (treatment) does have an effect on the dependent variable.

Question 11

Critical Region

Answer 11

Composed of the extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true. The boundaries for the critical region are determined by the alpha level. If sample data fall in the critical region, the null hypothesis is rejected.

Question 12

One-Tailed/Directional Hypothesis Test

Answer 12

In this, the statistical hypotheses (H0 and H1) specify either an increase or a decrease in the population mean. That is, they make a statement about the direction of the effect.

Question 13

Effect Size

Answer 13

A measure of this is intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the sample(s) being used.

Question 14

Hypothesis Test

Answer 14

A statistical method that uses sample data to evaluate a hypothesis about a population.

Question 15

Null Hypothesis (H0)

Answer 15

This states that in the general population there is no change, no difference, or no relationship. In the context of an experiment, H–0 predicts that the independent variable (treatment) has no effect on the dependent variable (scores) for the population.

Question 16

Power

Answer 16

The probability that the test will correctly reject a false null hypothesis. That is, power is the probability that the test will identify a treatment effect if one really exists.

Question 17

Statistically Significant

Answer 17

A result is said to be this if it is very unlikely to occur when the null hypothesis is true. That is, the result is sufficient to reject the null hypothesis. Thus, a treatment has a significant effect if the decision from the hypothesis test is to reject H0.

Question 18

Type I Error

Answer 18

This occurs when a researcher rejects a null hypothesis that is actually true. In a typical research situation, a Type I error means the researcher concludes that a treatment does have an effect when in fact it has no effect.

Question 19

Type II Error

Answer 19

This occurs when a researcher fails to reject a null hypothesis that is really false. In a typical research situation, a Type II error means that the hypothesis test has failed to detect a real treatment effect.

Question 20

t Distribution

Answer 20

The complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df). The t distribution approximates the shape of a normal distribution.

Question 21

t Statistic

Answer 21

Used to test hypotheses about an unknown population mean, μ, when the value of σ is unknown. The formula for the t statistic has the same structure as the z-score formula, except that the t statistic uses the estimated standard error in the denominator.

Question 22

Degrees of Freedom

Answer 22

Describe the number of scores in a sample that are independent and free to vary. Because the sample mean places a restriction on the value of one score in the sample, there are n–1 degrees of freedom for the sample (see Chapter 4).

Question 23

Estimated Standard Error (sM)

Answer 23

This is used as an estimate of the real standard error σM when the value of _ is unknown. It is computed from the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean M and the population mean μ.