chapter 13

statistics

statistics

are quantitative measurements of samples

descriptive statistics

describe sample central tendency and variability

inferential statistics

allow us to draw conclusions about a parent population from a sample.

population

is a set of people, animals, or objects that share at least one characteristic in common (like college sophomores)

sample

is a subset of the population that we use to draw inferences about the population

statistical inference

is the process by which we make statements about a parent population based on a sample

variability

• For a set of dependent variable measurements, there is — when the scores are different.

• — “spreads out” a sample of scores drawn from a population

null hypothesis (H0)

— is the statement that the scores came from the same population and the independent variable did not significantly affect the dependent variable.

statistically significant

Results are — when the difference between our treatment groups exceeds the normal variability of scores on the dependent variable

alpha level (.01 or .05)

Statistical significance means that there is a treatment effect at an — we have preselected

alternative hypothesis (H1)

is the statement that the scores came from different populations the independent variable significantly affected the dependent variable

frequency distribution

displays the number of individuals contributing a specific value of the dependent variable in a sample.

X-axis (abscissa)

The values of the dependent variable are indicated on the horizontal —-

Y-axis (ordinate)

the frequencies of these values are indicated on the vertical —-

reject the null hypothesis

The greater the normal variability in the population, the larger the difference between
groups required to

directional hypothesis

• predicts the “direction” of the difference between two groups on the dependent variable.

• For example: The experimental group will lower their systolic blood pressure more than the control group

nondirectional hypothesis

• predicts that the two groups will have different values on the dependent variable:

• For example: The experimental group and control group will achieve different systolic blood pressure reductions.

significance level (alpha)

is our criterion for deciding whether to accept or reject the null hypothesis

.05

• Psychologists do not use a significance level larger than —

• A significance level of — means that a pattern of results is so unlikely that it could have occurred by chance fewer than 5 times out of 100.

type 1 error (a)

• is rejecting the null hypothesis when it is correct.

• The experimenter determines the risk of a — by selecting the alpha level.

type 2 error (B)

is accepting the null hypothesis when it is false

American Psychological Association

task force recommended that researchers include estimates of effect size and confidence intervals, in addition to p values.

p value

When you calculate a —e that is statistically significant, this means that your results are
unlikely to be due to chance (are probably real)

effect size

estimates the strength of the association between the independent and dependent variable—the percentage of the variability in the dependent variable is due to the independent variable

confidence interval

is a range of values above and below a sample mean that is likely to contain the population mean (usually 95% or 99% of the time).

critical region

• is a region of the distribution of a test statistic sufficiently extreme to reject the null hypothesis.

• For example, if our criterion is the .05 level, the — consists of the most extreme 5% of the distribution.

one-tailed test

• has a critical region at one tail of the distribution.

• We use a — with a directional hypothesis

two-tailed test

• has two critical regions, found at opposite ends of the distribution.

• We use a — with a nondirectional hypothesis

inferential statistics

• allow us to predict the behavior of a population from a sample

• examples: t test and f test