Chapter 13 UNDERSTANDING RESEARCH RESULTS: STATISTICAL INFERENCE

Degrees of freedom

A concept used in tests of statistical significance; the number of observations that are free to vary to produce a known outcome.

Analysis of variance

A statistical significance test for determining whether two or more means are significantly different. F is the ratio of systematic variance to error variance.

t test

A statistical significance test used to compare differences between means.

The F Test (analysis of variance)

An extension of the t test - typically used when there is more than one level of an independent variable

Type II error

An incorrect decision to accept the null hypothesis when it is false.

Type I error

An incorrect decision to reject the null hypothesis when it is true.

Confidence interval

An interval of values within which there is a given level of confidence (e.g., 95%) where the population value lies.

Type II Errors

Made when the null hypothesis is accepted although in the population the research hypothesis is true

Error variance

Random variability in a set of scores that is not the result of the independent variable. Statistically, the variability of each score from its group mean.

Statistical significance

Rejection of the null hypothesis when an outcome has a low probability of occurrence (usually .05 or less) if, in fact, the null hypothesis is correct.

Confidence Intervals

The % of confidence that we have that the result falls between two specific values (tied to sample size, and precision of estimation of population value)

Statistical Significance

The confidence researchers have that their result obtained was not due to chance. Tied to population size AND effect size - larger effects + larger populations = increased likelihood of finding statistical significance

Research hypothesis

The hypothesis that the variables under investigation are related in the population—that the observed effect based on sample data is true in the population.

Null hypothesis

The hypothesis, used for statistical purposes, that the variables under investigation are not related in the population, that any observed effect based on sample results is due to random error.

Probability

The likelihood that a given event (among a specific set of events) will occur.

Effect Size

The magnitude of the differences between groups, or the magnitude of the relationship between variables

Research Hypothesis

The means of the populations from which the samples were drawn ARE NOT equal

Null Hypothesis

The means of the populations from which the samples were drawn ARE equal

Power

The probability of correctly rejecting the null hypothesis.

Alpha level

The probability of incorrectly rejecting the null hypothesis that is used by a researcher to decide whether an outcome of a study is statistically significant (most commonly, researchers use a probability of .05).

Sampling distribution

Theoretical distribution of the frequency of all possible outcomes of a study conducted with a given sample size.

Systematic variance

Variability in a set of scores that is the result of the independent variable; statistically, the variability of each group mean from the grand mean of all subjects.

T Value

a ratio of two aspects of the data The difference between the group means and The variability within groups

Inferential statistics

allows us to make conclusion/inferences about the population, on the basis of sample data

There is universal agreement that the consequences of making a Type I error

are more serious than those associated with a Type II error

Larger sample sizes help us obtain

more accurate estimations of population values. With larger sample sizes, we are more likely to find significant results if indeed there are really results to be found.

Inferential statistics are

necessary because the results of a given study are based on data obtained from a single sample of participants and Data are not based on an entire population of scores

Type I Errors

o Made when the null hypothesis is rejected but the null hypothesis is actually true o Obtained when a large value of t or F is obtained by chance alone o We DO NOT WANT to make a Type I error!!!

Inferential statistics gives us a tool to determine whether the differences between groups in our sample is due to

random error or due to an actual difference between groups in the population of interest.

The "critical value" that t needs to be in order to obtain a significant result changes based on

sample size and whether or not the hypothesis is directional

If sample sizes are too small

sometimes true differences between groups (or true relationships among variables) are not uncovered in our statistical analyses

p < .05, or p < .01

this is referring to a 5% or a 1% likelihood that the results (the group relationships, or group differences) occurred by chance.

Goal Of Statistical Inference

to see if we can "reject" the idea that the null hypothesis is true. If we can "reject" the null hypothesis, then we can "accept" the research hypothesis

The T Test Is Conducted..

to see if we can reject the null hypothesis

Steps in analysis

• Input data o Rows represent cases or each participant's scores o Columns represent for a participant's score for a specific variable • Conduct analysis • Interpret output

COMPUTER ANALYSIS OF DATA

• SPSS • SAS • Minitab • Microsoft Excel

IMPORTANCE OF REPLICATIONS

• Scientists attach little importance to results of a single study • Detailed understanding requires numerous studies examining same/similar variables under different situations/conditions • Researchers look at the results of studies that replicate/extend previous investigations