Statistics Primer

(To help in understanding statistics found in readings—does not include the rules for reporting, etc. Some information has been drawn from Williams, F., (1986). __Reasoning with statistics, 3 ^{rd} ed.__ New York: Holt, Rinehart, & Winston.)

**Parameter**: characteristic of a population

**Statistic**: characteristic of a sample

**Statistical Inference**: estimating parameters from statistics.

**Probability**—How likely is the result that was found likely to be due to chance?

**Significance** p < 0.1 p < .05 p <.01 p < .001

Confidence 90% 95% 99% 99.9%

Descriptive Statistics

Number/frequency N = 245

Means M = 3.45

Standard Deviation SD = 4.18

Median Mdn = 22

**Degrees of Freedom (df)**: the number of values in a calculation that are free to vary (often it is the size of the sample minus 1; n-1, or the number of categories minus 1). It is used to determine what value of a statistic is needed for significance.

Two Basic Analyses: Differences and Relationship

Differences

**T-Test**—Tests the difference between means of two groups.

*t *(df of participants) = value, *p *< value

*t* = (153) = -1.83, *p *< .05

This means that in a sample of 154 respondents, a t value of –1.83 was obtained in calculating the difference in two means, and that that value would occur by chance only 5% of the time.

**Analysis of Variance (ANOVA)—**tests the difference between three or more groups by examining the variance of each group to a grand mean (between group) and within each group (within group) on one independent variable (factor)

* F *(df of categories, df of participants) = value,

(sometimes eta squared is provided to further support the strength)

*F *(2, 154) = 3.47, *p *<.05

**Multiple Factor Analysis of Variance (MANOVA**)—the same as ANOVA except that it can handle more than one independent variable (factor) and determine the interaction effects among those factors.

Shows as F tests among the various configurations.

Interaction Effects

Sex x Age x Education on Affectionate Communication

*F *(3, 65) = …

Sex x Age on Affect. Comm.

*F *(2, 65) =

Sex x Education on AC

*F *(2, 65) =

Age x Education on AC

*F *(2, 65) =

Main Effects

Sex on Affectionate Communication F (1, 65) =

Age on Affect. Comm. F (5, 65) =

Education on AC F (7, 65) =

Tests of Relationship

**Correlation (Pearson’s Product-Moment Correlation)**—tests whether two variables vary together either positively or negatively.

Coefficient of Correlation is a number between 1.0 and –1.0 (shows magnitude and direction)

+1.0 means there is a perfect positive relationship

0.0 means there is no relationship

-1.0 means there is a perfect negative relationship

The square of the correlation coefficient indicates how much variance is accounted for between the two variables (called the coefficient of determination).

r = .40 produces . r^{2} = .16, meaning 16% of the variance is

accounted for (84% is due to other factors)

r = .70 produces r^{2} = .49, meaning 49% of the variance is

accounted for (51% by other factors)

r = -.20 become s r^{2} = .04, meaning only 4% is accounted

A correlation can be statistically significant but account for very little variance between the two variables.

**Multiple Correlation**—a correlation calculated between three or more variables. *R* = +1.0 to –1.0

**Partial Correlation**—a correlation between two variables (X & Y) in which the effect of one or more other variables (Y) is removed from between the two variables (X & Y).

Factor Analysis—A method for determining which set of variables are most closely related to one another, and which ones aren’t.

Regression Analysis