(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, 3rd 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%
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
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)
(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.
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) =
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 . r2 = .16, meaning 16% of the variance is
accounted for (84% is due to other factors)
r = .70 produces r2 = .49, meaning 49% of the variance is
accounted for (51% by other factors)
r = -.20 become s r2 = .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.