Leedy and Ormrod Ch. 11
Gray Ch. 14
The difference between Parametric
and Non-Parametric statistics
-appropriate for interval/ratio data
-generalizable to a population
-assumes normal distributions
-used with nominal/ordinal data
-not generalizable to a population
-does not assume normal distributions
Contingency (Cross-Tabs) Analysis
and Chi-Square or Gamma/Tau-b
- non-parametric (non-normal distributions)
Nominal or ordinal (categorical) data
Any type of distribution
The hypothesis test: The null hypothesis:
the two (or more) samples come from the
Conducting the Analysis:
a. calculate percentages within the categories
of the IV and compare across the categories of
the DV. Are there differences in the outcomes?
b. for nominal
Chi-square statistic: is the relationship (the above
Phi, Cramer's V, etc.: how strong is the relationship?
c. for ordinal
t-testfor gamma, tau-b: is the relationship (the above
Gamma, tau-b: how strong and what direction?
T-Tests (parametric) for Means and
The t-test is used to determine whether
sample(s) have different means. Essentially, the
t-test is the ratio between the sample mean
difference and the standard error of that
difference. The t-test makes some important
one or two levels of one or two variables
equal variances (relatively). Use the Levene’s test to
determine whether variances are equal.
a. The one sample t-test:
tests a sample mean against a known population mean The null hypothesis
tests if the sample mean is equal to the population mean.
b. The independent samples t-test:
tests whether the mean of one sample is different from the mean of another
sample. The null hypothesis tests if the mean of sample 1 is equal to the
mean of sample 2.
Note: With independent t-tests, you must pay attention to the standard error
of the sample(s). There are two ways to estimate the standard error. The
Levene test is used in SPSS to do this.
Equal variances: the two samples are relatively equal in size & distribution
Non-equal variances: the two samples are not equal in variance (large
c. The paired group t-test (dependent or related samples)
tests if two groups within the overall sample are different on the same
dependent variable The null hypothesis tests if the mean of (var1 - var2) is
equal to 0.
Overall, you will be looking for the t-value and its corresponding p-value.
Depending on your alpha level, you will accept/reject the null hypothesis
based on these numbers.
Analysis of Variance, or ANOVA, is testing the difference in
the means among 3 or more different samples.
One-way ANOVA Assumptions:
One independent variable -- categorical with two+ levels
Dependent variable -- interval or ratio
Two-way ANOVA Assumptions
Two or more independent variables -- categorical with two+
Dependent variable -- interval or ratio level
Analysis will include main effects and an interaction term.
ANOVA is testing the ratio (F) of the mean squares between
groups and within groups. Depending on the degrees of
freedom, the F score will show if there is a difference in the
means among all of the groups.
One-way ANOVA will provide you with an F-ratio and its
corresponding p-value. If there is a large enough difference
between the between groups mean squares and the within
groups mean squares, then the null hypothesis will be
rejected, indicating that there is a difference in the mean
scores among the groups. However, the F-ratio does not tell
you where those differences are. You can do ad-hoc
comparisons such as the Tukey-b, Bonferroni or Scheffe
test to do this.
Two-way ANOVA will provide you with an F-ratio and its
corresponding p-value as well as F-ratios and p-values for
each main effect and interaction term. When the interaction
is significant, the interaction means (in SPSS, ask for this
under options in GLM) should also be interpreted.
Used to test the presence, strength and direction
of a linear relationship among variables.
Correlation is a numerical expression that signifies
the relationship between two variables. Correlation
allows you to explore this relationship by
'measuring the association' between the variables.
Correlation is a 'measure of association' because
the correlation coefficient provides the degree of
the relationship between the variables. Correlation
does not infer causality! Typically, you need at
least interval and ratio data. However, you can run
correlation with ordinal level data with 5 or more
a. The relationships: Essentially, there are four types of
relationships: (1) positive, (2) negative, (3) curvilinear, and (4) no
b. The hypotheses and tests: The correlation statistic (Pearson's
r) tests the null hypothesis that there is no relationship between the
c. The Correlation Coefficient : Pearson's r, the correlation
coefficient, is the numeric value of the relationship between
variables. The correlation coefficient is a percentage and can vary
between -1 and +1. If no relationship exists, then the correlation
coefficient would equal 0. Pearson's r provides an (1) estimate of
the strength of the relationship and (2) an estimate of the direction
of the relationship.
If the correlation coefficient lies between -1 and 0, it is a negative
(inverse) relationship, 0 and +1, it is a positive relationship and is 0,
there is no relationship The closer the coefficient lies to -1 or +1, the
stronger the relationship.
d. Coefficient of determination: Related to the
correlation coefficient is the coefficient of
determination. This statistic provides the
percentage of the variance accounted for both
variables (x & y). To calculate the determination
coefficient, you square the r value. In other
words, if you had an r of 90, your coefficient of
determination would account for just 81 percent
of the variance between the variables.
e. Partial Correlation: When you need to
'control' for the effect of variables, you can use
Simple (Bivariate) and Multiple
Regression is used to model, calculate, and predict
the pattern of a linear relationship among two or
There are two types of regression -- simple &
Note: Variables should be approximately normally
distributed. If not, recode and use non-parametric
Dependent Variable: at least interval (can use ordinal if
using summated scale)
Independent Variable: should be interval. Independent
variables should be independent of each other, not
related in any way. You can use nominal if it is binary or
'dummy' variable (0,1)
Overall: The null tests that the regression
(estimated) line no better predicting dependent
variable than the mean line
Coefficients (slope "b", etc.): That the estimated
coefficient equals 0
Overall: R-squared, F-test
Coefficient: t tests
Only addresses linear patterns
Multicollinearity may be a problem
Agresti and Finley Statistical Methods
for the Social Sciences
Tabachnick and Fidell (2001) Using
For writing up the above statistics,
“From Numbers to Words”
Links at bottom of Soc302 webpage