Transcript Class Review Week # 10 - University of Saint Joseph

Research Methods for
Counselors
COUN 597
University of Saint Joseph
Class # 9
Copyright © 2014 by R. Halstead. All rights reserved.
Class Objectives
Salkind Chapter 13 - Correlational Tests
Salkind Chapter 14 - Chi-square
Testing Correlation Coefficients
Let’s think way back in the semester to that time
when we were learning about correlation.
You will recall that the correlation coefficient
expressed the strength of relationship between two
sets of distributed scores.
We can establish if the correlation between two
variables is significant.
This is a very easy procedure very similar to the
ones that we have seen in recent weeks.
Steps in Computing the
Test Statistic
Step 1: A statement of the null hypothesis and
research hypotheses – the is no relationship between
the variables and the alternative.
The Null Hypothesis
Ho: Rxy = 0
The Research Hypothesis
H1: rxy = 0
Note: A directional research hypothesis is
reflected in the direction (+ or -) of the correlation
Step 2: Set the level of risk (or level of significance)
upon which your decision will be made to reject the
null hypothesis and risking Type I Error.
Steps in Computing the
Test Statistic
Step 3: Select the appropriate test statistic using
Salkind’s flow chart.
Step 4: Consult the appropriate table to determine
the Critical Value needed for rejecting the null
hypothesis for the statistic you are using.
To use the table you must determine the Degrees
of Freedom (df). Here, df is determined by n-2.
Steps in Computing the
Test Statistic
Step 6: Compare the Obtained Value and the Critical
Values or correlation for rejecting the null
hypothesis
Step 7: Commit to a decision. If the Obtained Value
is more extreme than the critical value (further out in
the tail of the normal curve) the test has been met.
We can reject the null hypothesis and conclude that
the correlation between the two variables is
Significant and can risk saying the strength of the
relationship is not do a chance occurrence.
r(28) = .393, p < .05
In the Salkind text we see the expression of the
results. So what does that mean?
r represents the test statistic that was used
28 is the number of degrees of freedom
.393 is the obtained value using the Person
Product Moment formula introduced in Chapter 5
p < .05 indicates that the probability is less than
5% on any one test of the null hypothesis that the
relationship between the two variables is due to
chance alone.
Significance vs. Meaningfulness
Again we must ask, “Just because something is
found to be significant, does that mean it is
meaningful?
Let’s take a look again at this problem. Say we use
the same correlation as in our example (.393). If we
square it to get the Coefficient of Determination, we
find that we can account for 15.4% of the variance.
This means that 84.6% of the variance is left
unaccounted for which is really worth noting when
we are trying to determine meaningfulness.
Chi-Square
Probability Probaschmility! What about when we
can’t use parametric tests?
Simple. We use nonparametric tests (also called
distribution-free statistics).
Nonparametric statistics allows you to effectively
deal with data that come in the form of frequencies
or proportions.
One-Sample Chi-Square
 Chi-square (“Ki – square) allows you to determine if what
you observe in a distribution of frequencies would be what
you would expect to occur by chance.
 A one-sample Chi-Square includes only one dimension
(logically, a two-sample Chi-square includes two
dimensions).
2
(O-E)
2
X
=
E
Steps in Computing Chi-Square
Step 1: A statement of the null hypothesis and
research hypotheses - no difference in the frequency
or the proportion of occurrences in each category.
The Null Hypothesis
Ho: P1 = P2
The Research Hypothesis H1: P1 = P2
Step 2: Set the level of risk (or level of
significance) upon which your decision will be
made to reject the null hypothesis and risking
Type I Error (e.g., .05).
Steps in Computing Chi-Square
Step 3: Select the appropriate test statistic. Here we
do not use Salkind’s statistic selection chart because
we are working with nonparametric data.
Step 4: Consult the appropriate table to determine
the Critical Value needed for rejecting the null
hypothesis for the statistic you are using.
See Table B.5 Critical Values for the Chi-Square
Steps in Computing Chi-Square
Step 6: Compare the Obtained Value and the Critical
Value.
Step 7: Commit to a decision. If the Obtained Value
is more extreme than the Critical Value then the null
hypothesis will be rejected thus concluding that the
two proportions are different.
2
X(2) = 20.6, p < .05
 In the Salkind text we see the expression of the results.
Chi-Square is the test statistic that was used
2 is the number of degrees of freedom
20.6 is the obtained value
p < .05 indicates that the probability is less than 5% that
on any one test of the null hypothesis that the frequency
of occurrence (votes) is equally distributed across all
categories.