Hypothesis Testing
- Relationships
Updated 16 November 2008
“I’ve learned that you can’t be taken
seriously in any scientific discipline without an understanding of
statistics.” Bethany
Williams, PhD (HU 2004)
You are expected to
read the corresponding textbook chapters as we cover them in class.
Working the exercises at the end of the chapters will enhance
your understanding.
(click
for answers to all exercises)
Analysis of relationships (among cases of
variables)
A. Correlation
(=association); no functional dependence (e.g., wing length vs. tail length)
B. Example: positive,
negative, and no relationship
C. 2 questions:
1. are two variables
related in a linear way? (significant? =reject null of no relationship)
a. if answer is
“no”, do not go further
b. if answer is
“yes”, ask:
2. what is the strength
of the relationship? (value of correlation coefficient)
a. may have a “weak”
relationship (low value of correlation coefficient) that is “highly
significant” (P<0.01)
b. may have a
“strong” relationship (high value of correlation coefficient) that is “not
significant” (P>0.05; in reality, no correlation)
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Parametric |
Nonparametric |
·
Data
represent random samples and are ·
Data
are measured on a ratio/interval scale. ·
Variables
are continuous or discrete (if n ·
Data
are normally distributed for each ·
For
questions regarding means, variances Assumptions for non-parametric tests
·
Data
represent random samples and are |
Guidelines for determining appropriate
analyses ·
Read the question
carefully; make sure you understand what the question is asking ·
Look
for key words: difference, relationship, association, correlation ·
A “v”
word, (vary, variance, variation) will be present for questions of
differences in variances ·
If a
“v” word does not appear in a difference question and the question does not
concern frequencies, assume that the question concerns differences in means ·
The
word “affect” (or “effect”) can be used in both difference and relationship
questions – you must understand the use of the word in context |
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Differences |
Means (2) |
Indep. samples t |
Mann-Whitney |
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Paired samples t |
Wilcoxon |
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Means (>2) |
ANOVA |
Kruskal-Wallis |
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Variances |
Bartlett’s
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Levene’s |
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Frequencies |
----- |
Goodness-of-fit |
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Relationships |
Variables |
Pearson correlation |
Spearman
correlation |
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Regression |
----- |
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Frequencies |
----- |
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Pearson
correlation (Chap. 13)
1. Purpose: Test whether the cases of two variables are
correlated
2. Comments: if variables are related, the relationship is
linear
3. Null
hypothesis: H0: r(var1, var2) = 0
4. Test statistic
(correlation coefficient, r (varies
from -1 to +1) and probability source: Systat/Systat
5. r2
(coefficient of determination) - proportion of variation in Y that is explained
by variation in X
6. SYSTAT path: Analyze®Correlation®Simple (enter
variables; Continuous Data)
SYSTAT output: (EGGSIZE.SYD; select sex=1 and year=81); pic Pearson correlation matrix
HWGT HSVL HWGT