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)

 

Statistical Tests

 

Parametric

Nonparametric

Assumptions for parametric tests

·          Data represent random samples and are
independent of each other (except
paired/repeated measures tests). 

·          Data are measured on a ratio/interval scale.

·          Variables are continuous or discrete (if n
and number of possible data values are large).

·          Data are normally distributed for each
group of each variable.

·          For questions regarding means, variances
among groups are homogeneous.

Assumptions for non-parametric tests

·          Data represent random samples and are
independent of each other (except
paired/repeated measures tests).

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

Differences

Means (2)

Indep. samples t

Mann-Whitney

Paired samples t

Wilcoxon

Means (>2)

ANOVA

Kruskal-Wallis

Variances
Bartlett’s

Levene’s

Frequencies

     -----

Goodness-of-fit

Relationships

Variables

Pearson correlation

Spearman correlation

Regression

     -----

Frequencies

     -----

Independence

 

 

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