Overview of Class

1
Overview of Class

• Background Information
• Bivariate Tests
• Correlational Analysis

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Bivariate Statistical Analysis

• An Overview

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The Null Hypothesis

• Bivariate statistical tests are used in order to
  test the null hypothesis.
• The null hypothesis is a statement that there is
  no relationship between the two variables of
  interest (or there are no differences).
• We always test the null.
• Our finding allow us to either reject or not
  reject the null hypothesis.

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One-tailed vs. Two-tailed Hypotheses

• A one tailed hypothesis states the direction of a
  relationship.
• Part-time MSW students will have higher levels of
  preparation scores than full-time students.
• A two tailed hypothesis states that a
  relationship exists but does not state the
  direction.
• Students preparation scores are related to
  program track.

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Probability Continued...

• Probability is a measure of likelihood.
• Probability states the likelihood of an event
  occurring.
• The likelihood of an event occurring can range
  from 0 (never) to 1 (absolute certainty).
• Probability level is reported as a p-value (or
  sig. level).
• Conventional significance level is .05 (95
  confident that a relationship exists).

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Major Points of Discussion

• Test of Differences vs. Tests of Association
• Parametric vs. Non-parametric bivariate tests
• The Decision Tree
• Tests of Association (correlation)

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Tests of Differences vs. Tests of Relationships

• Differences
• Between groups
• Experimental and control
• Demographic factors
• Change over time
• Contain a nominal level (grouping variable)

• Relationships
• Association
• Correlation
• Surveys
• Contain ordinal and interval/ratio level variables

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Parametric vs. Nonparametic Tests

• Parametric Tests
• A normal distribution (dependent variable).
• Level of measurement (interval/ratio).
• Large sample size.

• Nonparametric Tests
• A non-normal distribution.
• Level of measurement not at the interval/ratio
  level.
• Smaller sample size.

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Bivariate Tests

• Parametric
  Non-parametric
• (Relationships)
• Pearsons R ? Spearmans Rho
• (Differences)
• Independent T-Test ? Mann Whitney U
• Paired Samples T-Test ? Wilcoxon Matched
• Oneway ANOVA ? Kruskal Wallis
• 
  Chi-square

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Tests of Association

• Introduction to Correlation Analysis

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Correlation

• The purpose of a correlational analysis is to
  determine whether there is a relationship or
  association between two variables. Two variables
  are related if knowing the value of one variable
  tells you something about the other variable.
• Correlation does not equate to causality.

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Correlation Symbols

• The r coefficient states mathematically what
  relationship exists between two variables. This
  is called the strength of the relationship.
• The r coefficient also indicates what type of
  relationship exists.
• The correlation coefficient may range from 1 to
  -1.

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Correlation Symbols continue...

• The p value indicates the significance of the
  relationship. (The probability of finding this
  relationship by chance -- the mathematical
  confidence in which there is in fact an observed
  relationship.)
• A p value of .05 or less would indicate that you
  are reasonably assured that an observed
  relationship exists. (see page 149)

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p-values

• The mathematical probability that a relationship
  between two variables (or difference between
  groups) has been produced by chance or sampling
  error.
• A p-value is the bottom line. All bivariate
  analyses produce a p-value.

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Correlation Symbols continue...

• Statistical significance is greatly affected by
  sample size.
• It is important to distinguish between
  significance and meaningfulness.
• The r squared is often used as a measure of the
  meaningfulness of r. This is a measure of the
  amount of variance that the variables share or
  the amount of explained variance.

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Understanding the SPSS Output
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Writing Up Results

• The write-up for a correlation analysis should
  include
• The statistical test utilized.
• The variables under examination.
• The value of r.
• The p level (statistical significance).
• The direction of the relationship (if
  applicable).
• If p is significant (less than .05), you should
  describe the meaningfulness of the relationship
  (r squared).