Overview

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Overview

• Revisiting key concepts
• Tests of Differences
• Independent T-Test and Mann Whitney U

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Parametric vs. Nonparametic Tests

• Parametric Tests
• A normal distribution (dependent variable).
• Level of measurement (interval/ration).
• 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
• (Association)
• 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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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 Theory An Overview

• Utilized as the basis for determining if a
  relationship exists between two variables or if
  there are differences between variables.
• Tells us the (mathematical) likelihood of an
  event occurring. (i.e., What is the probability
  of this relationship occurring simply due to
  chance?)
• 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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Forging Ahead Test of Differences

• Parametric
  Non-parametric
• (Relationships)
• Pearsons R ? Spearmans Rho
• (Differences)
• Independent t-test ? Mann Whitney U

8
Z-scores The Underpinning Concept

• Tests of differences allow one to specify if
  there are significant differences between two
  scores.
• Statistical differences are calculated based on
  probability theory and the use of confidence
  intervals/rejection regions.
• Rejection regions are developed using z-score
  principles.

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Establishing Rejection Regions

• Two tailed hypothesis
• Divide the selected rejection criteria (.05) by
  2.
• Subtract the derived value from .50, and multiply
  by 100.
• Locate the derived proportion in the normal
  distribution table.
• Determine the corresponding z-score.
• Any score having an associated z-score above the
  rejection criteria is said to be statistically
  different from the mean.

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Rejection continues...

• One-tailed hypothesis
• Simply skip the first step
• .50-.05 .45 x 100 45.00
• Associated z-score of 1.65

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Comparing Differences Between Two Groups

• Independent Samples T-test
• Used to compare two groups on an interval/ratio
  level variable when all other parametric
  assumptions are met.
• Mann Whitney U
• Used to compare two groups when all parametric
  assumptions are not met.

12
Independent Samples T-Test

• Locate mean for both groups.
• Determine if the variance (spread) for each
  group is comparable.
• Identify t-value and associated p-value.

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SPSS Printout
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The Mann Whitney U

• Identify/compare the mean rank scores.
• Locate the z-value and the associated p-value.
• If the groups have the same distributions, their
  mean rank scores should be similar. The two
  tailed probability indicates if the distributions
  are significantly different.

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Write-up

• Always set up for the reader the test that was
  used.
• Always report the t-value or z-value and the
  associated significance level.
• Always explain the finding. This is a sentence
  which helps put the statistical tests into
  human terms.

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Forging Ahead Test of Differences

• Parametric
  Non-parametric
• (Relationships)
• Pearsons R ? Spearmans Rho
• (Differences)
• Independent t-test ? Mann Whitney U
• Chi-square

19
Chi-square Cross-tabulation

• Comparing two nominal level variables.
• Test of differences.
• Is there a difference between what is observed
  and what is expected?
• Basic percentages are used to determine what is
  expected.
• Frequency Distributions play a vital role.

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Frequencies
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Frequencies
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Rejection Scores Continued

• Standard Deviation of the parent population
  divided by the square root of the sample size.
• Standard Deviation 5
• Sample Size16
• 5 divided by 4 1.25
• 1.96 x .1.25 2.45 points higher or lower than
  the mean score