Hypothesis Tests, Statistical Significance

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Hypothesis Tests, Statistical Significance
Correlation Coefficients
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What is a hypothesis?
An assumption subject to verification or proof
An educated guess about what is true in the
world
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Two Types of Hypotheses

• The Null Hypothesis Ho
• There is no difference between groups.
• There is no relationship between variables.
• Ho mmales mfemales
• vs.
• The Alternative Hypothesis Ha
• There is a difference between groups.
• There is a relationship between the variables.
• Ha mmales ? mfemales (for two-tailed test)
• mmales gt or lt mfemales (for
  one-tailed test)

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Statistical Significance

• Are results due to random sampling error or
  chance? Or, is it unlikely that the results
  observed are due to chance?
• If the test results are statistically
  significant, reject the null hypothesis and
  conclude there are real differences
• The researchers decision is subject to error

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Errors in Hypothesis Testing

• Type I Errors (called alpha, or a error)
• The error of rejecting the null hypothesis when
  it is in fact true, or concluding there are
  relationships or differences when none really
  exist.
• To avoid a Type I error a conservative alpha
  level like .01 might be used.
• Type II Error (beta errors)
• The error of retaining the null hypothesis when
  it is in fact false, or
• concluding there are no relationships or
  differences when in fact they
• do exist.
• To avoid a Type II error a liberal alpha level
  such as .10 might be used

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Standard Normal Distribution
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Graphic Demonstrating Hypothesis Testing for a
Two-Tailed Test
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Steps in Statistical Significance
(Hypothesis)Testing

• STEPS
• Step 1 Set alpha level ( a ) reflects level
  of Type I error the researcher is willing to risk
• Results must have probability of error equal
  to or less than alpha before the researcher will
  reject the null hypothesis and conclude the
  results are statistically significant

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Steps in Statistical Significance Testing

• Step 2 Conduct the appropriate data analysis
  procedures for the test
• Step 3 You will get a TEST statistic
  (coefficient, chi square, t value, F value, etc.)
  that measures how close the sample has come to Ho
• Step 4 Look at the probability (p-value) of
  error associated with getting your test statistic
• Step 5 Compare the p-value to your alpha level
  

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The Research Decision

• Retain the null if the p-value is GREATER than
  your alpha level
• For example, if a .05 and p .10, retain the
  null and conclude results are NOT statistically
  significant
• Reject the null if the p-value is equal to or
  LESS than your alpha level, conclude Ha
• For example, if a .05 and p .001, reject the
  null, results are statistically significant

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Practical vs. Statistical Significance

• Results can sometimes be statistically
  significant, but the difference or strength isnt
  enough to be of any practical consequence
• Statistical significance is easier to obtain when
  sample is large (because SE is lower)

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Bivariate Measures of AssociationThe Pearson PM
Correlation Coefficient (r)

• Relationship, not causation, between 2 variables
  
• Both variables must be INTERVAL level
• Measures the direction degree of a relationship
  Direction is positive or negative
• POSITIVE The variables move in the same
  direction (i.e., when one is high (low) the other
  is high (low)
• NEGATIVE The variables move in OPPOSITE
  directions (i.e., when one is high the other is
  low)

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The Pearson PM Correlation Coefficient ( r )

• Can range from 1.00 to 1.00
• Degree Generally r gt .60 considered strong,
  between .40 and .60 moderate, r lt .40 weak (lt .10
  to 0.00 no relationship)
• A correlation of 0.00 indicates no linear
  relationship between the variables
• Coefficient of determination (r2) shows
  proportion of change in one variable explained by
  change in another (explained variance)

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Correlation Example

• Example A interpretation
• There is a strong, positive relationship between
  yrs in school and income level (r .90, p
  .000). More years in school is associated with
  higher income level.
• Example B interpretation
• There is a strong, negative relationship between
  income level and of children (r -.72, p
  .000). Lower income households tend to have more
  children in the home.
• Example C interpretation
• There is no relationship between income level and
  weight.