Methodology

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Chapter Fifteen
Statistical Testing of Differences and
Relationships
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Chapter Fifteen Statistical Testing of Differences

• Become aware of the nature of statistical
  significance
• Understand the concept of hypothesis development
  and how to test hypotheses
• Understand the difference between type I and
  type II errors
• Be familiar with several of the more common
  statistical tests of goodness of fit, hypotheses
  about one mean, hypotheses about two means, and
  hypotheses about proportions
• Learn about analysis of variance.

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Statistical Significance

• Mathematical Differences
• By definition, if numbers are not exactly the
  same, they are different. This does not,
  however, mean that the difference is either
  important or statistically significant.
• Statistical Significance
• If a particular difference is large enough to be
  unlikely to have occurred because of chance or
  sampling error, then the difference is
  statistically significant.

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Statistical Significance

• Managerial Important Differences
• One must be able to distinguish between
  mathematically differences and statistically
  significant differences in using the data
  analysis in managerial decision making.
• Hypothesis
• An assumption, argument, or theory that a
  researcher or manager makes about some
  characteristics of the population under study.

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Hypothesis Testing

• The Key Steps

• Step One Stating the hypothesis
• Null Hypothesis the status quo is proven to be
  true.
• Alternative Hypotheses - another alternative is
  proven to the true.
• Step Two Choosing the appropriate test
  statistic
• Test of means, test or proportions, ANOVA, etc.
• Step Three Developing a decision rule
• Determine the significance level.
• Needed to determine whether to reject or fail to
  reject the null hypothesis.

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Hypothesis Testing

• The Key Steps

• Step Four Calculating the value of the test
  statistic
• Use the appropriate formula to calculate the
  value of the statistic.
• Step Five Stating the conclusion
• Stated from the perspective of the original
  research question.

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Hypothesis Testing Error Types
Type I

• Rejection of the null hypothesis when, in fact,
  it is true.
• Acceptance of the null hypothesis when, in fact,
  it is false.

Type II

• Tests are either one or two-tailed. This
  approach depends on the nature of the situation
  and what the researcher is demonstrating.
• One-Tailed
• If you take the medicine, you will get better
• Two-Tailed
• If you take the medicine, you will get either
  better or worse.

• One and Two
• Tailed Tests

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Error Issues

• Type I and Type II Errors

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Common Statistical Tests

• Independent Samples
• Samples in which measurement of a variable in
  one population has no effect on measurement of
  the variable in the other.
• Related Samples
• Samples in which measurement of a variable in
  one population might influence measurement of
  the variable in the other.
• Degrees of Freedom
• Is equal to the number of observations minus the
  number of assumptions or constraints necessary to
  calculate a statistic.

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Types of Hypothesis Tests

• About One Mean

• Z-Test
• Hypothesis test used for a single mean if the
  sample is large enough and drawn from a normal
  population. Usually for samples of about 30 and
  above.
• t-Test
• Hypothesis test used for a single mean if the
  sample is too small to use the Z-test. Usually
  for samples below 30.

• About Two Means

Hypothesis testing that tests the difference
between groups of data.
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Types of Hypothesis Tests

• Proportion in One Sample
• Test to determine whether the difference between
  proportions is greater than would be expected
  because of sampling error.
• Two Proportions in Independent Samples
• Test to determine the proportional differences
  between two or more groups.
• p-value
• The exact probability of getting a computed test
  statistic that was largely due to chance. The
  smaller the p-value, the smaller the probability
  that the observed result occurred by chance.

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Statistics and the Internet Some Valuable Links
ActivStats - www.datadesk.com/ActivStats Autobox
- www.autobox.com Math Software -
http//gams.nist.gov Minitab -
www.minitab.com NCSS - http//amsquare.com/ncss
SAS - www.sas.com SPSS - www.spss.com Stata -
www.stata.com SYSTAT - www.spssscience.com/systat
Vizion - www.datadesk.com/viz!on xISTAT -
www.xlstat.com
In Slide Show mode, click on the arrow to be
taken to the respective web page.
Chapter 15