Inferential Statistics

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Inferential Statistics

• Educational Technology 690

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Inferential statistics

• Projecting data from sample to population
• Signal-to-Noise
• Level of significance (a)/confidence level
• Two basic types
• Parametric
• Non-parametric

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Inferential Statistics

• Inferential Statistics are
• Used to make inferences about populations based
  on the behavior of a sample
• Concerned with how likely it is that a result
  based on a sample or samples are the same as
  results that might be obtained from an entire
  population

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• Examples
• Homeschooler in SD to homeschoolers in CA
• Infants in CA to Infants in the West Coast
• Does a sample perfectly represent the population?
• No!

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Function

• Therefore inferential statistics identify
• How likely the sample results represent the
  results that would occur in the population?
• 90, 95, or 99
• Confidence interval
• By being ? Confident, we make
• probability statements that the results we see in
  samples would also be found in the population

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Level of Significance

• Level of Significance (a)
• An estimate of the probability that we are wrong
  when we say the results are due to chance--our
  null hypothesis
• a0.1, 0.05 0.01 (10, 5, 1 of being wrong)
• 0.10 (10) for an exploratory test
• .05 (5) for many educational research tests
• .01 (1) if you are very confident
• Comparing p with a?
• Probability of the differences are due to chance
  needs to lt 0.05 (a) ?

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Inferential Statistics

• Two Basic Types
• Parametric techniques which make the assumption
  that you are working with a normal distributions
  and that the sample is random
• Nonparametric techniques which make few if any
  assumptions about the nature of the population
  from which the sample is taken

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Parametric versus Nonparametric

• Parametric
• Characteristic is normally distributed in the
  population sample was randomly selected data
  is interval or ratio
• Nonparametric
• Use when you have a specialized population,
  youve not randomly selected, or data is ranked
  or nominal
• Cooking
• steamed versus fried
• mashed potatoes versus French fries
• Link to a Table
• Resource http//coe.sdsu.edu/ed690/mod/mod06/defa
  ult.htm

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Inferential Statistics

• Parametric Techniques
• T-Test for means
• Analysis of Variance
• Analysis of Covariance

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More Inferential Statistics

• Nonparametric Techniques for Quantitative Data
• The Mann-Whitney U Testfor T(ea) test
• The Kruskal-Wallis One Way Analysis of
  Variancefor ANOVA
• The Friedman Two-Way Analysis of Variancefor
  ANOVA
• Nonparametric Technique for Categorical Data
• Chi-Squared test of frequencies

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Null Hypothesis

• Cultural difference and fear of fat
• Mean of Australian students 100
• Mean of Indian students 125
• Is this difference really significant?
• Due to the cultural difference?
• Due to chance (such as sampling error)?
• If you make a null hypothesis
• There is no significant difference or
  relationship.
• Assuming the difference is due to chance
• Chance explanation for the difference

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Tails of A Test

• Two-tailed test (non-directional/both)
• a research hypothesis that allows for differences
  by either group (in either direction)
• There is no difference in content acquisition
  between "discovery learning" and "direct
  instruction.
• One-tailed test (directional/upper/lower)
• difference will be in one direction only
• Students who use "discovery learning" exhibit
  greater gains in content acquisition than
  students who use "direct instruction"

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Degree of Freedom

• State a null hypothesis
• Select a level of significance
• Select the appropriate test
• Run statistics-gtget a result
• Set degrees of freedom
• The No. of instances in a distribution that is
  free to vary
• to name 5 numbers, the mean needs to be 4
• Four numbers are free to vary (1, 2, 3, ,4)
• The 5th number is set (10)

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Degree of Freedom

• Why?
• If calculate the test by hand, the intersection
  of P and df determine the level needed to reject
  the null hypothesis
• Refer to T table
• Each test has its own formula
• No. of groups, and no. of participants
• Correlation r, N-2
• T test
• one group N-1
• two groups N1-1N2-1