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Inferential Statistics

Inferential Statistics. Educational Technology 690. *Inferential statistics. Projecting data from sample to population Signal-to-Noise Level of significance (a)/confidence level Two basic types Parametric Non-parametric. Inferential Statistics. Inferential Statistics are:

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Inferential Statistics

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  1. Inferential Statistics Educational Technology 690

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

  3. 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

  4. 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!

  5. 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

  6. 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 • a=0.1, 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 < 0.05 (a) ?

  7. 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

  8. 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, you’ve 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/default.htm

  9. Inferential Statistics • Parametric Techniques • T-Test for means • Analysis of Variance • Analysis of Covariance

  10. More: Inferential Statistics • Nonparametric Techniques for Quantitative Data • The Mann-Whitney U Test—for T(ea) test • The Kruskal-Wallis One Way Analysis of Variance—for ANOVA • The Friedman Two-Way Analysis of Variance—for ANOVA • Nonparametric Technique for Categorical Data • Chi-Squared test of frequencies

  11. 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…

  12. 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"

  13. Degree of Freedom • State a null hypothesis • Select a level of significance • Select the appropriate test • Run statistics->get 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)

  14. 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: N1-1+N2-1

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