Inferential Statistics Minjuan Wang Educational Technology
*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: • 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
Video from learner.org • http://learner.org/resources/series65.html# • What Is Probability? • From 0-1 • Watch the rules of probability from minutes 23 or later • 50% will find an atypical driver in NYC • Significance Tests: • Watch it from 16:20 • Confidence Intervals
Examples • Homeschoolers in SD to homeschoolers in CA • Graduate students in SDSU to .. in the West Coast • Terrorists in the US to …around the world • Does a sample perfectly represents the population? • No!
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
Level of Significance • An estimate of the probability that we are wrong when we say the results are due to chance • 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/effect/treatment are due to chance needs to < 0.05 (a)
Types of Hypothesis • Null hypothesis • There is no change, difference or relationship between A and B • A starting point or a benchmark • Coffee maker is broken • no relationship between its broken and the humming birds on the tree outside my balcony
Alternative/Research Hypothesis • Hypothesis that is implicitly accepted if the null hypothesis is rejected • Directional (one-tailed test) • Non-directional (two-tailed test) • Hypothesis: not to be proven but to be supported • Does your study fail if your hypothesis is not supported by the data?
Tails of A Test • Two-tailed test (non-directional/both) • 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"
Hypothesis Testing Procedure • Come up with a hypothesis • Set a: level of risk you are willing to take • Select the test • Compute the obtained value: t, f, r, etc. • Find the critical value in the respective table • To reject a null hypothesis->Obtained value must be > critical value • Otherwise, fail to reject null hypothesis (H0) • But, never “accept” null hypothesis • Many tests are needed to confirm that A is not different from or associated with B. • When rejecting null-P, the alternative 2-tailed P is implicitly accepted.
P from Fancy Schmancy Software • Inferential statistics • T, ANOVA, Correlation, Regression • P is the probability of chance (indicator of significance) • Free us from the test tables • Results vary • P<.05 • P<.001 • P=.013 (the exact probability of the outcome/effect due to chance—SPSS) • Outcome: difference, change, or association • P>.05 or p=ns (nonsignificant) • The probability of rejecting a null-P exceeds 0.05 (the cut-off point) (Salkind) • So reject it
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
Does Culture Make a Difference? • The survey: • Perceptions about being equal with their instructor • Chinese, American, Korean students • Tests conducted • Kruskal-Wallis Analysis of Variance • Non-parametric of ANOVA • Results and Interpretation • P=0.02 comparing with a=0.05 • ???
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 • Streamed broccoli versus baked pumpkin pie • Link to a Table • Resource: http://coe.sdsu.edu/ed690/mod/mod06/default.htm
Inferential Statistics • Parametric Techniques • T-Test for means • Analysis of Variance • Analysis of Covariance
More: Inferential Statistics • Nonparametric Techniques for Quantitative Data • The Mann-Whitney U Test—for T(ea) for two • 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 • Is there a relationship between eye and hair color?
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…
Which Test to Use? • Tea for one or two? • Paired vs. unpaired • One: Pre- post- comparison • Two groups • ANOVA? • Chi-Square? • Correlational (Pearson r)? All these choices, you decide!
What If…..? • Adding one group to the study • New Zealand • Correlational? • Chi-Square? • ANOVA?
What If… • Variables are Nominal? • Is there a Statistically significant difference between EDTEC graduate students’ study preference (solo vs. teamwork)? • Data solo solo solo solo solo solo solo solo solo team team team team team team team team team team team
Types of Chi-Square • A one-dimensional Chi Square • Determine if the observed frequencies are significantly different from the expected frequencies Solo Team 10 10 9 12 Testing group distribution!
Types of CHI-SQUARE • A two-dimensional Chi Square • Frequencies are categorized along more than one dimensions • Gender relative to study preferences Solo Team 10 10 9 (5) 12 (10) Test the association between IV and DV Female Male
Chi Square • used when data are nominal (both IV and DV) • Comparing frequencies of distributions occurring in different categories or groups • Tests whether group distributions are different • EDTEC students’ preference for solo or teamwork • Determines the association between IV and DV by counting the frequencies of distribution • Gender relative to study preference
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)
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