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McMillan

Educational Research: Fundamentals for the Consumer, 6e 2012 Pearson Education, Inc. All rights reserved.

Educational Research:

Fundamentals for the Consumer

Woolfolk / PerryChild and Adolescent Development 2012 Pearson Education, Inc. All rights reserved.

Sixth Edition


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McMillanEducational Research: Fundamentals for the Consumer, 6e 2012 Pearson Education, Inc. All rights reserved.

Understanding StatisticalInferences

Chapter 9


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McMillanEducational Research: Fundamentals for the Consumer, 6e 2012 Pearson Education, Inc. All rights reserved. 3

Discussion Topics

Inferential statistics Purpose

Error Terminology

Hypothesis testing

Inferential tests

Criteria for evaluating the inferentialstatistics reports in studies


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Inferential Statistics

The purpose of inferential statistics is todraw inferences about a population on

the basis of an estimate from a sample Inferential statistics - specific statistical

procedures that accomplish thispurpose

The ultimate goal is to draw accurateconclusions about the population


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Two types of errors

Sampling errors

Without measuring the entire population, the results

can be inaccurate due to sampling error The larger the proportion of the population that is

sampled, the lower the sampling error; the smaller theproportion of the population that is sampled, the higherthe sampling error

A sample of 99% of a population is likely to show resultsthat are very, very similar to those that would have beenfound if everyone in the population was measured

A sample of 1% is likely to show results that are differentfrom those in the population - the question is howdifferent are the sample results

Need to estimate the level of sampling error relative tothe inferences being drawn


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Measurement errors

Regardless of the sample size, the results

can be inaccurate due to measurementerror

Lack of validity

Lack of reliability

Need to estimate the level of measurementerror relative to the inferences being drawn


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Terminology

Null hypothesis No differences between groups No relationships between variables

Level of significance Probability of being wrong in rejecting the null

hypothesis Known as alpha (a)

Types of errors Type I - rejecting the null hypothesis when it is true Type II - not rejecting (i.e., accepting) the null

hypothesis when it is not true


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Issues related to statistical and practicalsignificance

Statistical significance The typical or atypical nature of the comparison of the

observed difference to the sampling distribution canbe estimated using statistical theory

The estimate is the probability of being wrong inrejecting the null hypothesis

It is stated asp = xwherexis the specific probability ofthe comparison (e.g.,p = .001,p = .042,p = .56) or asp < ywhere yis the alpha level (e.g., .10, .05, .01)


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Statistical significance (continued)

There is always the possibility of making a mistakegiven that this is based on a probability model

Type I error - deciding to reject the null hypothesis whenin reality it is true

Type II error - accepting the null hypothesis when it inreality it is false

Typical levels of significance in education - .10, .05,and .01

Factors affecting the level of significance The actual differences between the groups

The degree to which sampling and measurement errorsexist

The size of the sample


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Practical significance

Practical significance is related to the importanceand usefulness of the results

Estimates of practical significance For correlations the coefficient of determination

(i.e., r2) is used

For comparisons an effect size is used

Effect size is the difference between two group

means in terms of the control group standarddeviationCohens d

Evaluating effect sizessmall (.30), moderate (.50),and large (.75)


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Each consumer of the research

must judge the balance between

the statistical significance and thepractical significance of the

statistical results given the context

in which the results might be used.


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Inferential Tests

Two types of inferential tests

Parametric - inferential procedures usinginterval or ratio level data

Non-parametric - inferential proceduresusing nominal or ordinal data


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Parametric Tests

T-test A comparison of the means for two groups

Do the mean scores on the final exam differ forthe experimental and control groups?

Independent samples t-test - compares themeans of two separate groups on one variable

Posttest means for Group 1 and Group 2

Dependent sample t-test - compares the meansof two variables for one group

Pre-test and posttest means for Group 1


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Parametric Tests

T-test (continued)

A determination of whether a relationship

exists Does a correlation of +.63 between students

math attitudes and math achievement indicate arelationship exists between these two variables?

Correlation t-test - compares the magnitude of

the difference between a correlation coefficientand 0.00


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Parametric Tests

Analysis of variance (ANOVA)

A comparison of the means for two or more

groups Omnibus ANOVA - a procedure that

indicates whether one of more pairs ofmeans are different

Do the mean scores differ for the groupsusing co-operative group, lecture, or web-based instruction?


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Parametric Tests

ANOVA (continued)

Multiple comparisons (i.e., post-hoc)

Procedures that indicate which specific pairs of meansare different as a follow-up to a significant omnibusANOVA result

Do the mean scores differ between the co-operativegroup and lecture, co-operative group and web-based,and lecture and web-based instruction?

Two common tests Tukey

Scheffe


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Parametric Tests

Factorial ANOVA

A procedure that analyzes the difference betweengroups across two or more independent variables

Do the mean scores differ for co-operative group,lecture, and web-based instruction for males andfemales?

Effects Main effects - differences between the levels of each

independent variable Interaction effects - differences between combinations

of the levels of each independent variable


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Parametric Tests

Analysis of covariance (ANCOVA)

A procedure that compares means after

statistically adjusting them for pretestdifferences between groups

Very stringent assumptions that must bemet to use this procedure

Adjusts for small to moderate - not large -pretest differences


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Parametric Tests

Multivariate statistics

Comparisons or relationships involving two or more

dependent variables Comparison of means

Are there differences in the attitudes andperformances of students being taught with lecture orweb-based instruction?

Specific tests Multivariate ANOVA (MANVOA)

Multivariate ANCOVA (MANCOVA)

Hotellings T


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Non-Parametric Tests

Chi-square - differences in frequenciesacross different categories

Do mothers and fathers differ in theirsupport of a year-round school calendar?

Do the percentages of undergraduate,graduate, and doctoral students differ interms of their support for the new classattendance policy?


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Non-Parametric Tests

Comparison of means

Mann Whitney U-test

Wilcoxon test

Kruskal-Wallis ANOVA

Relationships Spearman r


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Evaluation Criteria

Basic descriptive statistics are neededto evaluate the inferential results

Inferential analyses report statisticalsignificance, not practical significance

Inferential analyses do not indicate

internal or external validity The results depend on sample sizes


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Evaluation Criteria

The appropriate statistical proceduresare used

The level of significance is interpretedcorrectly

Caution is used to interpret non-parametric results from studies with fewsubjects in one or more groups orcategories

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