EDLD 6392Advanced Topics in Statistical Reasoning

Texas A&M University-Kingsville

Research Designs and Statistical Research Designs and Statistical ProceduresProcedures

Research Designs by Purpose

Educational Research is conducted for four Educational Research is conducted for four primary purposes:primary purposes:

1-Description1-Description

2-Prediction2-Prediction

3-Improvement3-Improvement

4-Explanation4-Explanation

Research Designs by Similarities

Experimental & Quasi-experimentalExperimental & Quasi-experimental

-Involves Researcher Intervention-Involves Researcher Intervention

Non-experimental Non-experimental

- Examines phenomena as they exist- Examines phenomena as they exist

Descriptive, Causal-Comparative, and Descriptive, Causal-Comparative, and CorrelationalCorrelational

Descriptive Research Designs

The PurposeThe PurposeThe description of natural or man-made The description of natural or man-made phenomena-their form, actions, changes over time, phenomena-their form, actions, changes over time, and similarities-with other phenomena, an effort and similarities-with other phenomena, an effort to describe. Involves making careful descriptions to describe. Involves making careful descriptions of educational phenomena, viewed as of educational phenomena, viewed as understandingunderstanding what people or things mean. what people or things mean.Studies primarily concerned with determining Studies primarily concerned with determining “what is.”“what is.”

Descriptive Research (Cont’d)

Types of MeasurementsTypes of Measurements

standardized achievement scores, classroom standardized achievement scores, classroom observation instruments, attitude scales, observation instruments, attitude scales, questionnaires, and interviewsquestionnaires, and interviews

StatisticsStatistics

Central Tendency (mean, median, mode)Central Tendency (mean, median, mode)

Measures of Variability (SD, variance, range)Measures of Variability (SD, variance, range)

Causal-Comparative Research

The PurposeThe Purpose

Purpose of explaining educational phenomena Purpose of explaining educational phenomena through the study of cause-and-effect through the study of cause-and-effect relationships. The presumed cause is called the relationships. The presumed cause is called the independent variableindependent variable and the presumed effect is and the presumed effect is called the called the dependent variabledependent variable. Designs where the . Designs where the researcher does not manipulate the independent researcher does not manipulate the independent variable are called variable are called ex post facto researchex post facto research..

Causal-Comparative (Cont’d)

Causal-Comparative research is also a type of Causal-Comparative research is also a type of non-experimental investigation in which non-experimental investigation in which researchers seek to identify cause-effect researchers seek to identify cause-effect relationships by forming groups of relationships by forming groups of individuals in whom the independent individuals in whom the independent variable is present or absent and than variable is present or absent and than determining whether the groups differ on determining whether the groups differ on the dependent variable.the dependent variable.

Quasi-Experimental Research

Parametric TestsParametric TestsStatistical Analysis: The Statistical Analysis: The tt Test Test

For testing the significance of difference between For testing the significance of difference between two sample meanstwo sample means

Basic AssumptionsBasic Assumptions1-1-Scores form an interval or ratio scaleScores form an interval or ratio scale2-Scores are normally distributed2-Scores are normally distributed3-Score variances for the populations under study 3-Score variances for the populations under study are equal (SD=SD)are equal (SD=SD)

Quasi-Experimental (Cont’d)

Analysis of Variance (ANOVA)Analysis of Variance (ANOVA)Comparison of two or more group meansComparison of two or more group means

Multivariate Analysis of Variance (MANOVA)Multivariate Analysis of Variance (MANOVA)

Statistical technique for determining whether groups differ Statistical technique for determining whether groups differ on more than one dependent variableon more than one dependent variable..

Basic AssumptionsBasic Assumptions1-1-Scores form an interval or ratio scaleScores form an interval or ratio scale2-Scores are normally distributed2-Scores are normally distributed3-Score variances for the populations under study 3-Score variances for the populations under study are equal (SD=SD)are equal (SD=SD)

Quasi-Experimental (Cont’d)

Nonparametric TestsNonparametric TestsNonparametric statistics tests statistical significance that Nonparametric statistics tests statistical significance that do not rely on any assumptions about shape or variance of do not rely on any assumptions about shape or variance of population scores.population scores.Used with measures that yield categorical or rank scores, Used with measures that yield categorical or rank scores, or do not have equal intervals. Nonparametric tests are or do not have equal intervals. Nonparametric tests are less powerful, they require larger samples to yield the less powerful, they require larger samples to yield the same level statistical significance.same level statistical significance.1-1-The Chi-Square TestThe Chi-Square Test = used to determine whether = used to determine whether research data in the form of frequency counts are research data in the form of frequency counts are distributed differently for different samples.distributed differently for different samples.

Quasi-Experimental (Cont’d)

Nonparametric Tests (Cont’d)Nonparametric Tests (Cont’d)

2-2-The Mann-Whitney U test=used to determine whether the distributions of scores of two independent samples differ significantly from each other.

3-The Wilcox signed rank test=used to determine whether the distributions of scores of two samples differ significantly from each other when the scores of the samples are correlated.

Quasi-Experimental (Cont’d)

Nonparametric Tests (Cont’d)Nonparametric Tests (Cont’d)

4-4-The Kruskal-Wallis testThe Kruskal-Wallis test=If more than two =If more than two groups of subjects are to be compared, a groups of subjects are to be compared, a nonparametric one-way analysis of nonparametric one-way analysis of variance (Kruskal-Wallis) can be used.variance (Kruskal-Wallis) can be used.

Classification of Research Design (Causal-Comparative)

XO1 O2 One-group pretest-posttest design

Group 1:

Group 2:

O1

O3

X O2

O4

Nonequivalent control group

O1X1 X2 O2 Equivalent time-samples design

Non-experimental Research:Correlational DesignsThe PurposeThe Purpose

To discover relationships between variables through the To discover relationships between variables through the use of correlational statistics. Involves correlating data on use of correlational statistics. Involves correlating data on two or more variables for each individual in a sample and two or more variables for each individual in a sample and computing a correlation coefficient.computing a correlation coefficient.

Two major purposesTwo major purposes::

1-To explore causal relationships between variables;1-To explore causal relationships between variables;

2-To predict scores on one variable from research 2-To predict scores on one variable from research participants’ scores on other variables.participants’ scores on other variables.

Correlation Research Design

AdvantagesAdvantages1-1-Enables researchers to analyze the relationships among a large Enables researchers to analyze the relationships among a large number of variables in a single study. number of variables in a single study. 2-They provide information concerning the degree of the relationship 2-They provide information concerning the degree of the relationship between the variables being studied.between the variables being studied.

Parametric TestParametric TestPearson r statistical procedurePearson r statistical procedure

Basic AssumptionsBasic Assumptions1-1-Scores form an interval or ratio scaleScores form an interval or ratio scale2-Scores are normally distributed2-Scores are normally distributed3-Score variances for the populations under study are equal 3-Score variances for the populations under study are equal (SD=SD)(SD=SD)

Scattergrams Representing Different Degrees and Directions of Correlation between Two Variables

I.Q.

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Positive correlation (r=.99)

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Negative correlation (r=-.73)

Grade point gpa I.Q. Computer use Age

Choosing Statistical Procedures

START

Interval DataRelate Compare

NormalNot Normal

=SD=SD

Dependent Independent

2 groups >2 groups

Wilcoxon Friedman

ANOVA

2 groups >2 groups

Mann-Whitney

Kruskal-Wallis

IndependentDependent

>2 groups2 groups

Independent Samples t

Test

ANOVA

2 groups >2 groups

Related Samples

t-Test

Repeated Measures ANOVA

Spearman Correlation

Pearson Correlation