EDLD 6392 Advanced Topics in Statistical Reasoning Texas A

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EDLD 6392Advanced Topics in Statistical
ReasoningTexas AM University-Kingsville

• Research Designs and Statistical Procedures

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Research Designs by Purpose

• Educational Research is conducted for four
  primary purposes
• 1-Description
• 2-Prediction
• 3-Improvement
• 4-Explanation

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Research Designs by Similarities

• Experimental Quasi-experimental
• -Involves Researcher Intervention
• Non-experimental
• - Examines phenomena as they exist
• Descriptive, Causal-Comparative, and
  Correlational

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Descriptive Research Designs

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

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Descriptive Research (Contd)

• Types of Measurements
• standardized achievement scores, classroom
  observation instruments, attitude scales,
  questionnaires, and interviews
• Statistics
• Central Tendency (mean, median, mode)
• Measures of Variability (SD, variance, range)

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Causal-Comparative Research

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

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Causal-Comparative (Contd)

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

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Quasi-Experimental Research

• Parametric Tests
• Statistical Analysis The t Test
• For testing the significance of difference
  between two sample means
• Basic Assumptions
• 1-Scores form an interval or ratio scale
• 2-Scores are normally distributed
• 3-Score variances for the populations under
  study are equal (SDSD)

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Quasi-Experimental (Contd)

• Analysis of Variance (ANOVA)
• Comparison of two or more group means
• Multivariate Analysis of Variance (MANOVA)
• Statistical technique for determining whether
  groups differ on more than one dependent
  variable.
• Basic Assumptions
• 1-Scores form an interval or ratio scale
• 2-Scores are normally distributed
• 3-Score variances for the populations under
  study are equal (SDSD)

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Quasi-Experimental (Contd)

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

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Quasi-Experimental (Contd)

• Nonparametric Tests (Contd)
• 2-The Mann-Whitney U testused to determine
  whether the distributions of scores of two
  independent samples differ significantly from
  each other.
• 3-The Wilcox signed rank testused to determine
  whether the distributions of scores of two
  samples differ significantly from each other when
  the scores of the samples are correlated.

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Quasi-Experimental (Contd)

• Nonparametric Tests (Contd)
• 4-The Kruskal-Wallis testIf more than two
  groups of subjects are to be compared, a
  nonparametric one-way analysis of variance
  (Kruskal-Wallis) can be used.

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Classification of Research Design
(Causal-Comparative)
X
O1
O2
One-group pretest-posttest design
Group 1
O1
X
O2
Nonequivalent control group
Group 2
O3
O4
O1
X1
X2
O2
Equivalent time-samples design
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Non-experimental ResearchCorrelational Designs

• The Purpose
• To discover relationships between variables
  through the use of correlational statistics.
  Involves correlating data on two or more
  variables for each individual in a sample and
  computing a correlation coefficient.
• Two major purposes
• 1-To explore causal relationships between
  variables
• 2-To predict scores on one variable from
  research participants scores on other variables.

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Correlation Research Design

• Advantages
• 1-Enables researchers to analyze the
  relationships among a large number of variables
  in a single study.
• 2-They provide information concerning the degree
  of the relationship between the variables being
  studied.
• Parametric Test
• Pearson r statistical procedure
• Basic Assumptions
• 1-Scores form an interval or ratio scale
• 2-Scores are normally distributed
• 3-Score variances for the populations under
  study are equal (SDSD)

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Scattergrams Representing Different Degrees and
Directions of Correlation between Two Variables
Positive correlation (r.99)
Negative correlation (r-.73)
Grade point
I.Q.
Age
gpa
Computer use
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Choosing Statistical Procedures
START
Interval Data
Relate
Compare
Normal
Not Normal
SD
SD
Spearman Correlation
Pearson Correlation
Dependent
Independent
2 groups
gt2 groups
2 groups
gt2 groups
Mann-Whitney
Wilcoxon
Friedman ANOVA
Kruskal-Wallis
Independent
Dependent
gt2 groups
2 groups
2 groups
gt2 groups
Independent Samples t Test
ANOVA
Related Samples t-Test
Repeated Measures ANOVA