Mean, variance, & correlation of test scores and composites

 

Purpose of this section is to:

  1. Review some basic statistical concepts so that we can later build on these concepts to understand how the reliability coefficient is computed.
  2. Understand the relationship among the mean, variance, and correlation so that we can later use these concepts in conducting an item analysis or constructing a new test.

 

This section will review how the mean, variance, & correlation is computed for:

1.      Continuous data

2.      Dichotomous data

3.      Sub-tests

4.      Composite scores

Test scores as composites

 

 Definitions of

  1. Sub-test scores
  2. Composite test score

 Examples:

 1.

Cognitive test: 

GRE (Graduate Record Examination)

Sub-test

verbal

quantitative

analytic

Composite score

verbal+quantitative+analytic

 

2.

Affective domain:

Self-efficacy in screening/preventing

Sub-test   

self-efficacy in screening
self-efficacy in preventing

Composite   

self-efficacy in screening +
self-efficacy in preventing

                                                    

 sub-scale=sub-test

and

global index=composite

 


 

Type of data

 

Dichotomous:  T/F, M/C, & A/D (Likert)

Non-Dichotomous:  Essay (continuous), 5-point Likert (ordinal)

 

Statistics for non-dichotomous data

(Essay or 5-point likert* scale)

Mean

Variance

Correlation

 

 

 

OR

Written in deviation score

 *Likert data: (mode, median, & mean if data are not normally distributed)


 

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