This document discusses quantitative data analysis and statistical measures. It describes levels of quantitative description, types of data analysis including descriptive and inferential analysis, and statistical measures used in descriptive analysis such as measures of central tendency, spread, relative position, and relationship. Specific statistical measures are defined, like mean, median, mode, range, variance, standard deviation, percentile scores, correlation coefficients, and when they are appropriate to use. Computational data analysis tools like IBM SPSS Statistics are also mentioned.

2. Synopsis
 Levels of Quantitative Description
 Types of Data Analysis
 Statistical Measures Applied to Descriptive Analysis

Measures of central tendency/average
 Mean
 Median
 Mode

Measure of spread/dispersion
 Range
 Variance
 Standard deviation

Measure of relative position
 Standard scores
 Percentile rank
 Percentile score

Measures of relationship
 Coefficient of correlation
 Computational Data Analysis

3. Scales of Quantitative Description
Level Scale
Process
4
Ratio
Equal intervals
True zero
Ratio relationship
3
Interval
Equal Intervals
No true zero
2
Ordinal
Data
Ranked in order
Descriptive
Parametric
Nonparametric
1
Nominal
Classified and
counted
Some Appropriate Statistics
Inferential
Mean
Standard deviation
Pearson’s r
Median
Mann-Whitney
Quartile deviation Wilcoxin
Stanines
Spearman’s rho (ρ)
Mode
Chi square
Sign

4. Choosing Statistical Tests for Data

6. Descriptive and Inferential Analysis
Descriptive Analysis
Inferential Analysis
Descriptive statistical analysis limits
generalization to the particular group
of individuals observed. That is:
 No conclusions are extended
beyond this group.
 Any similarity to those outside
the group cannot be assumed.
 The data describe one group
and that group only.
Examples: assessment findings,
findings of a much simpler action
research
Inferential analysis selects a small
group (sample) out of a larger group
(population) and the finding are
applied to the larger group. It is used
to estimate a parameter, the
corresponding
value
in
the
population from which the sample is
selected.
It is necessary to carefully select the
sample or the inferences may not
apply to the population.

7. Descriptive Analysis
Statistical measures applied to descriptive data are as follows:
Measures of central tendency/average
 Mean
 Median
 Mode
Measure of spread/dispersion
 Range
 Variance
 Standard deviation
Measure of relative position
 Standard scores
 Percentile rank
 Percentile score
Measures of relationship
 Coefficient of correlation

10. Descriptive Analysis: Measure of
Spread/Dispersion

11. Descriptive Analysis: Measure of Relative Position/Standard Scores

13. Measures of Relationship
These indicate the degree of relationship (correlation coefficient)
between two or more quantifiable variables from a single group of
participants. The correlation can be positive (+), negative (-), or
none . When one variable increases with the other, the correlation is
positive; when one variable increases while the other decreases or
the vice versa, the correlation is negative. There may be variables
that have no correlation. A perfect positive correlation is +1; a
perfect negative correlation is -1; a complete lack of correlation is 0.
The sign of the coefficient indicates the direction of the relationship.
A perfect positive correlation specifies that for every unit increase
in one variable there is a proportional unit increase in the other. The
perfect negative correlation specifies that for every unit increase in
one variable there is a proportional unit decrease in the other.

14. Measures of Relationship: Pearson’s
Product-Moment Coefficient of
Correlation (r)

15. Measures of Relationship: Rank Order
Correlation/Spearman’s rho (ρ)

16. Computational Data Analysis
Computers are used to easily and flawlessly arrange
and analyze data and apply statistical formulae. The
following software programs can be used for this
purpose:





IBM SPSS Statistics
Minitab
MS Excel
iNZight
R

17. IBM SPSS Statistics integrates with a broad range of
capabilities for the entire analytical process.

18. References and Further Reading
Best, J. W., & Kahn, J. V. (2006). Research in
Education (10th ed.). Pearson Education Inc.
Cohen, L., Manion, L., & Morrison, K. (2011).
Research Methods in Education (7th ed.).
Routledge.
Gay, L. R., & Geoffrey E. Mills, P. A. (2011).
Educational Research: Competencies for Analysis
and Applications (10th ed.). Pearson.