A Short Guide to Action Research4th Edition

Andrew P. Johnson, Ph.D.Minnesota State University, Mankato

www.OPDT-Johnson.com

Chapter 8: Quantitative Design in Action Research

• Quantitative research is based on the collection and analysis of numerical data

• Three quantitative research designs can fit within the action research paradigm:

1. correlational research

2. causal–comparative research

3. quasi-experimental research

CORRELATIONAL RESEARCH

Seeks to determine whether and to what degree a statistical relationship exists between two or more variables

Used to describe an existing condition or something that has happened in the past

Correlation Coefficient• Correlation coefficient = the degree or strength of a

particular correlation

• Positive correlation = when one variable increases, the other one also increases

• Negative correlation = when one variable increases, the other one decreases

• Correlation coefficient of 1.00 = a perfect one-to-one positive correlation

• Correlation coefficient of .0 = absolutely no correlation between two variables

• Correlation coefficient of –1.00 = a perfect negative correlation

Misusing Correlational Research

• Correlation does not indicate causation

• Just because two variables are related, we cannot say that one causes the other

Negative Correlation • Increase in one variable causes a decrease in another

Making Predictions

• Correlation coefficient identified by the symbol r

• When r = 0 to .35, the relationship between the two variables is nonexistent or low

• When r = .35 to .65, there is a slight relationship.

• When r = .65 to .85, there is a strong relationship

CAUSAL-COMPARATIVE RESEARCH

Used to find reason for existing differences between two or more groups

Used when random assignment of participants for groups cannot be met

Like correlational research, used to describe an existing situation

compares groups to find a cause for differences in measures or

scores

QUASI-EXPERIMENTAL RESEARCH

Like true experiment; but no random assignment of subjects to groups

random selection is not possible in most schools and classrooms

Pre-tests and matching used to ensure comparison groups are relatively similar

Five Quasi-Experimental Designs

• Exp = experimental group• Cnt = control group• O = observation or measure• T = treatment

Pretest-Posttest Design

Group Time

Exp O T O

Cnt O — O

Pretest-Posttest Group Design

Group Time

Exp O T O

Cnt O — O

Time Series Design

Group Time

Exp O O O O T O O O O

Group Time

Exp T1 O O O O T2 O O O O

Time Series Group Design

Group

Time

Exp O O O O T O O O O

Cnt O O O O — O O O O

Group

Time

Exp T1 O O O O T2 O O O O

Cnt T1 O O O O T1 O O O O

Equivalent Time-Sample Design

Group Time

Exp T O — O T O — O

THE FUNCTION OF STATISTICS

• Descriptive statistics = statistical analyses used to describe an existing set of data

• Measures of central tendency describes a set of data with a single number

a. mode - score that is attained most frequently

b. median - 50% of the scores are above and 50% are below

c. mean - the arithmetic average

Frequency Distribution = all the scores that were attained and how many people attained each score

Scores Number of Students

99 1

97 1

92 2

90 1

85 2

84 4

83 6

80 12

79 5

78 6

75 4

Line graph for frequency distribution

Measures of variability = the spread of scores or how close the scores cluster around the mean

Range = the difference between the highest and lowest score

Variance = the amount of spread among the test scores

standard deviation = how tightly the scores are clustered around the mean in a set of data

Scores with a Small Variance

xx xxxxxxx

xxxx

xxxxxx

xxxx

xxx

Scores with a Large Variance

x x x x x x x x x x x xx

xx

x x x x x x x x x x

Small Standard Deviation: Closely Distributed Scores

Large Standard Deviation: Widely Distributed Scores

INFERENTIAL STATISTICS• Inferential statistics = statistical analyses used to determine how

likely a given outcome is for an entire population based on a sample size

• make inferences to larger populations by collecting data on a small sample size

• Statistical significance = that difference between groups was not

caused by chance or sampling error