Transcript Three Broad Purposes of Quantitative Research

Three Broad Purposes of
Quantitative Research
• 1. Description
• 2. Theory Testing
• 3. Theory Generation
Four Things to Know About
Statistics
• What statistical methods are used to analyze
quantitative data.
• When to use these statistical methods (with
what kinds of data).
• How to use these statistical methods (the
calculations).
• What the results of statistical tests mean.
Whenever a researcher has a large
number of test scores, it is
advisable to describe the many
scores with a few simple indicators
that provide some important
information about the set of scores.
3 Measures of Central
Tendency:
• Mean: the arithmetic average in a
distribution of scores.
• Median: the midpoint in a distribution
of scores (most typical score).
• Mode: the most frequently-occurring
score in a distribution of scores.
Three Measures of Variability
• Range: the difference between the highest
and lowest scores in a distribution of scores.
• Variance: a measure of dispersion
indicating the degree to which scores cluster
around the mean score.
• Standard deviation: index of the amount of
variation in a distribution of scores.
Calculating a Mean Score
Scores:
79
81
82
86
86
88
91
93
95
97
total = 878
Divide by n = 10 scores
Mean = 87.8
Computing a Median Value
in a Distribution of Scores
Two distributions of scores
Distribution 1
• 24
• 24
• 25
• 25
• 26
• 26
– Mean = 25
– Range = 3
Distribution 2
• 16
• 19
• 22
• 25
• 28
• 30
• 35
– Mean = 25
– Range = 20
COMPUTING DEVIATION SCORES
Raw
Mean DEV. SQUARED
score
score
deviation score
4
- 10
= -6
36
8
- 10
= -2
4
9
- 10
= -1
1
10
- 10
= 0
0
10
- 10
= 0
0
10
- 10
= 0
0
12
- 10
= 2
4
13
- 10
= 3
9
14
- 10
= 4
16
90/9 = 10.00 = MEAN
70/9 = 7.77 = Variance
STANDARD DEVIATION: (Square Root of Variance) = 2.79
Statistical Tests and Related
Procedures
• t-test
– independent groups
– non-independent
• Analysis of variance
• chi-square
• Correlation
– Regression
– Multiple regression
• Factor analysis
Let’s conduct an educational
experiment!
Compare two methods for
teaching 6th grade science
Students randomly assigned to:
Method A: “creative exploration”
or
Method B: “interactive collaboration”
Results:
Mean scores on “Science Achievement
Test”:
Method A = 90.3 (s.d.= 2.89)
Method B = 84.9 (s.d.= 3.77)
Must interpret this observed
difference in mean scores:
(1) Method A caused the difference;
or
(2) The difference between the groups
occurred by chance (the null
hypothesis).
The null hypothesis:
Ho: There will be no significant difference
in mean science test performance between
6th grade students taught by Method A and
those taught by Method B.
We need to choose between the
chance explanation (null
hypothesis) and the alternative
hypothesis that there is a
relationship between teaching
method and test performance.
Two potential errors!
• TYPE I ERROR:
– occurs when a null
hypothesis is
rejected, but null
hypothesis is true.
– Practical result is
that changes may
be made that are
not warranted.
• TYPE II ERROR
– occurs when null
hypothesis is
accepted, but null is
false.
– Practical result is
that educators may
fail to make needed
changes.
Calculating the two-group t-test statistic:
t = Mean group 1 – Mean group 2
standard error
Standard error =>
1. Divide standard deviation for Group 1 by n of Group 1
2. Divide s.d. for Group 2 by n of Group 2.
3. Sum.
4. Compute square root of this sum.
What do you do with this
t-value?
If calculated t value is equal to or
greater than the critical t value (found
in a t-table) based on (1) alpha level
and (2) degrees of freedom, then
reject the null hypothesis that there is
no difference between the groups.
What’s an alpha level?
The predetermined “level of significance,”
usually p = .05, meaning that the null
hypothesis (no difference) occurs by
chance alone no more than five times out
of 100 hypothetical studies.
What are degrees of freedom?
df = n1 + n2 - 2
n1= number of subjects in group 1
n2 = number of subjects in group 2
What is a t-table?
One-Way Analysis of Variance
(F-test)
variation between groups
F = ______________________
variation within groups
What do you do with the
derived F value?
If derived F value is equal to or
greater than the critical F value
(found in F-table, based on sample
size, alpha level, and degrees of
freedom), then reject the null
hypothesis.
What does an F table look like?
The X2 (chi-square) Statistic
X2 = 
(observed count – expected count)2
expected count
What do you do with the
calculated X2 statistic?
If derived value is equal to or greater
than the critical value (found in a X2
table, based on alpha level and
degrees of freedom), then reject the
null hypothesis.
What does a X2 table look like?