Transcript Quantitative Data Analysis

Assessment Committee 2009
Division of Campus Life,
Emory University
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What is quantitative data analysis?
Types of quantitative data used in
assessment
Descriptive statistics
◦ Utilizing Microsoft Excel
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Introduction to inferential statistics
Presenting quantitative data
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Making sense of numbers.
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Using numbers to inform decision-making.
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Categorical
◦ Nominal: names
◦ Ordinal: 1st, 2nd, 3rd.
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Continuous
◦ Ratio: consistent distance between each point
◦ Interval: there is a zero starting point
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There is an important difference in how you
work with categorical and continuous
variables!
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Not everything can be quantified!
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Just like it sounds – these describe aspects
things about a group of numbers.
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Sum
Mean
Median
Range
Variance
Standard deviation
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What is it?
◦ The total
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How to get it:
◦ Add up all of the numbers.
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There are a total of 13 participants.
Sum is used to calculate other statistics.
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What is it?
◦ The average of all of the numbers
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How to get it:
◦ Add up all of the numbers and divide by total
sample size. In math-speak: (x1+x2+…+xn)/n.
Often notated as (Σxn)/n
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For our example:
◦ Mean age: 19.3
◦ Mean GPA: 2.84
◦ Mean hours mentored: 4.53
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What is it?
◦ The middle number, when all of the numbers are
arranged in increasing order
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How to get it:
◦ Put numbers in order from least to greatest, and find the
middle number. If you have an even-sized sample the
median is the mean of the two middle numbers.
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For our example:
◦ Median age: 19
◦ Median GPA: 2.85
◦ Median hours mentored: 5
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What is it?
◦ The spread between the smallest and largest
number in the sample.
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How to get it:
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For our example:
◦ Find the smallest and largest numbers. Subtract
the smallest from the largest.
◦ Age: 23-17 = 6
GPA: 4.0 – 1.50 = 2.5
◦ Hours mentored: 8-1 = 7
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What is it?
◦ A measure of the variation in the sample, or how spread
out it is. How far does each number vary from the mean?
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How to get it:
◦ In math-speak: Σ(x – M)2/(n-1).
◦ Hit the easy button and use Excel to calculate this for
you.
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In our example:
◦ Age: 2.39744
◦ GPA: .05437
◦ Hours mentored: 5.6026
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What is it?
◦ A commonly used measure of how spread out
individual numbers are from the median
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How to get it:
◦ Take the square root of the variance. Or use the
easy button and have Excel calculate it for you.
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In our example:
◦ Age: 1.54837
◦ GPA: 0.7374
◦ Hours mentored: 2.367
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Used to show relationships between variables.
Can be used to explain or predict these
relationships.
Don’t be intimidated! Inferential statistics are
a tool that you can learn to utilize with
patience and practice.
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Variety of statistical tests: Chi-squared, Ttests, analysis of variance, regression, et
cetera.
Conveniently many of these tests can be done
using software that can be downloaded for
FREE if you are an Emory staff member.
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Statistical tests look for significance, a
concept that measures the degree to which
your results can be obtained due to chance.
In social science/educational research the
term α = .05 is often used. This means there
is a 5% or less chance that the results are due
to chance.
Beware the correlation-causation fallacy.
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Consider the use of inferential statistics when
you are designing your assessment project.
Consult with someone who has statistical
experience as you develop your own
statistical confidence.
Inferential statistical are not always necessary
or desirable!
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Consider practical vs. statistical significance.
Don’t be beholden to statistics. Inferential
statistics are a tool, not the answer!
Age
GPA
Gender
Hours
Dick
20
1.9
M
1
Edward
19
1.5
M
1
Emmett
20
2.1
M
2
Lauren
20
2.4
F
3
Mike
19
2.75
M
4
Benjie
18
3
M
4
Joe
19
2.85
M
5
Larry
17
2.75
M
5
Rose
18
3.3
F
5
Bob
18
3.1
M
6
Kate
19
3.4
F
7
Sally
21
4
F
8
Sylvia
23
3.9
F
8
Sum
251
36.95
59
Avg
19.308
2.8423
4.5385
Variance
2.3974
0.5437
5.6026
Std Dev
1.5484
0.7374
2.367
19
2.85
5
Median
Relationship between GPA and hours
mentored
4.5
4
3.5
3
2.5
Achieved GPA
2
Series1
1.5
1
0.5
0
1
2
3
4
5
Hours mentored
6
7
8
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Thirteen students participated in the minority
mentoring program. A strong positive
correlation was found between the number of
hours mentored and achieved GPA (.965),
between hours mentored and gender (.578),
and between gender and achieved GPA (.622).