Assessment Committee 2009 Division of Campus Life, Emory University.

Quantitative Data Analysis

Assessment Committee 2009Division of Campus Life, Emory University

What is quantitative data analysis? Types of quantitative data used in

assessment Descriptive statistics

◦ Utilizing Microsoft Excel Introduction to inferential statistics Presenting quantitative data

Outline

Expected Learned Outcomes

Making sense of numbers.

Using numbers to inform decision-making.

What is quantitative data analysis?

Categorical◦ Nominal: names◦ Ordinal: 1st, 2nd, 3rd.

Continuous◦ Ratio: consistent distance between each point◦ Interval: there is a zero starting point

There is an important difference in how you work with categorical and continuous variables!

Types of quantitative data

Not everything can be quantified!

A common mistake

Just like it sounds – these describe aspects things about a group of numbers.

Descriptive Statistics

Sum Mean Median Range Variance Standard deviation

Terms

What is it?◦ The total

How to get it:◦ Add up all of the numbers.

There are a total of 13 participants. Sum is used to calculate other statistics.

Sum

What is it?◦ The average of all of the numbers

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

For our example:◦ Mean age: 19.3◦ Mean GPA: 2.84◦ Mean hours mentored: 4.53

Mean

What is it?◦ The middle number, when all of the numbers are arranged

in increasing order

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.

For our example:◦ Median age: 19◦ Median GPA: 2.85◦ Median hours mentored: 5

Median

What is it?◦ The spread between the smallest and largest

number in the sample.

How to get it:◦ Find the smallest and largest numbers. Subtract

the smallest from the largest.

For our example:◦ Age: 23-17 = 6

GPA: 4.0 – 1.50 = 2.5◦ Hours mentored: 8-1 = 7

Range

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?

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.

In our example:◦ Age: 2.39744◦ GPA: .05437◦ Hours mentored: 5.6026

Variance

What is it?◦ A commonly used measure of how spread out

individual numbers are from the median

How to get it:◦ Take the square root of the variance. Or use the easy

button and have Excel calculate it for you.

In our example:◦ Age: 1.54837◦ GPA: 0.7374◦ Hours mentored: 2.367

Standard deviation

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.

Inferential statistics

Variety of statistical tests: Chi-squared, T-tests, 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.

Inferential statistics

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.

Significance

A common mistake

Beware the correlation-causation fallacy.

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!

Using inferential statistics

Consider practical vs. statistical significance. Don’t be beholden to statistics. Inferential statistics are a tool, not the answer!

A common mistake

Presenting the data  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

Median 19 2.85 5

Presenting the data

1 2 3 4 5 6 7 80

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Relationship between GPA and hours mentored

Series1

Hours mentored

Achieved GPA

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).

Presenting the data