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Quantitative Data Analysis

Quantitative Data Analysis. Assessment Committee 2009 Division of Campus Life, Emory University. Outline. What is quantitative data analysis? Types of quantitative data used in assessment Descriptive statistics Utilizing Microsoft Excel Introduction to inferential statistics

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Quantitative Data Analysis

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  1. Quantitative Data Analysis Assessment Committee 2009 Division of Campus Life, Emory University

  2. Outline • What is quantitative data analysis? • Types of quantitative data used in assessment • Descriptive statistics • Utilizing Microsoft Excel • Introduction to inferential statistics • Presenting quantitative data

  3. What is quantitative data analysis? • Making sense of numbers. • Using numbers to inform decision-making.

  4. Types of quantitative data • 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!

  5. A common mistake • Not everything can be quantified!

  6. Descriptive Statistics • Just like it sounds – these describe aspects things about a group of numbers.

  7. Terms • Sum • Mean • Median • Range • Variance • Standard deviation

  8. Sum • 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.

  9. Mean • 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

  10. Median • 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

  11. Range • 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 = 6GPA: 4.0 – 1.50 = 2.5 • Hours mentored: 8-1 = 7

  12. Variance • 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

  13. Standard deviation • 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

  14. Inferential statistics • 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.

  15. 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.

  16. Significance • 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.

  17. A common mistake Beware the correlation-causation fallacy.

  18. Using inferential statistics • 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!

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

  20. Presenting the data

  21. Presenting the data

  22. Presenting the data • 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).

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