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EDU 660

EDU 660. Methods of Educational Research Descriptive Statistics John Wilson Ph.D. Definitions. Quantitative data numbers representing counts or measurements. Definitions. Quantitative data numbers representing counts or measurements

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EDU 660

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  1. EDU 660 Methods of Educational Research Descriptive Statistics John Wilson Ph.D.

  2. Definitions • Quantitative data • numbers representing counts or measurements

  3. Definitions • Quantitative data • numbers representing counts or measurements • Qualitative (or categorical or attribute) data • can be separated into different categories that are distinguished by some non-numeric characteristics

  4. Definitions • Quantitative data • the incomes of college graduates

  5. Definitions • Quantitative data • the incomes of college graduates • Qualitative (or categorical or attribute) data • the genders (male/female) of college graduates

  6. Definitions • Discrete data result when the number of possible values is a ‘countable’ number 0, 1, 2, 3, . . .

  7. Definitions • Discrete data result when the number is or a ‘countable’ number of possible values 0, 1, 2, 3, . . . • Continuous (numerical) data result from infinitely many possible values that correspond to some continuous scale 2 3

  8. Definitions • Discrete The number of students in a classroom.

  9. Definitions • Discrete The number of students in a classroom. • Continuous The value of all coins carried by the students in the classroom.

  10. Levels of Measurement of Data • nominal level of measurement characterized by data that consist of names, labels, or categories only. The data cannot be arranged in an ordering scheme (such as low to high) Example: Your car rental is a: Ford, Nissan, Honda, or Chevrolet

  11. Levels of Measurement of Data • ordinal level of measurement involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless. Example: Course grades A, B, C, D, or F. Your car rental is an: economy, compact, mid-size, or full-size car.

  12. Levels of Measurement of Data • interval level of measurement like the ordinal level, with the additional property that the difference between any two data values is the same. However, there is no natural zero starting point (where none of the quantity is present) Example: The temperature outside is 5 degrees Celsius.

  13. Levels of Measurement of Data • ratio level of measurement the interval level modified to include the natural zero starting point (where zero indicates that none of the quantity is present). For values at this level, differences and ratios are meaningful. Examples: Prices of textbooks. The Temperature outside is 278 degrees Kelvin.

  14. Levels of Measurement • Nominal- categories only • Ordinal- categories with some order • Interval– interval are the same, but no natural starting point • Ratio– intervals are the same, anda natural starting point

  15. Measures of the centre a value at the centre or middleof a data set Mean Median Mode

  16. Definitions Mean (Arithmetic Mean) AVERAGE The number obtained by adding the values and dividing the total by the number of values

  17. Notation •  denotes the addition of a set of values • x is the variable usually used to represent the individual data values • n represents the number of data values in a sample • N represents the number of data values in a population

  18. x x x = n Notation is pronounced ‘x-bar’ and denotes the mean of a set of sample values

  19. x x x = n x µ = N Notation is pronounced ‘x-bar’ and denotes the mean of a set of sample values µis pronounced ‘mu’ and denotes the mean of all values in a population

  20. Definitions • Median the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude The Median is used to describe house prices in Toronto. Why not the Mean?

  21. Definitions • Mode the score that occurs most frequently Bimodal Multimodal No Mode denoted by M the only measure of central tendency that can be used with nominal data

  22. Examples • Mode is 5 • Bimodal - 2 and 6 • No Mode a. 5 5 5 3 1 5 1 4 3 5 b. 1 2 2 2 3 4 5 6 6 6 7 9 c. 1 2 3 6 7 8 9 10

  23. Waiting Times of Bank Customers at Different Banks (in minutes) TD RBC 6.5 4.2 6.6 5.4 6.7 5.8 6.8 6.2 7.1 6.7 7.3 7.7 7.4 7.7 7.7 8.5 7.7 9.3 7.7 10.0

  24. Waiting Times of Bank Customers at Different Banks in minutes TD RBC 6.5 4.2 6.6 5.4 6.7 5.8 6.8 6.2 7.1 6.7 7.3 7.7 7.4 7.7 7.7 8.5 7.7 9.3 7.7 10.0 RBC TD Mean Median Mode Midrange 7.15 7.20 7.7 7.10 7.15 7.20 7.7 7.10

  25. Measures of Variation Range Variance Standard Deviation

  26. lowest highest value value Measures of Variation Range

  27. Measures of VariationVariance • Mean Squared Deviation from the Mean

  28. Measures of Variation Standard Deviation (Root Mean Squared Deviation)

  29. Population Standard Deviation Formula Root Mean Squared Deviation (x - x)2 s= N

  30. Basketball Starting Line

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