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EDPSY 511-001

EDPSY 511-001. Chp. 2: Measurement and Statistical Notation. Populations vs. Samples. Population The complete set of individuals Characteristics are called parameters Sample A subset of the population Characteristics are called statistics.

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EDPSY 511-001

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  1. EDPSY 511-001 Chp. 2: Measurement and Statistical Notation

  2. Populations vs. Samples • Population • The complete set of individuals • Characteristics are called parameters • Sample • A subset of the population • Characteristics are called statistics. • In most cases we cannot study all the members of a population

  3. Descriptive vs. Inferential • Descriptive statistics • Summarize/organize a group of numbers from a research study • Inferential statistics • Draw conclusions/make inferences that go beyond the numbers from a research study • Determine if a causal relationship exists between the IV and DV

  4. Common Research Designs • Correlational • Do two qualities “go together”. • Comparing intact groups • a.k.a. causal-comparative and ex post facto designs. • Quasi-experiments • Researcher manipulates IV • True experiments • Must have random assignment. • Why? • Researcher manipulates IV

  5. Variables • Variables • Characteristics that takes on different values • Achievement • Age • Condition • Independent variable (IV) • Manipulated or Experimental • Condition • Subject • Personality • Gender • Dependent variable (DV) • The outcome of interest • Achievement • Drop-out status

  6. Measurement • Is the assignment of numerals to objects. • Nominal • Examples: Gender, party affiliation, and place of birth • Ordinal • Examples: SES, Student rank, and Place in race • Interval • Examples: Test scores, personality and attitude scales. • Ratio • Examples: Weight, length, reaction time, and number of responses

  7. Categorical, Continuous and Discontinuous • Categorical (nominal) • Gender, party affiliation, etc. • Discontinuous • No intermediate values • Children, deaths, accidents, etc. • Continuous • Variable may assume an value • Age, weight, blood sugar, etc.

  8. Values • Exhaustive • Must be able to assign a value to all objects. • Mutually Exclusive • Each object can only be assigned one of a set of values. • A variable with only one value is not a variable. • It is a constant.

  9. Chapter 2: Statistical Notation • Nouns, Adjectives, Verbs and Adverbs. • Say what? • Here’s what you need to know • X • Xi = a specific observation • N • # of observations • ∑ • Sigma • Means to sum • Work from left to right • Perform operations in parentheses first • Exponentiation and square roots • Perform summing operations • Simplify numerator and divisor • Multiplication and division • Addition and subtraction

  10. Pop Quiz (non graded) • In groups of three or four • Perform the indicated operations. • What was that?

  11. Chapter 3 Exploratory Data Analysis

  12. Exploratory Data Analysis • A set of tools to help us exam data • Visually representing data makes it easy to see patterns. • 49, 10, 8, 26, 16, 18, 47, 41, 45, 36, 12, 42, 46, 6, 4, 23, 2, 43, 35, 32 • Can you see a pattern in the above data? • Imagine if the data set was larger. • 100 cases • 1000 cases

  13. Three goals • Central tendency • What is the most common score? • What number best represents the data? • Dispersion • What is the spread of the scores? • What is the shape of the distribution?

  14. Frequency Tables • Let say a teacher gives her students a spelling test and wants to understand the distribution of the resultant scores. • 5, 4, 6, 3, 5, 7, 2, 4, 3, 4

  15. As groups • Create a frequency table using the following values. • 20, 19, 17, 16, 15, 14, 12, 11, 10, 9

  16. Banded Intervals • A.k.a. Grouped frequency tables • With the previous data the frequency table did not help. • Why? • Solution: Create intervals • Try building a table using the following intervals <=13, 14 – 18, 19+

  17. Stem-and-leaf plots • Babe Ruth • Hit the following number of Home Runs from 1920 – 1934. • 54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22 • As a group let’ build a stem and leaf plot • With two classes’ spelling scores on a 50 item test. • Class 1: 49, 46, 42, 38, 34, 33, 32, 30, 29, 25 • Class 2: 39, 38, 38, 36, 36, 31, 29, 29, 28, 19 • As a group let’ build a stem and leaf plot

  18. Landmarks in the data • Quartiles • We’re often interested in the 25th, 50th and 75th percentiles. • 39, 38, 38, 36, 36, 31, 29, 29, 28, 19 • Steps • First, order the scores from least to greatest. • Second, Add 1 to the sample size. • Why? • Third, Multiply sample size by percentile to find location. • Q1 = (10 + 1) * .25 • Q2 = (10 + 1) * .50 • Q3 = (10 + 1) * .75 • If the value obtained is a fraction take the average of the two adjacent X values.

  19. Box-and-Whiskers Plots (a.k.a., Boxplots)

  20. Shapes of Distributions • Normal distribution • Positive Skew • Or right skewed • Negative Skew • Or left skewed

  21. How is this variable distributed?

  22. How is this variable distributed?

  23. How is this variable distributed?

  24. Descriptive Statistics

  25. Statistics vs. Parameters • A parameter is a characteristic of a population. • It is a numerical or graphic way to summarize data obtained from the population • A statistic is a characteristic of a sample. • It is a numerical or graphic way to summarize data obtained from a sample

  26. Types of Numerical Data • There are two fundamental types of numerical data: • Categorical data: obtained by determining the frequency of occurrences in each of several categories • Quantitative data: obtained by determining placement on a scale that indicates amount or degree

  27. Measures of Central Tendency Central Tendency Average (Mean) Median Mode

  28. Mean (Arithmetic Mean) • Mean (arithmetic mean) of data values • Sample mean • Population mean Sample Size Population Size

  29. Mean • The most common measure of central tendency • Affected by extreme values (outliers) 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Mean = 5 Mean = 6

  30. Median • Robust measure of central tendency • Not affected by extreme values • In an Ordered array, median is the “middle” number • If n or N is odd, median is the middle number • If n or N is even, median is the average of the two middle numbers 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Median = 5 Median = 5

  31. Mode • A measure of central tendency • Value that occurs most often • Not affected by extreme values • Used for either numerical or categorical data • There may may be no mode • There may be several modes 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 No Mode Mode = 9

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