4.15.04a.ppt

4.15.04a.ppt

• 1.
  Descriptive Statistics Statistics usedto describe and interpret sample data. Results are not really meant to apply to other samples or to the larger population • Frequency Distribution • Central Tendency (Mean, Median, Mode) • Percentile Values
• 2.
  Inferential Statistics Statistics usedto make inference about the population from which the sample was drawn. Correlation T-test ANOVA (Analysis of Variance) Regression
• 3.
  Population vs. Sample Population:A large group of people to which we are interested in generalizing. ‘parameter’ Sample: A smaller group drawn from a population. ‘statistic’
• 4.
  Measures of CentralTendency Statistics that identify where the center or middle of the set of scores are. Mode : Most frequently occurring scores. Median : the 50th percentile, the second quartile Mean : Arithmetic means, average, Add all the scores and divide by the number of scores.
• 5.
  Which central tendencyto use? Depends on : • The level of measurement of the data. 2. The shape of the score distribution. (Skewness)
• 6.
  Level of Measurement Nominal:Categorical scale e.g. Male/Female, Blue eye/Brown eye/Green eye Ordinal: Ranking scale (Differences between the ranks need not be equal) e.g. Scored highest (100 pts), middle (85 pts), lowest (20 pts) Interval: The distance between any two adjacent units of measurement (intervals) is the same but there is no meaningful zero point. e.g. Fahrenheit temperature Ratio: The distance between any two adjacent units of measurement is the same and there is a true zero point. e.g. Height measurement, Weight measurement
• 7.
  Which central tendencyto use? 1. The level of measurement of the data. Mode---Nominal, Ordinal, Interval or Ratio Median--- Ordinal, Interval, or Ratio Mean---Interval or Ratio
• 8.
  Shape of thedistribution: Skewness A measure of the lack of symmetry, or the lopsidedness of a distribution. (> or < 2) Use “median”
• 9.
  Shape of Distribution:Kurtosis Leptokurtic Mesokurtic (Normal Distribution) Platykurtic How flat or peaked a distribution appears. (Does not affect the central tendency)
• 10.
  Shape of thedistribution: unimodal, bimodal Bimodal --- 2 Modes Mode is not a good indicator of the central tendency.
• 11.
  Which central tendencyto use? Symmetric, unimodal, Normal distribution --- Mode, Median, Mean all the same. Skewed --- use the Median. Bimodal --- do not use the Mode.
• 12.
  Describing data usingTables and Charts Frequency table Stem and leaf Polygon Histogram Box and whisker
• 13.
  Measures of Variability Reflectshow scores differ from one another. - spread - dispersion Example: 7, 6, 3, 3, 1 3, 4, 4, 5, 4, 4, 4, 4, 4, 4,
• 14.
  Measures of Variability Range Highestscore – lowest score Example: 7, 6, 3, 3, 1 ---- range = 6 3, 4, 4, 5, 4 ---- range = 2 4, 4, 4, 4, 4 ---- range = 0 Variance Standard Deviation
• 15.
  Measures of Variability Range StandardDeviation Variance
• 16.
  Standard Deviation Standard Deviation:A measure of the spread of the scores around the mean. Average distance from the mean. Example:Can you calculate the average distance of each score from the mean? (X=4) 7, 6, 3, 3, 1 (distance from the mean: 3,2,-1,-1,-3) 3, 4, 4, 5, 4, (distance from the mean: -1,0,0,1,0) You can’t calculate the mean because the sum of the ditance from the mean is always 0.
• 17.
  Formula for StandardDeviation s = (X-X)2 n-1 Standard deviation of the sample Sigma: sum of what follows Each individual score Mean of all the scores Sample size
• 18.
  Why n-1? s (lowercase sigma) is an estimate of the population standard deviation ( :sigma) . In order to calculate an unbiased estimate of the population standard deviation, subtract one from the denominator. Sample standard deviation tends to be an underestimation of the population standard deviation.
• 19.
  Variance Variance: Standard deviationsquared. S = (X-X)2 n-1 Not likely to see the variance mentioned by itself in a report. Difficult to interpret. But it is important since it is used in many statistical formulas and techniques.