Psy 202 Chapter 3
Psy 202 Chapter 3 Psy 202
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This 5 page Class Notes was uploaded by T'Keyah Jones on Saturday September 3, 2016. The Class Notes belongs to Psy 202 at University of Mississippi taught by Dr. Melinda Redding in Fall 2016. Since its upload, it has received 7 views. For similar materials see Elementary Statistics in Psychology (PSYC) at University of Mississippi.
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Date Created: 09/03/16
Psy 202 Elementary Statistics Chapter 3: Measures of Central Tendency and Variability a. Central Tendency A single value used to represent the typical score in a set of scores b. Three Measures of Central Tendency Mean Median Mode c. Mean The average Influenced by outliers Formula: ΣX N µ Mean of population M Mean of sample Mx My Mean of "X" variable Mean of "Y" variable d. Median The middle score The midpoint of right distribution Not influenced by outliers Right distribution Scores listed in order If "N" is odd The median is the middle score If "N" is even Find the two middle scores and find midpoint e. Mode Score that occurs the most The peak(s) of a simple frequency distribution There can be more than 1 Center of a normal distribution f. Distributing Shapes Symmetrical Distribution: Uni There is only 1 peak Symmetrical Distribution: Bi There are two peaks Skewed Distribution The mean is pulled toward the tail If the mean is high If the mean is low Positive Negative g. Reporting Central Tendency Nominal data Mode Ordinal data Median Interval/Ratio Data Depends on the shape of the distribution Normal Distribution Skewed/OpenEnded Distribution Mean Median h. Variability Descriptive statistics Refers to the "spread" of scores in a distribution To describe distribution Shape Central Tendency Variability Types Range Variance Interquartile Range Standard Deviation Range Simplest measure X high X low Disadvantage not very stable because it uses only two scores heavily influenced by outliers Interquartile Range Uses only the middle 50% of the score X high X low the middle 50% distribution Good for skewed distribution Population V. Sample The variability within a population is greater than the variability within a sample Variability statistics will always underestimate variability parameter (biased estimate) When calculating variance and standard deviation on a sample, a correction is made in the formula to yield an "unbiased estimate" of the population variance Unbiased estimate For variance Using a corrector factor for a more accurate answer i. Variance Uses all scores The average of squared deviations from the mean 1. Find the deviation scores (Xµ) or (XM) 2. Square the deviation scores 3. Sum the square deviation scores 4. find the average of squared deviation scores Advantage Uses all scores Not heavily influenced by outliers Disadvantage Difficult to interpret squared units Scores that are similar Scores that are different Little variability (spread) Large variability (spread) j. Standard Deviation How much do the scores deviate from the mean on average Easier to interpret than variance because it is in the same units as the original data 1. Find the variance 2. Take the square root of the variance k. Variance (Definitional Formulas) Variance population Variance sample o s 2 2 2 2 o = Σ(Xµ) s = Σ(XM) N N1 SS Sum of squares Example Population data set: 12,9,15,13,11 N = 5 M = 12 2 X X µ (deviation score) (X µ) 12 0 0 9 3 9 15 3 9 13 1 1 11 1 1 Σ(X µ) = 20 2 o = 20 = 4.00 Standard Deviation: 2.00 5 s = 20 = 5.00 Standard Deviation: 2.24 4 l. Variance (Computational Formulas) 2 2 2 o = ΣX (ΣX) _______N N s = ΣX (ΣX) 2 ______N N1 Example 2 X X 6.95 48.3025 7.09 50.2681 7.08 50.1264 7.19 51.6961 7.15 51.1225 6.92 47.8864 N = 6 ΣX = 42.38 2 ΣX = 299.40 o = 299.40 (42.38) 2 = 0.01 _________6 6
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