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# BU PSYC 243 - Variability

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Psych 243 1st Edition Lecture 5 Outline of Last Lecture I. Frequency Distributionsa. Normal Distributionb. Positively skewedc. Negatively Skewedd. Bimodal Distributione. Important Notef. 2 Very Important General PointsII. Central Tendencya. What is the most representative score?b. The Medianc. The Meand. The Modee. Why Mode isn’t greatf. Which Measure of Central Tendency should you use?Outline of Current Lecture I. Frequency Distributiona. Mean, Median & Mode in Frequency DistributionII. Variabilitya. Different Ways to Measure Variabilityb. Deviation from the Meanc. Formulasd. Population Variancee. Sample Variance & Sample Standard Deviationf. What Does S^2 Mean?g. Interpreting Standard DeviationThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.h. Unbiased Estimator of σi. Why is N-1 in the Denominator?j. What to Use and When to Use itCurrent Lecture***Reminder: Test next week on Chaps. 1-5***Mean, Median & Mode in Frequency Distribution- Normal Distribution: mean, mode & median are about the same score- Positively skewed: mean>median>mode- Negatively Skewed: mode>median>meanVariabilityDifferent Ways to Measure Variability- Range: highest score (minus) lowest score rough measure of variability- Variance- Standard DeviationDeviation from the Mean- Deviation from the mean: Each score in a data set can be described as a deviation from the mean by subtracting the mean from the score- Size of the deviation indicates how far a particular score is from the mean the higher the score, the higher the deviationo In a normal distribution, the greater the deviation, the less frequent the score- Scores that are equal to the mean will have a deviation of zero- Positive deviations indicate that the score is higher than the mean- Negative deviations indicate that the score is lower than the mean- The sum of deviations from the mean will always = 0 because the pluses & minuses cancel each other outo To get around this, first square all the deviations (to remove the neg. signs) & then sum the squared deviations & divide by NFormulas - Many analyses have a definitional & computing formula- Definitional formulas are easier to grasp conceptually, but the computations can be tedious- Computational formulas don’t make sense when you look at them, but involve fewer steps- Will yield identical answers but she rather use definitional formulaPopulation Variance (it’s more work for me to actually write it)- Steps:o Find the No Find the meano Find the simple deviation by subtracting the mean from each scoreo Square each simple deviationo Sum the simple deviationso Divide by N (this is the variance)o Take the square root to find xSample Variance & Sample Standard Deviation (Formulas)What Does S^2 mean?- The variance is hard to interpret & conceptualize because it is in square unitsInterpreting Standard Deviation- Standard deviation is the average amount that the scores in your sample deviate from the mean- It will always be positive - The larger the standard deviation, the more spread out the scores in your sampleUnbiased Estimator of σWhy is N-1 in denominator?- Describe variability of a sample but underestimate variability in a population- Why?o Samples tend to have less variability from parent populationo Extreme scores occur infrequently and are less likely to end up in samples- (N-1) instead of N is the denominator of the formulas dividing by a smaller number results in a slightly higher estimate of variability- As your N becomes larger & larger, sample statistics are better & better estimators of population parameterso (N-1) has less of an impact on final product of formulas as N becomes largerWhat To Use & When To Use It- Describing sample?  Use S2x & Sx- Tested EVERY member of population of interest?  Use σ2x & σx- Want to infer the population standard deviation, but you have only tested a sample of the population? Use unbiased estimates s^2x &

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