10 - Class Notes The Normal Distribution Objective To...

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8/26/10 Class Notes: The Normal Distribution Objective: To understand the normal distribution and the ways we will use it to make inferences from our data Characteristics of Normal Distributions: Unimodal, symmetrical, bell-shaped Theoretical distributions, not empirical distributions 1. Based on logic and mathematics (not observations) 2. A normal distribution never drops to baseline at either end 3. Normal distributions are very valuable Theoretically- the area between the curve and the baseline is taken to be 100% Importance of Normal Distributions: Measurements of many naturally occurring phenomena (intelligence, height, aggressiveness, etc) The sampling distribution of the means The Normal Distribution Table (or the z-table) and z scores Because the normal distributions are exactly defined, it is possible to compute the exact percentage of the scores that will fall between any two points in the distribution (or to compute the exact probability that a score taken at random will fall between any two points in the distribution. That is, it is possible to determine the exact percentage of cases between any two z scores. Getting to Know the z table (do this well!) Probability x 100 = % Find percentage of scores below (or above) a specific raw score using the z table 1. Draw a distribution 2. Convert the raw score into a z score 3. Look up the z table, find the z score, and then see the corresponding p 4. Multiply by 100 Find the percentage of scores that falls BETWEEN two raw scores? 1. Draw a distribution 2. Convert raw scores into z scores 3. Look up the z table, find the z scores and then find appropriate probability 4. Add or subtract to get at total probability 5. Multiply by 100 Find the raw score that represents a certain cut-off probability 1. Draw the curve 2. Look up the normal curve table and find the closest % 3. Find the z score in the z column 4. Convert the z score into a raw score
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8/26/10 Class Notes: Sampling Objective: To identify differences between samples and populations; to understand what makes a good sample and what samples represent Why do we study samples instead of populations? Review of Definitions: Population: Sample: M Methods of Sampling *****The ability to generalize from a sample to the population depends on the REPRESENTATIVENESS of the sample**** Random sampling: Every element of the population being studied has an equal probability of being included in the sample Random Sampling vs. Random Assignment Review of Definitions: Population: Sample:
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10 - Class Notes The Normal Distribution Objective To...

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