Presentation on theme: "The Normal Distribution PSYC 6130, PROF. J. ELDER 2 is the mean is the standard deviation The height of a normal density curve at any point x is given."— Presentation transcript:
PSYC 6130, PROF. J. ELDER 2 is the mean is the standard deviation The height of a normal density curve at any point x is given by Normal Distribution
PSYC 6130, PROF. J. ELDER 3 Normal Distribution A Normal Distribution has a symmetric, unimodal and bell- shaped density curve. The mean and standard deviation completely specify the curve. The mean, median, and mode are the same.
PSYC 6130, PROF. J. ELDER 4 Probabilities and the Normal Distribution Shaded area = 0.683Shaded area = 0.954Shaded area = 0.997 and 99.7% chance of falling between and
PSYC 6130, PROF. J. ELDER 5 Z-Scores The z-score is a normalized representation of a random variable with zero mean and unit variance. z-scores are dimensionless. The z-score tells you how many standard deviations a score lies from the mean.
PSYC 6130, PROF. J. ELDER 6 The Standard Normal Table: (Appendix z) A table of areas (probabilities) under the standard normal density curve. The table entry for each value z is the area under the curve between the mean and z.
8 Estimating percentiles using z-scores From a frequency table we can directly compute percentiles and percentile ranks. If we model the data as normal, we can also calculate percentiles and percentile ranks using z-scores.
PSYC 6130, PROF. J. ELDER 27 Underlying Assumptions Population is normally distributed Random sampling –Every sample of size n has the same probability of being selected. All individuals have the same probability of being selected. Selection of each individual is independent of the selection of all other individuals. Technically, sampling should be with replacement, but in Psychology, sampling is normally without replacement.