PSYC 3500: Terms and Definitions

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• Statistics - The process of representing or analyzing numerical data.

• Descriptive Statistics - 1) Organizing data from a sample in a meaningful way. 2)

Conclusions cannot be drawn beyond that sample. 3) The five most common descriptive

statistics are percentiles, frequency distributions, graphs, and measures of central

tendency.

• Percentiles - Most commonly used on standardized tests. If you score 750 on the subject

test, you are in the 97th percentile, meaning you scored higher than 97% of the group of

people that have taken the test.

• Frequency Distributions - 1) Explain how data in a study looked. 2) Might show how

often different variables appeared. 3) Common types of variables: nominal, ordinal,

interval, and ratio.

• Graphs - Used to plot data.

• Frequency Polygon - A type of graph that has plotted points with connected lines. Often

used to plot data that are continuous (lacking clear boundaries).

• Histograms - A type of graph with vertical bars in which the sides of the bars touch.

Useful for discrete variables that have clear boundaries and for interval variables in

which there is some order.

• Bar graph - A type of graph that is like the histogram except the bars do not touch.

• Measures of Central Tendency - Indicate where on a number line the data set generally

falls. Three types of central tendency: mean, median, and mode.

• Mean - 1. The average. 2. Highly affected by extreme scores (in which case the median is

used for computations).

• Standard error of the mean - Calculates how 'off' the mean might be in either direction.

• Median - The value that is the center of the distribution. If there is an even number of

values, take the average of the middle two numbers.

• Mode - The value that most frequently occurs within the data set.

• Variability - Provides additional information to central tendency. Shows how the scores

are spread out overall. Includes range, variance, and standard deviation.

PSYC 3500: Terms and Definitions

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• Range - Subtract the lowest value from the highest value. Gives an idea of the overall

spread of the data.

• Variance - Tells us how much variation there is among n numbers of scores in a

distribution

• How to find variation - 1. Subtract the mean from each score. 2. Square all values (to

eliminate negative values). 3. Add all the squared deviations to get the sum of squares. 4.

Divide this number by the number of scores you had in the beginning.

• Standard Deviation - The average extent to which scores were different from the mean. If

the average SD is large, the scores were highly dispersed. If the average SD is small, the

scores were very close together. Different standard distributions make it hard to compare

scores from two different tests.

• How to find the standard deviation - Take the square root of the variance.

• The Normal Distribution - Known as the bell curve. The larger the sample, the greater the

likelihood of having a normal distribution of values. It is unimodal.

• Unimodal - Only has one bump. The majority of scores fall in the middle ranges. Fewer

scores at the extremes. Mean, median, and mode are all equal in a normal distribution.

• Z-scores - Refers to how many standard deviations a score is from the mean. Range on a

normal distribution, +3 to -3 because this covers the vast majority of scores.

• T-scores - A transformation of z-scores in which the mean is 50 and the standard

deviation is 10. Formula for calculating: T = 10(Z) + 50.

• Why are normal distributions standardized? - In order to combat the problem of

comparing scores and distributions of scores with different standard deviations.

• Standard normal distributions - The mean is 0 and the SD is 1.

• The 34:14:2 ratio - Applies to both sides of the normal distribution curve.

- 34% on either side of the mean by one standard deviation (50th percentile, z-score

is 0.

- 14% on either side of the mean by two standard deviations (84th percentile, z-

score is +1.

- 2% on either side of the mean by three standard deviations (97th percentile, z-

score is +2.