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Appendix

Behavioral Statistics

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Types of Statistics in Psychology

Descriptive Statistics: Summarize numbers so they become more meaningful and easier to communicate to other people

Inferential Statistics: Used for making decisions, for generalizing from small samples, and for drawing conclusions

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Graphical StatisticsPresenting numbers pictorially (usually in a graph) so they are easier to visualize Subset of descriptive statistics

Frequency Distribution: Table that divides an entire range of scores into a series of equal classes and then records the number of scores that fall into each classHistogram: Graph of a frequency distribution; scores are represented by vertical barsFrequency Polygon: Number of scores in each class is represented by points on a line

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Fig. A.1 Frequency histogram of hypnotic susceptibility scores contained in Table A.2.

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Fig. A.2 Frequency polygon of hypnotic susceptibility scores contained in Table A.2.

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Measures of Central Tendency

A number that describes a typical score around which the other scores fall

Mean: Add all the scores for each group and then divide by the total number of scores; one type of averageSensitive to extremely high or low scores in

a distribution; not always the best measure of central tendency

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Measures of Central Tendency (cont.)

Median: Arrange scores from highest to lowest and then select the score that falls in the middle; half the values fall above the median, and half fall below it

Mode: Identifies the most frequently occurring score in a group Easy to obtain but often unreliable Main advantage: Gives the score actually obtained

by the most people

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Measures of Variability

Provide a single number that tell us how spread out the scores are

Range: Difference between the highest and lowest scores

Standard Deviation: Index of how much a typical score differs from the mean of a group of scores

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Standard Scores

Z Score: Indicates how many standard deviations above or below the mean a score is

Normal Curve: Bell-shaped curve, with a large number of scores in the middle and very few extremely high and low scores

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Fig. A.3 The normal curve. The normal curve is an idealized mathematical model. However, many measurements in psychology closely approximate a normal curve. The scales you see here show the relationship of standard deviations, z-scores, and other measures to the curve.

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Fig. A.4 Relationship between the standard deviation and the normal curve.

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Inferential Statistics

Population: Entire set of subjects, objects, or events of interest (all married students in the United States) Impossible or impractical to obtain

Samples: Smaller cross section of a population Easier and more practical (and cheaper!) to obtain More cost effective

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Inferential Statistics (cont.)

Sample must be representative The membership and characteristics of the larger

population must be reflected accurately

Members of sample must be chosen randomly Each member of the population must have an

equal chance of being selected for the sample

Statistical Significance: Degree to which an event (results of an experiment, results of a drug trial) is unlikely to have occurred by chance alone

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Correlation

Consistent, systematic relationship between two variables, measures, or eventsScatter Diagram: Best way to visualize correlation; plots intersection of paired measures Positive Relationship: Increases in one measure (X) are matched by increases in the other (Y) The more cigarettes you smoke, the more likely

you are to contract lung cancer

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Correlation (cont.)

Zero Correlation: No relationship exists between two variables Relationship between hair color and intelligence

test scores (IQs)

Negative Relationship (or Correlation): As values of one measure increase (X), values in the other measure decrease (Y) The more alcohol you drink, the lower your

coordination test scores will be

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Fig. A.5 Scatter diagrams showing various degrees of relationship for a positive, zero, and negative correlation. (Adapted from Pagano, 1981.)

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Coefficient of Correlation

Statistical index ranging from –1.00 to +1.00; the sign indicates the direction of the relationship, and the number, the strength Perfect Positive Relationship: Correlation of +1.00 Perfect Negative Relationship: Correlation of –

1.00 Perfect correlations are rarely found in psychology It is statistically impossible to have a correlation

coefficient greater than +1.00 or lesser than –1.00

Percent of Variance: Amount of variation in scores accounted for by the correlation

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Utility of Correlations

Correlations help us identify relationships that are worth knowingCorrelations are valuable for making predictionsIf a correlation exists, the two variables are relatedCorrelation does NOT demonstrate causation! Many times a third, or perhaps an extraneous,

variable could be creating the correlation