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1

Statistics

Focuses on the organization, analysis, and interpretation of a group of numbers
Method of pursuing truth

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2 Types of Statistics

Descriptive
Inferential

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Descriptive Statistics

Summarizing a group of scores or otherwise making them more understandable
To describe a group of numbers from a research study

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Inferential Statistics

Drawing conclusions based on the scores collected in a research study but going beyond them

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Example of Interferential Statistics

Making inferences about a large group of individuals based on a research study in which a much smaller number of individuals took part in

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Variable

Characteristic that can have different values

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Values

Possible number/category that a score can have

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Score

Particular persons value on a variable

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Numerical Variable

Values are number
Quantitative variable

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Types of Numeric Variables

Equal-Interval Variable
Rank-Order Variable
Nominal Variable

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Equal-Interval Variable

The numbers stand for approximately equal amounts of what is being measured

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Example of Equal-Interval Variables

Difference between 2.5 and 2.8 is = to the difference 3.0 and 3.3

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Ratio Scale

An equal-interval variable is measured on a ratio scale if it has an absolute zero point
The value of zero on the variable indicates a complete absence of the variable.

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Rank-Order Variable

Numeric variable in which the values are ranks
Ordinal variable

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Example of Rank-Order Variable

Class standings,
Place finished in a race

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Nominal Variable

Values that are categories
Names, not numbers
Also called categorical variable

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Levels of Measurement

Types of underlying measures and numerical information provided by a measure, such as equal-interval, rank-order, and nominal

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Discrete Variable

Has specific values and that cannot have values between these specific values (whole numbers)

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Continuous Variable

Infinite number of values between any two values

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Frequency Tables

Ordered listing of number of individuals having each of the different values for a particular variable

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Grouped Frequency Tables

Frequency table in which the number of individuals (frequency) is given for each interval of values

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Intervals

Range of values in a grouped frequency tables that are grouped together

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Histograms

Bar-like graph of a frequency distribution in which the values are plotted along horizontal axis and bar height is the frequency

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Frequency Distribution

Pattern of frequencies over the various values

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Unimodal Distribution

FD with 1 value clearly having a larger frequency than any other

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Bimodal Distribution

FD with 2 approximately equal frequencies, clearly larger than any of the others

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Multimodal Distribution

FD with 2+ high frequencies separated by a lower frequency

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Rectangular Distribution

FD where all values have approximately the same frequency

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Symmetrical Distribution

Pattern of frequency on the left and right side are mirror images of each other

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Skewed Distribution

Scores pile up on one side of the middle and are spread out on the other side

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Skewed to the Left

Also called negatively skewed
Tail to the left

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Skewed to the Right

Also called positively skewed
Tail to the right

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Floor Effect

Many scores pile up at the low end of a distribution because it is not possible to have any lower

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Ceiling Effect

Many scores pile up at the high end because it is not possible to have a higher score

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Normal Curve

Specific, mathematically defined , bell-shaped frequency distribution that is symmetrical and unimodal

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Kurtosis

Extent to which a FD deviates from a normal curve in terms of whether its curve in the middle is more peaked or flat than the normal curve

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Controversy

Misleading graphs
Failure to use equal interval sides
Exaggeration of proportions