Statistics Notations and Scales, Slides of Psychology

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Simple Notations

• Variables = X or Y
• Number used in a sample or population = N
• X subscript used to designate a particular score or number - X 1 , X 2 , etc.

SUMMATION

• Captial Greek letter Sigma used to designate a summation of scores - Simply add the scores - Two possible variations

∑^ X

X

2

∑ (∑^ X )

NOMINAL

• Classification of objects and placing them into specific categories (“Naming them”)
• Tends to be more of a qualitative measure rather than a quantitative
• There is no way to measure between the categories
• Nominal Scale – Religious affiliation
  • Buddhist, Christian, Jewish, etc.

ORDINAL

• Shows the magnitude of whether a particular variable is present - Less than, Same as, more than - Rank ordering
• Example – College Basketball rankings
  • 1. Duke, 2. Kansas University, 3. Wake Forest, etc.

RATIO

• Contains all the properties of interval scales but does contain an absolute zero point - Ratios allow for multiplication of factors on the scale - Scores may be twice or three times as high or lower than other scores

VARIABLES

• Continuous Variables
  • Variable that may obtain a variety of measures, infinite - Weight, height, time
• Discrete Variables
  • Variables has values that are fixed with no intermediate measures - Children, students in a class, etc.

MEASURES OF CENTRAL

TENDENCY

• Arithmetic Mean
  • The Average score
  • Sum of the scores divided by the number of scores
    • Sample mean
    • Population mean
    • Computations are the same for a sample or population

X

μ

MEDIAN

• Score below which 50% of the scores fall
• For raw ungrouped scores the median is:
  • Center score if the scores are an odd number
  • Average of the two center scores center if the scores are an even number

STANDARD DEVIATION

• Deviation score – shows the distance between the mean and a particular score
• Sum of the deviations from the mean is always equal to zero - Sample deviation score - Population deviation score

X X

X μ

−

−

STANDARD DEVIATION

• Symbol for sample
• Symbol for population

s

σ

STANDARD DEVIATION FOR

POPULATION

• Deviation Method (for demonstration only)

σ =

SS

N

( X^ − μ)

2 ∑

N

STANDARD DEVIATION FOR SAMPLE

SCORES

• Deviation Method (For Demonstration Only) - Same as for population scores but N is decreased by one

( )

2

1 1

SS^ X s N N

− μ = = − −

∑