Data Transformation Data conversion Changing the original form of the data to a new format More appropriate data analysis New variables

Data Transformation Summative Score = VAR1 + VAR2 + VAR 3

Descriptive Analysis The transformation of raw data into a form that will make them easy to understand and interpret; rearranging, ordering, and manipulating data to generate descriptive information

Tabulation Tabulation - Orderly arrangement of data in a table or other summary format Frequency table Percentages

Frequency Table The arrangement of statistical data in a row-and-column format that exhibits the count of responses or observations for each category assigned to a variable

Measure of CentralMeasure of Type of ScaleTendencyDispersion NominalModeNone OrdinalMedianPercentile Interval or ratioMeanStandard deviation Central Tendency

Base The number of respondents or observations (in a row or column) used as a basis for computing percentages

Index Numbers Score or observation recalibrated to indicate how it relates to a base number CPI - Consumer Price Index

Measures of Central Tendency Mean - arithmetic average –µ, Population;, sample Median - midpoint of the distribution Mode - the value that occurs most often

Population Mean

Sample Mean

Measures of Dispersion or Spread Range Mean absolute deviation Variance Standard deviation

The Range as a Measure of Spread The range is the distance between the smallest and the largest value in the set. Range = largest value – smallest value

Deviation Scores The differences between each observation value and the mean:

Low Dispersion Value on Variable Frequency Low Dispersion Verses High Dispersion

Frequency High dispersion Value on Variable Low Dispersion Verses High Dispersion

Average Deviation

Mean Squared Deviation

The Variance

Variance

The variance is given in squared units The standard deviation is the square root of variance:

Sample Standard Deviation

The Normal Distribution Normal curve Bell shaped Almost all of its values are within plus or minus 3 standard deviations I.Q. is an example

2.14% 13.59% 34.13% 13.59% 2.14% Normal Distribution

Normal Curve: IQ Example

Standardized Normal Distribution Symetrical about its mean Mean identifies highest point Infinite number of cases - a continuous distribution Area under curve has a probability density = 1.0 Mean of zero, standard deviation of 1

Standard Normal Curve The curve is bell-shaped or symmetrical About 68% of the observations will fall within 1 standard deviation of the mean About 95% of the observations will fall within approximately 2 (1.96) standard deviations of the mean Almost all of the observations will fall within 3 standard deviations of the mean

z A Standardized Normal Curve

The Standardized Normal is the Distribution of Z –z+z

Standardized Scores

Standardized Values Used to compare an individual value to the population mean in units of the standard deviation

Linear Transformation of Any Normal Variable into a Standardized Normal Variable Sometimes the scale is stretched Sometimes the scale is shrunk    X