due on 02/22/2016 - STATISTICS- RESEARCH METHOD - GRAPHIC REQUIRED - central tendency and dispersion measures
allisky
chapter_11_quantitative_measures_handout.pdf
Chapter 11: Quantitative Measures
Percent Proportion Percent: reports number of units as proportion of 100
o Divide category frequency by total and multiply by 100 o Percent = (f/N) x 100
Proportion: divide category frequency by total Proportion = f/N Percent Change: degree of change in the frequency or amount over time
o Percent Change = ((N2 – N1)/ N1) x 100 where N1 is the value of the variable at the earlier time
Ratio Compares the frequency of one variable category to the frequency of another variable category Ratio is reduced to lowest terms
o Example: Public agency has 50 employees, 35 men and 15 women o Ratio of men to women is 35 to 15 or 7 to 3
Rates The number of occurrences of an event divided by the number of possible occurrences of that event over
some period of time Calculation: Rate = (N1)/ N2) (Base Number) Rules for selecting base number:
o Be consistent with rates already in use for given properties o The base number should produce a rate with a whole number between 1 and 4 digits o Base number is usually an exponent of 10 (10
2 , 10
3 , etc)
o Use the same base number when comparing rates for comparison
Incidence, Prevalence Two of the most common rate measures developed by health care professionals Incidence: number of people who get a disease over a specified period of time
o Incidence rate = (# people w/disease/total at risk) o Only includes new cases during period of time
Prevalence: total number of people who have a disease at a given time o Prevalence = (# people w/disease/total at risk) o Includes carry-over from previous
Measures of central tendency Indicate what a typical value or case in the distribution is like Mode: The category or value that occurs most frequently
o For nominal and many ordinal variables, the mode will have a name o For interval and ratio variables, the mode is a number
Median: Value or category of the case that is in the center of the distribution o Values are ordered, median is the middle value or average of middle two values o Data must be ordinal or interval level
Arithmetic mean: Most commonly used measure of central tendency o Balance point or center of the distribution o Requires variables to be measured at interval or ratio level
Geometric mean: Used to average ratios and rates of change o Defined as the n-th root of the product of n values
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x x i
Chapter 11: Quantitative Measures
Guidelines for selecting appropriate measure of central tendency Median and mean require ordinal and interval levels of measurement. Only the mode can be used for nominal data
In a distribution of interval or ratio data, if the distribution is unimodal and symmetric, use the mean: Mean, median and mode will be nearly equal
Skewed distribution – few data values, outliers, not symmetric – use median Income data are skewed – use median Geometric mean: use for ratios and rates of change
Measures of Dispersion or Variation Indicate how the individual values in the distribution vary from one another Measures of dispersion describe the uniformity of the data Maximum variation for ordinal, interval, and ratio variables occurs when all cases are equally divided
between two extreme values Maximum variation for nominal variables occurs when the cases are evenly distributed across all
categories Range: Difference between highest and lowest value in a distribution
o Indicates the range over which the data values are spread Interquartile Range IQR: Range of values between which the middle 50% of the observations lie
o Q1: First Quartile: value below which 25% of cases lie o Q2: Second Quartile: Median o Q3: Third Quartile: value below which 75% of cases lie o IQR = Q3 – Q1 o Useful for comparing variation of two or more distributions
Standard Deviation, Variance: Use all data values in distribution o Standard deviation is a measure of the average distance of the values in a distribution o Variance is the square of the standard deviation
Average Deviation measures how far, on average, the cases deviate from the mean
Median Absolute Deviation calculates the average deviation using the median in place of the mean
Guidelines for selecting appropriate measure of central tendency In a distribution of interval or ratio data, if the distribution is unimodal and symmetric, use the standard
deviation Skewed distribution – few data values, outliers, not symmetric – use IQR
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2
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