Describing Numerical Variables

1
Describing Numerical Variables

• Examining each numerical variable in your analysis

2
Numerical Variables

• Variables measured with meaningful numerical
  values.
• Ratio
• True zero (ex., weight, height, age)
• Interval
• equal interval between values but no true zero
  point (ex., sociological or psychological scales)
• Discrete
• Values can only take whole numbers as values
• Continuous
• Values have no real breaking point
• Have infinite number of possible values

3
Univariate Analyses with Numerical Variables

• Measures of Central Tendency
• Mean the arithmetic average
• Mode the most popular/common value of response
• Median the value at which 50 of the cases lie
  above or below
• Measures of Dispersion
• Range the distance between the highest and
  lowest value in the variable. Include minimum
  and maximum value of variable.
• Variance how much values for a variable vary
  from the mean. Sum of the squared deviations
  from the mean
• Standard Deviation the square root of the
  variance is typically used to evaluate the
  dispersion of cases around the mean.
• Skewness how evenly/symmetrically the cases are
  distributed around the mean.

4
Steps for Conducting a univariate analysis of
numerical variables

• Calculate the range.
• Order all of the cases for your numerical data
  from hi to low values. Take the maximum value
  and subtract from it the minimum value. The
  result is the range.
• Calculate the mean.
• Sum together the values for all cases and then
  divide by the total number of cases (?(xi X)/n)
• Calculate the median
• Ordered cases from high to low. It is the point
  value where half the cases lie above and half
  below it.

5
Steps for Conducting a univariate analysis of
numerical variables

• Calculate the mode.
• Ordered cases from high to low, select the most
  common value.
• Calculate the variance
• For each case, take the value and subtract the
  mean from it. Take this result and square it.
  Take and sum the squared deviations for all cases
  of the variable. Divide the result by the number
  of cases. (?(xi X))2/n)
• Calculate the standard deviation
• The square root of the variance
• Create a histogram
• A graph which plots the frequency for values of
  the variable. The x axis is the value of the
  values for the variable. The y axis is the total
  number of cases.

6
Once completed the steps for univariate analysis

• Examine each variable for skewness,
• case distributions across values
• outliers
• decide if need to recode any variable
• Decide which measure of central tendency best
  describes your variable. Means are not very
  useful for skewed distributions.

7
A created sample dataset
8
Using Example to Calculate Range of Age

• Arrange cases fro hi to lo values.
• Find the minimum value
• 18
• Find the maximum value
• 65
• Subtract the maximum from the minimum.
• 65-18 47

9
Using Example to Calculate Mean Age

• Sum all values for all cases
• 18202130323645526065 379
• Divide by the total number of valid cases
• 379/10 37.9

10
Using Example to Calculate mode and Median of Age

• What is it the mode?
• What is the median?
• 323668/234

11
Using Example to Calculate Variance

• Subtract the mean from the value
• Square the result
• Sum the squared deviation
• 396.01320.41285.61
• 62.4131.3636.150.41
• 198.81488.41734.41
• 2603.94
• Divide the result by the total number of cases
• 2603.94/10260.394

S 16.14
12
Using SPSS Short Assignment

• Follow along the exercise in Assignment 2 of
  Ready, Set, GO Text.
• Use the Frequency procedure
• Get frequencies for all of your categorical
  variables
• Get range, mean, median, mode,standard deviation
  and variance
• Use the Charts command to get histograms for all
  of your variables
• Discuss results for each variable spread,
  skewness, best measure of central tendency,
  frequency distribution
• Turn in by next Tuesday.
• This will be the first part of the results for
  Project 2.