Data analysis: Explore

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Data analysis Explore
GAP Toolkit 5
Training in basic drug abuse data
management and analysis
Training session 9
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Objectives

• To define a standard set of descriptive
  statistics used to analyse continuous variables
• To examine the Explore facility in SPSS
• To introduce the analysis of a continuous
  variable according to values of a categorical
  variable, an example of bivariate analysis
• To introduce further SPSS Help options
• To reinforce the use of SPSS syntax

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SPSS Descriptive Statistics

• Analyse/Descriptive Statistics/Frequencies
• Analyse/Descriptive Statistics/Explore
• Analyse/Descriptive Statistics/Descriptives

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Exercise continuous variable

• Generate a set of standard summary statistics for
  the continuous variable Age

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Explore Age
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Explore Descriptive Statistics
Descriptives
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Exercise Help

• Whats This?
• Results Coach
• Case Studies

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Measures of central tendency

• Most commonly
• Mode
• Median
• Mean
• 5 per cent trimmed mean

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The mode

• The mode is the most frequently occurring value
  in a dataset
• Suitable for nominal data and above
• Example
• The mode of the first most frequently used drug
  is Alcohol, with 717 cases, approximately 46 per
  cent of valid responses

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Bimodal

• Describes a distribution
• Two categories have a large number of cases
• Example
• The distribution of Employment is bimodal,
  employment and unemployment having a similar
  number of cases and more cases than the other
  categories

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The median

• The middle value when the data are ordered from
  low to high is the median
• Half the data values lie below the median and
  half above
• The data have to be ordered so the median is not
  suitable for nominal data, but is suitable for
  ordinal levels of measurement and above

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Example median

• Seizures of opium in Germany, 1994-1998
• (Kilograms)
• Source United Nations (2000). World Drug Report
  2000 (United Nations publication, Sales No.
  GV.E.00.0.10).

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• Sort the seizure data in ascending order
• The middle value is the median the median annual
  seizures of opium for Germany between 1994 and
  1998 was 42 kilograms

Ranked 1 2
3 4
5
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The mean

• Add the values in the data set and divide by the
  number of values
• The mean is only truly applicable to interval and
  ratio data, as it involves adding the variables
• It is sometimes applied to ordinal data or
  ordinal scales constructed from a number of
  Likert scales, but this requires the assumption
  that the difference between the values in the
  scale is the same, e.g. between 1 and 2 is the
  same as between 5 and 6

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Example mean

• Seizures of opium in Germany, 1994-1998
• Sample size 5
• 36 15 45 42 286 424
• 424/5 84.8

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The 5 per cent trimmed mean

• The 5 per cent trimmed mean is the mean
  calculated on the data set with the top 5 per
  cent and bottom 5 per cent of values removed
• An estimator that is more resistant to outliers
  than the mean

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95 per cent confidence interval for the mean

• An indication of the expected error (precision)
  when estimating the population mean with the
  sample mean
• In repeated sampling, the equation used to
  calculate the confidence interval around the
  sample mean will contain the population mean 95
  times out of 100

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Measures of dispersion

• The range
• The inter-quartile range
• The variance
• The standard deviation

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The range

• A measure of the spread of the data
• Range maximum minimum

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Quartiles

• 1st quartile 25 per cent of the values lie below
  the value of the 1st quartile and 75 per cent
  above
• 2nd quartile the median 50 per cent of values
  below and 50 per cent of values above
• 3rd quartile 75 per cent of values below and
  25 per cent of the values above

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Inter-quartile range

• IQR 3rd Quartile 1st Quartile
• The inter-quartile range measures the spread or
  range of the mid 50 per cent of the data
• Ordinal level of measurement or above

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Variance

• The average squared difference from the mean
• Measured in units squared
• Requires interval or ratio levels of measurement

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Standard deviation

• The square root of the variance
• Returns the units to those of the original
  variable

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Example standard deviation and variance
Seizures of opium in Germany, 1994-1998
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Distribution or shape of the data

• The normal distribution
• Skewness
• Positive or right-hand skewed
• Negative or left-hand skewed
• Kurtosis
• Platykurtic
• Mesokurtic
• Leptokurtic

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The normal distribution

• Symmetrical data the mean, the median and the
  mode coincide

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Right-hand skew ()

• Right-hand skew the extreme large values drag
  the mean towards them

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Left-hand skew (-)

• Left-hand skew the extreme small values drag the
  mean towards them

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Bivariate analysis

• Continuous Dependent Variable
• Categorical Independent Variable

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Explore
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Explore Options button
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Explore Plots button
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Explore Statistics button
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Descriptives
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Male Female
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Boxplot of Age vs Gender
Outlier
Median
Inter-quartile range
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Syntax Explore

• EXAMINE
• VARIABLESage BY gender /IDid
• /PLOT BOXPLOT HISTOGRAM
• /COMPARE GROUP
• /STATISTICS DESCRIPTIVES
• /CINTERVAL 95
• /MISSING LISTWISE
• /NOTOTAL.

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Summary

• Measures of central tendency
• Measures of variation
• Quantiles
• Measures of shape

• Bivariate analysis for a categorical independent
  variable and continuous dependent variable
• Histograms
• Boxplots