Statistics as a Tool

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Statistics as a Tool

• A set of tools for collecting, organizing,
  presenting and analyzing numerical facts or
  observations.

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Descriptive Statistics

• Numerical facts or observations that are
  organized describe the frequencies, measures of
  central tendency, and degree of dispersion of
  variables in a sample of a larger population.

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Levels of Measurement

• Reflects type of information measured and helps
  determine what descriptive statistics and which
  statistical test can be used.

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Four Levels of Measurement

• NOIR -- no one is ready
• Nominal lowest level, categories, no rank
• Ordinal second lowest, ranked categories
• Interval next to highest, ranked categories
  with known units
  between rankings
• Ratio highest level, ranked categories
  with known intervals and an absolute
  zero

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Descriptives for nominal and ordinal data

• Frequencies and percentages
• Frequencies absolute number of cases
• Percentages relative number of cases

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Frequencies for a nominal variable
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Descriptives for ordinal data
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Descriptives for interval/ratio (scale) variables

• Measures of central tendency
• Mean -- sum of all cases divided by number of
  cases
• Median case for which half of all other cases
  are above and half of all other cases are below.
• Mode most frequently occurring case

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Descriptives for scale variables

• Measures of dispersion
• Range Value of cases from minimum to maximum
• Standard Deviation number which when added or
  taken away from each case adds up to zero.
• Variance Standard deviation squared

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Descriptives for a ratio variable
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More descriptives for a ratio variable
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Inferential statistics

• Procedures used to make inferences from sample
  data and generalize findings to the population

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Probability

• Statistical significance the probability that
  the difference or the association found in the
  sample would be present in the population.
• Three common probabilities used
• lt.05
• lt.01
• lt.001

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Sampling bias

• The systematic differences between sample in
  study and the larger population of interest.
• The use of inferential statistics allows us to
  calculate the odds that what is found in the
  sample is due to sampling bias.

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Statistical significance (p-levels)

• When p lt .05, the degree of difference or
  association being tested would only occur by
  chance alone five times out of a hundred.
• When p lt .01, the difference or association being
  observed would only occur by chance alone one
  time out of a hundred.
• When p lt .001

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Testing for statistically significant differences

• When you want to see if there is a difference in
  outcome by group membership, or by treatment
  approach.
• SPSS
• Analyze
• Compare means
• Independent t-test

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Is there a significant difference in months of
service and type of outcome?
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Statistically significant differences i.v.
nominal and d.v. interval/ratio

• Analyze
• Univariate (One d.v. multiple predictors)
• Multivariate (Multiple d.v. multiple predictors)
• Repeated measures (time series of dependent
  measures one predictor.

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Statistically significant associations at higher
levels of measurement

• Analyze
• Correlate
• Bi-variate
• Pearsons (two interval/ratio variables)
• Kendalls tau (two ordinal variables)
• Spearmans rho (two ordinal variables)

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Test of Pearson Correlation Coefficient (r)
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Independent t-test to determine statistical
significance
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Differences between groups at lower levels of
measurement

• Analyze
• Descriptives
• Crosstabs
• Identify variable in row and column
• Select statistics
• Two nominal (dichotomized) Chi-Square
• Nominal by ordinal Kendals tau-b
• Nominal by interval Eta

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Difference in LOS by referral
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Crosstabs to determine difference between groups
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Chi-Square tests
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Which test to use when?

• Decision is made by what the question is, the
  level of measurement of the variable and the
  extent to which assumptions of parametric
  statistics are met.
• Question Difference or Association?
• Level of measurement NOIR?
• Sample size and distribution (normal?)

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Tests comparing difference between 2 or more
groups
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Tests demonstrating association between two groups
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Tests demonstrating association between two
groups, controlling for third variable