Presenting Data

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Presenting Data

• Descriptive Statistics

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Nominal Level

• No order, just a name
• Can report
• Mode
• Bar Graph
• Pie Chart

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Ordinal Level

• Rank order only
• Can Report
• Mode
• Median
• Percentiles
• Histograms and Pie Charts

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Interval/Ratio Level

• Equidistant
• Can Report
• Mode, Median, Mean
• Standard Deviation
• Percentiles
• Frequency curves, Histograms

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Univariate Data

• Good to start at the univariate level
• Univariate one variable at a time
• Investigate the responses
• Assess usability for the rest of the analysis

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Frequency Table

• Shows how often each response was given by the
  respondents
• Most useful with nominal or ordinal
• Interval/ratio has too many categories
• In Minitab, Select StatgtTablesgtTally

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Charts and Graphs

• Use a bar graph or pie chart if the variable has
  a limited number of discrete values
• Nominal or ordinal measures
• Histograms and frequency curves are best for
  interval/ratio measures
• In Minitab, Select Graph gt (and then type)

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Normal Curve

• The normal curve is critical to assessing
  normality which is an underlying assumption in
  inferential statistical procedures
• And in reporting of results
• Kurtosis related to the bell-shape
• Skewness symmetry of the curve
• If more scores are bunched together on the left
  side, positive skew (right)
• If most scores are bunched together on the right
  side, negative skew

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Normal Curve

• To get a statistical summary, including an
  imposed normal curve in Minitab
• Select Stat gt Basic Statistics gt Display
  Descriptive Statistics gt Graph gt Graphical Summary

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Measures of Central Tendency

• Mode most frequently selected
• Bimodal two modes
• If more than two modes, either multiple modes or
  no mode
• Median halfway point
• Not always an actual response
• Mean arithmetic mean

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Percentiles

• The median is the 50 percentile
• A percentile tells you the percentage of
  responses that fall above and below a particular
  point
• Interquartile range 75th percentile 25th
  percentile
• Not affected by outliers as the range is

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Z-scores

• Standard deviations provide an estimate of
  variability
• If scores follow a normal curve, you can
  comparing any two scores by standardizing them
• Translate scores into z-scores
• (Value mean) / standard deviation

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Statistical Hypotheses

• Statistical Hypotheses are statements about
  population parameters.
• Hypotheses are not necessarily true.

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In statistics, we test one hypothesis against
another

• The hypothesis that we want to prove is called
  the alternative hypothesis, Ha.
• Another hypothesis is formed which contradicts
  Ha.
• This hypothesis is called the null hypothesis,
  Ho. Ho contains an equality statement.

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Errors
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P-value

• The choice of is subjective.
•  
• The smaller is, the smaller the critical
  region. Thus, the harder it is to Reject Ho.
•  
• The p-value of a hypothesis test is the smallest
  value of such that Ho would have been
  rejected.

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Interval Estimates

• Statisticians prefer interval estimates.
• Something depends on amount of variability in
  data and how certain we want to be that we are
  correct.
•  
• The degree of certainty that we are correct is
  known as the level of confidence.
• Common levels are 90, 95, and 99.

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Statistical Significance

• Statistically significant if the probability of
  obtaining a statistic by chance is less than the
  set alpha level (usually 5)

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P-value

• The probability, computed assuming that Ho is
  true, that the test statistic would take a value
  as extreme or more extreme than that actually
  observed is called the p-value of the test.
• The smaller the p-value, the stronger the
  evidence against Ho provided by the data.
• If the p-value is as small or smaller than alpha,
  we say that the data are statistically
  significant at level alpha.

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Power

• The probability that a fixed level alpha
  significance test will reject Ho when a
  particular alternative value of the parameter is
  true is called the power of the test to detect
  that alternative.
• One way to increase power is to increase sample
  size.

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Use and Abuse

• P-values are more informative than the results of
  a fixed level alpha test.
• Beware of placing too much weight on traditional
  values of alpha.
• Very small effects can be highly significant,
  especially when a test is based on a large
  sample.
• Lack of significance does not imply that Ho is
  true, especially when the test has low power.
• Significance tests are not always valid.