Describing Data and Interpreting Results

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Describing Data andInterpreting Results
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Doing Exploratory Data Analysis

• Use EXPLORATORY DATA ANALYSIS (EDA) to search for
  patterns in your data.
• Before conducting any inferential statistic, use
  EDA to ensure that your data meet the
  requirements and assumptions of the test you are
  planning to use (e.g., normally distributed).
• Steps involved in EDA
• 1. Organize and summarize your data on a
  data-coding sheet.
• 2. If desired, organize data for computer entry.
• 3. Graph data (bar graph, histogram, line graph,
  or scatterplot) so that you can visually inspect
  distributions. This will help you choose the
  appropriate statistics.
• 4. Display frequency distributions on a
  histogram, and create a STEMPLOT.
• 5. Examine your graphs for normality or skewness
  in your distributions.

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Measures of Center Characteristics and
Applications

• Mode
• Most frequent score in a distribution
• Simplest measure of center
• Scores other than the most frequent not
  considered
• Limited application and value
• Median
• Central score in an ordered distribution
• More information taken into account than with the
  mode
• Relatively insensitive to outliers
• Used primarily when the mean cannot be used
• Mean
• Average of all scores in a distribution
• Value dependent on each score in a distribution
• Most widely used and informative measure of center

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Measures of Center Applications

• Mode
• Used if data are measured along a nominal scale
• Median
• Used if data are measured along an ordinal or
  nominal scale
• Used if interval data do not meet requirements
  for using the mean
• Mean
• Used if data are measured along an interval or
  ratio scale
• Used if scores are normally distributed

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Measures of Spread Characteristics

• Range
• Subtract the lowest from the highest score in a
  distribution of scores.
• Simplest and least informative measure of spread.
• Scores between extremes are not taken into
  account.
• Very sensitive to extreme scores.
• Semi-Interquartile Range
• Less sensitive than the range to extreme scores.
• Used when you want a simple, rough estimate of
  spread.
• Variance
• Average squared deviation of scores from the
  mean.
• Standard Deviation
• Square root of the variance.
• Most widely used measure of spread.

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Measures of Spread Applications

• Range and standard deviation are sensitive to
  extreme scores. In such cases the
  sem-iinterquartile range is best.
• When your distribution of scores is skewed, the
  standard deviation does not provide a good index
  of spread.
• With a skewed distribution, use the
  semi-interquartile range.

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The Pearson Product-Moment Correlation (r)

• Most widely used measure of correlation.
• Value of r can range from 1 through 0 to -1.
• Magnitude of r tells you the degree of LINEAR
  relationship between variables.
• Sign of r tells you the direction (positive or
  negative) of the relationship between variables.
• Presence of outliers affects the sign and
  magnitude of r.
• Variability of scores within a distribution
  affects the value of r.
• Used when scores are normally distributed.

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Measures of Correlation and Regression

• Pearson Product-Moment Correlation
• Index of linear relationship between two
  continuously measured variables
• Point-Biserial Correlation
• Index of correlation between two variables, one
  of which is measured on a nominal scale and the
  other on at least an interval scale
• Spearman Rank-Order Correlation (rho)
• Index of correlation between two variables
  measured along an ordinal scale
• Phi Coefficient
• Index of correlation between two variables
  measured along a nominal scale
• Linear Regression and Prediction
• Used to find the straight line that best fits the
  data plotted on a scatterplot

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