Correlational Research

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Correlational Research
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Correlational Research

• The purpose of correlational research is to
  discover relationships between two or more
  variables.
• Relationship means that an individuals status on
  one variable tends to reflect his or her status
  on the other.

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Correlational Research

• Helps us understand related events, conditions,
  and behaviors.
• Is there a relationship between educational
  levels of farmers and crop yields?
• To make predictions of how one variable might
  predict another
• Can high school grades be used to predict college
  grades?

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Correlational Research

• To examine the possible existence of causation
• Does physical exercise cause people to lose
  weight?

CAUTION In correlational research you CAN NOT
absolutely say once variable causes something to
happen. This can only be done through
experimental research. You can say one variable
might cause something else to happen.
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Where does the data come from for correlational
research?

• Surveys
• Scores on various tests or rating scales
• Demographic information
• Judges or expert ratings

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Correlational Research Process

• Variables to be study are identified
• Questions and/or hypotheses are stated
• A sample is selected (a minimum of 30 is needed)
• Data are collected
• Correlations are calculated
• Results are reported

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Terminology

• Predictor variable the variable(s) that are
  believed to predict the outcome.
• Could be called an independent variable

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Terminology

• Criterion variable the variable to be
  predicted, the outcome
• Could be called the dependent variable

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Terminology

• Is level of education (predictor variable)
  related to family income (criterion variable)?
• Do people who eat more eggs (predictor variable)
  have higher cholesterol levels (criterion
  variable)?

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Which correlation to use?
Phi correlation
Pearson Product Moment
Spearman rho
Biserial Correlation
Kendall tau
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Pearson Product-Moment Correlation

• Used when both the criterion and predictor
  variable contain continuous interval data such as
  test scores, years of experience, money, etc.

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Examples of when to use the Pearson Correlation!
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How to Remember when to use a Pearson Correlation!

• A purse contains both bills and coins. Both
  bills and coins are interval types of data. So
  when the two variables being correlated are
  interval data (like coins and bills) use the
  Purse-un Correlation.

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Point Biserial Correlation

• When the predictor variable is a natural (real)
  dichotomy (two categories) and the criterion
  variable is interval or continuous, the point
  biserial correlation is used.

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Examples of when to use the Point Biserial
Correlation!
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How to Remember when to use a Point Biserial
Correlation!

• You have two bowls of cereal (remember bi means
  two such as in bicycle). One bowl is a china
  bowl, the other is not (this is a real
  dichotomy). Is there a relationship between the
  type of bowl and how many pieces of cereal you
  can put in the bowl? Since this is a rather
  stupid idea, what is the POINT? Thus Point
  Bi-Cereal.

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Biserial Correlation

• When the predictor variable is an artificial
  dichotomy (two categories) and the criterion
  variable is interval or continuous , the biserial
  correlation is used.

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Examples of when to use the Biserial Correlation!
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How to Remember when to use a Biserial
Correlation!

• Think about a two people, a male who dresses like
  a male and a male who likes to dress like a
  female. One male is an artificial female. Some
  people might call the male bisexual (which rhymes
  with biserial.) You are going to see if there is
  a relationship between sex role portrayal and
  self esteem scores.

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Phi Correlation

• When the both the predictor and criterion
  variables are natural dichotomies (two
  categories), the phi correlation is used.
• If the dichotomies are artificial, the
  tetrachoric correlation is used. This is rarely
  the case in educational research

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Examples of when to use the Phi Correlation!
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How to Remember when to use a Phi Correlation!
Variable 1

• When data used in Phi Correlations are visually
  depicted, it looks somewhat like a tic tac toe
  game. Phi is a 3 letter word just like tic tac
  and toe are.

Variable 2
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Spearman rho and Kendall tau

• When the both the predictor and criterion
  variables are rankings, use either the Spearman
  rho or Kendall tau correlation.
• More than 20 cases Spearman rho
• Less than 20 cases Kendall tau

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Examples of when to use the Spearman rho or
Kendall tau Correlation!
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How to Remember when to use Spearman rho

• Spearman rho reminds me of Spearmint gum because
  it sounds similar. Spearmint gum is made from a
  mint plant. To me a mint plant smells somewhat
  rank. And they sell Spearmint gum in big packages
  of 20 or more sticks.

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How to Remember when to use Kendall tau

• Kendall tau reminds me of a bull (tau is the
  first part of taurus, which is the zodiac sign of
  the bull). Some bulls are really rank. When you
  ride a bull in a rodeo you have to stay on for 8
  seconds, which is a small amount of time.

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Correlation Table
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Other Correlations

• You can perform multiple correlations using such
  approaches as partial correlation, multiple
  regression, discriminant analysis, and factor
  analysis.
• These are outside the scope of this class.

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Correlation Principles to Remember

• For each individual in the research, there must
  be at least two measures, or it will be
  impossible to calculate a correlation.

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Correlation Principles to Remember

• A correlation may be statistically significant
  (it didnt happen by chance) but be weak or low
  which means it is nothing to get excited about.It
  has no practical significance.

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More Principles to Remember

• A correlation is reported as r such as r.36.

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More Principles to Remember

• The statistical probability is reported as p.
• Some researchers report the probability of the
  correlation happening by chance was p.05 (more
  than 5 out of 100) or p
  100) we hope for the later as researchers
• Other researchers report the actual probability
  p.03
• The first approach was used before the age of
  computers
• Either approach is acceptable.

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More Principles to Remember

• In reporting correlations in research reports you
  report both the r value and the p.

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Correlations

• Correlations can range from 1.00 to 1.00
• A 1.00 is a perfect positive correlation
• As one variable increases, so does the other
• A -1.00 is a perfect negative correlation
• As one variable increases, the other variable
  decreases
• A .00 correlation indicates no correlation
• There is no relationship between one variable and
  another

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Interpretation of the Strength of Correlations

• .00 - .20 Very Weak
• .21 - .40 Weak
• .41 - .60 Moderate
• .61 - .80 Strong
• .81 1.00 - Very Strong

Different statisticians may have similar but
slightly different scales.
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Correlations

• Scatter plots are often used to depict
  correlations

This chart shows a strong positive correlation
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Correlations

• Scatter plots are often used to depict
  correlations

This chart shows a strong negative correlation
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Correlations

• Scatter plots are often used to depict
  correlations

This chart shows virtually no correlation
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How can I calculate correlations?

• Excel has a statistical function. It calculates
  Pearson Product Moment correlations.
• SPSS (a statistical software program for personal
  computers used by graduate students) calculates
  correlations.