PSYC 275 Introduction to Research Methods

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PSYC 275 Introduction to Research Methods

• SCC Chapter 13
• Normal Distributions

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Smoothed Curves

• Smoothed curves a replacement for histograms
• Advantages
• Better at showing the overall shape of a data
  distribution than a histogram
• No ragged edges to distract

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Remember to

• 1. Always plot your data.
• 2. Look for overall pattern (shape, center,
  spread) and deviations from the pattern
• 3. Choose either the five-number summary (min,
  Q1,median, Q3, max) or mean and standard
  deviation to describe the center and spread of
  your data
• Sometimes the overall pattern can be described by
  a smooth curve.

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Normal Curve

• A specific kind of smooth curve.
• Normal curves have special properties
• Use with very symmetric sampling data
• only some kinds of data fit normal curves.

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Density Curves

• Density curves
• Smooth curves scaled so that they display
  proportions rather than counts
• Entire area under the curve 1

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Density Curves - proportion

• An idealized picture of the distribution
• Curve is exactly symmetric
• Actual data are only approximately symmetric
• Useful for describing large numbers of
  observations
• We can use density curves to find proportions of
  scores rather than counts.
• The proportion of scores is exactly equal to a
  correctly identified area under the curve.

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Density Curve Center and Spread

• The median has an equal number of scores on
  either side.
• (median equal area point)
• The mean is the balance point for the curve if it
  were solid.
• (mean arithmetic average)

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Diagram Symmetric Curve
Mean and Median same for a symmetric density curve
Mean balance point
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Mean Balance point
Mean balance point
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Normal Distributions

• Family of normal curves
• The mean and standard deviation completely
  specify the normal density curve
• The standard deviation determines the shape of
  the distribution. (inflection points are at

1 s
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Normal Curves

• Symmetric
• Single peaked
• Bell shaped
• Tails fall off quickly
• Mean and median lie together at the peak of the
  center of the curve

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Normal Curves

• Can locate the standard deviation of the
  distribution by eye on the curve
• Point change of curvature takes place one
  standard deviation on either side of the mean
• Smaller standard deviation less spread out and
  more sharply peaked.

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Normal Density Curves

• Symmetric, bell shaped curves
• A specific normal curve is completely described
  by giving its mean and its standard deviation
• The mean determines the center of the
  distribution. It is located at the center of
  symmetry if the curve.
• Standard deviation is distance from the mean to
  the change of curvature points on either side of
  the curve.

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Normal Distribution a good descripter

• The normal distribution is a good descriptor of
  many real data distributions in the social and
  behavioral sciences.

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68-95-99.7 Rule

• This is a set of rules of thumb, that can be, and
  often are, applied to scores from normal
  distributions.
• 68 of the observations are within one standard
  deviation of the mean.
• 95 of the observations are within two standard
  deviations of the mean.
• 99.7 of the observations are within three
  standard deviations of the mean.

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Diagram 68-95-99.7 Rule
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Standard Scores

• Standard scores restate scores in terms of how
  many standard deviations above or below the mean
  a particular score is.
• Large standard scores represent scores that are
  farther away from the mean.
• Small standard scores represent scores that are
  closer to the mean.

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Standard Scores How to

• Calculate using
• Standard score __________________

(observation mean)
standard deviation
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Standard score example

• Observation value 90
• Mean value 70
• Standard deviation value 10

90 - 70
_________
20/10
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Standard score
2
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End Chapter 13