Understanding Statistical Relationships

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Understanding Statistical Relationships

• ...looking at distributions, sample statistics
  and statistical tests

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The Histogram(frequency distribution of scale
variables)
mean
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Measures of Central Tendency

• Mode the value most frequently assigned
• can be more than one in a distribution
• unstable, but useful with qualitative data
• Median the middle value
• effected by position, not value, of each score
• more stable than mode
• Mean used with interval or scale data
• effected by both position and value of each score
• most stable measure

In a normal distribution mean median mode
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Bimodal Distribution
Mode 1
Mode 2
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Kurtosis
leptokurtic (more homogeneous)
normal distribution
platykurtic (more heterogeneous)
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Positive Skew(skewed to the right)
normal distribution
Mean gt Median
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Negative Skew(skewed to the left)
normal distribution
Mean lt Median
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Measures of Variability

• Range difference between the highest and lowest
  scores
• used with mode or median
• neither precise, nor stable
• Standard deviation the amount that all scores
  differ from the mean
• Variance square of standard deviation
• with an N gt25
• if randomly selected

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Normal Distribution(smooth, symmetrical)
68
95
-1 sd
2 sd
-2 sd
1 sd
3 sd
-3 sd
z distribution mean 0 sd 1
99
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Hypothesis Testing (t-test)
p value (area under curve)
mean (x2)
p value the probability that the mean of the
sample distribution (x2) belongs in the first
sample distribution rather than in a second, and
different, distribution
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The Hypothesis

• H1 (alternative hypothesis) the mean of the
  second population sample is greater than (or less
  than) the mean of the first population sample (x2
  gt x1 x2 lt x1)
• H0 (null hypothesis) the mean of the second
  population is not significantly different than
  the mean of the first population sample

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Alpha, the Critical p Value

• .05 (95 confidence level to reject the null
  hypothesis and accept the alternative hypothesis)
• .01 (99 confidence level to reject the null
  hypothesis and accept the alternative hypothesis)

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Choosing the Correct Statistical Test