Statistics 95% formulafree

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Statistics (95 formula-free)
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Outline

• Descriptives Review
• Where is the middle?
• What is the shape?
• How spread out is it?
• Differences between two or more categories
• chi square
• Relatedness of variables
• correlations
• Difference between two or more means
• T-tests, ANOVA, effect size (ES)

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First step Look at the data
Test scores
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Central Tendency Where is the middle?
Median Divides equally
Mean Balancing point
Income
Mode Most frequent score
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1
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Standard Deviation

• Measure of variability
• Measures the extent to which scores in a
  distribution deviate from the mean
• Always report standard deviation when you report
  mean score or we will know nothing about your
  distribution!
• Example Find the means
• Scores 50, 50, 50, 50, 50 ------ Mean 50
• Scores 3, 75, 100, 12, 60 ------ Mean 50
• Can I draw the same conclusions about how well
  the intervention worked for students by looking
  only at these means?

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Life Expectancy with Disease
2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 months until dead
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Standard Deviation
2 x Standard Deviation
1/3
1/3
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• Find the mean and standard deviation of the two
  classes

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Percent and Chi-square

• Percentages
• Always report raw data with percentages
• Example
• 82 didnt follow the guidelines when
  administering state test (n 4)
• 82 didnt follow guidelines when administering
  state test (n 12,392)
• Chi Square
• Nominal data (counts)
• Ordinal data (fail, pass, etc.)

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Chi Square Categorical Data
p is the probability the difference was due to
chance alone
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T-test and correlation

• T-tests
• Were the differences in means simply due to
  chance?
• Correlations
• Was the correlation difference from 0 really due
  to chance?

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1
group mean

group median
Experimental
Control
-4
-3
-2
-1
0
1
2
3
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Effect size 0.5
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Effect size

• The difference between the two means, expressed
  as a proportion of the standard deviation
• ES (Me Mc) / SD
• Assumptions
• Standard deviations are similar
• Distribution is normal
• Reliable measures are used

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T-tests

• Test for statistical significance of difference
  between two means
• Assumptions
• Random samples (robust if n gt 30)
• From Normal distribution
• Equal std deviations (robust if n1 ? n2)
• Independence

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• Run a t-test to determine significance of the
  difference between the two classes

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ANOVA

• A t-test looked at the difference between two
  means, but an ANOVA can look at multiple means (2
  or more) simultaneously.
• It tells us whether there is a significant
  difference between the means, but not where .
• e.g., is there a difference based on ethnicity (6
  levels)? (1-way ANOVA)
• We can also look at multiple IVs simultaneously
  (e.g. ethnicity and gender) (2-way ANOVA) with
  possible interaction effects.

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• Run descriptives and a 1-way ANOVA to determine
  significance of differences in means

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A word about significance

• An alpha of .05 is completely arbitrary but
  seems reasonable.