Chapter 2: Statistical tools in evaluation Part I

1
Chapter 2 Statistical tools in evaluation (Part
I)

• after you go through the trouble of collecting
  data, what are you going to do with it?

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Statistical Tools

• The goal of testing is to collect data
  (measurement), then use that information for some
  reason (evaluation)
• There are several uses for statistics
• Summarizing data
• mean scores, how many accumulated think
  baseball!
• Comparing variables
• treatment group is different than a control group
• How 2 variables are related to each other
  (correlation)
• Many more

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Types of scores

• When deciding how to perform statistical analyses
  on variables, you have to understand the
  "structure" of the data
• ____________ scores scores that can have an
  infinite number of values because they can be
  measured with varying degrees of accuracy
• Can run a 100-meter dash to the nearest 100th of
  a second (10.49 seconds for women)
• ____________ scores scores that have a specific
  number of values and cannot be measured with
  varying degree of accuracy
• When shooting 5 free-throws, you cannot get 2.25
  in the hoop

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Further classification of scores

• N________ scores simplest types of scores
• Scores that cannot be rank ordered and are
  mutually exclusive e.g. gender, numbers on
  jerseys
• Scores do not imply better or worse, etc.
• O________ scores do not have a common unit of
  measurement between each score, but there is an
  order in the scores
• Wine preference, hunger, dietary restraint
• I________ scores common unit of measurement, but
  do not have a true zero
• 0 Celsius does not imply no temperature (darn
  cold!)
• R_______ scores highest level of classification
  common unit of measurement and a true zero
• Possible to long-jump 0 feet (did not move
  forward)

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Summarizing Test Scores

• After you collect data, you are generally
  interested in looking at or summarizing the
  results in some way
• How does an individual result compare to others?
• What do the scores for the group look like?
• Graphic display of the data
• Frequency distribution
• Measures of central tendency (what is the
  middle?)
• Mean, or average score
• Measures of variability (how "spread-out" are the
  scores?)
• Range, standard deviation, variance

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Organizing and graphing test scores

• Generating a frequency distribution is the most
  common way of looking at data

• Lowest score ___
• Highest score ___
• Most frequently occurring ____

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Drawing a frequency distribution

• Figure out the number of "groupings" you want to
  have
• The text uses 15 groups, so ___ -___/15 ____
• So the Interval Size is __
• Generate the necessary groupings
• Plot the groupings by the number of tallies
  observed

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Frequency Polygon
9
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The Histogram
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Shape of the curves

• Visual observations can give you a picture of
  how the scores look

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Descriptive Values

• After data has been collected, what is the best
  way to condense, or summarize the results?
• Measures of central tendency
• Where are most of the scores condensed?
• Where is the "center" of the data?
• Mean, median, mode
• Measures of variability
• Describes the spread or heterogeneity of the data
• Are the scores of a group similar, or very
  different?
• Range, standard deviation, and variance

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Measures of central tendency

• ___________
• Most frequently occurring scores can have more
  than one mode
• Not used very frequently
• used with nominal data
• ___________
• Middle score
• Half of the scores fall above, half below
• Not necessarily the same as the Mean
• __________
• Sum of the scores divided by the number of scores

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Mode

• Looking for the most commonly occurring score
  here
• Easiest to re-order the data
• In this case, the mode is ____
• What if 3 more people scored 56?
• Then there would be 2 modes (56 and 68)

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Median

• Order the scores from low to high
• Median (n 1)/2 where n the of scores
• In this case (__ __)/2 ____, or between the
  _____th and _____th scores (____)
• The text has a more complex calculation, but
  don't worry about being able to reproduce it

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Mean

• Generally the most appropriate, esp. with
  interval and ratio data
• Mean ( ) ?X/ n
• ?X sum of all scores
• ______in this case
• (______/_____)
• ________
• So, the mean is ____ in this case

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Overall

• When a series of scores fit a normal curve, then
  mode, median and mean are the same
• When scores are highly skewed, or lack a common
  interval between scores (________ data), then
  median is best option
• When data are interval or ratio data (as with
  most scientific results), the mean is generally
  the most common

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Measures of variability

• How are the scores from participants different
  from each other?
• Mean and median of groups 1 and 2 are _____
• Does this imply that the groups have equal
  ability?
• Clearly group 1 are much more "spread out" than
  group 2
• Need to report other statistics to indicate how
  different the groups really are

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Range

• Difference between the highest and lowest score
• Used when the measure of C.T. is the mode or
  median
• Group 1 (____ ____) __
• Group 2 (____ ____) __
• For the long jump scores
• (____ ___) ___
• Difficulty with using range is that only 1 score
  can have a large effect on the number

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Standard Deviation

• Measure of variability used with the mean
• Indicates the amount that scores deviate from the
  mean
• 1 standard deviation (s) 68 of all of the
  scores clustered around the mean (34 above and
  below)
• 2 s 95
• 3 s 99

• The higher the value for s, the greater the
  variability in scores

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Standard Deviation

• A number of ways to calculate s, but we will use
• s
• s
• 2.2

• s for group 2 is _________________

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Variance

• In simple terms, variance is s2
• Just a square of standard deviation
• Not usually a descriptive measure like range or
  standard deviation
• Used in more complex calculations, like multiple
  regressions

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Coefficient of variation (CV)

• CV indicates how variable scores are, relative to
  the mean (as a percentage)
• E.g. Group 1 s 2.2, mean 5.0

• This means that ______ of the scores varied by
  44!
• Scores within this group were very different from
  each other

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Practice Problems

• Draw frequency polygon and histogram
• Work with 5 groupings
• Calculate mode, median, mean
• Calculate range, standard deviation, and variance
• Calculate coefficient of variation
• Want to be able to plot/ calculate these by hand
  and show your work!