Chapter 6: Part II

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Chapter 6 Part II
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Statistics Basics

• Before we start getting into advanced
  statistical issues, there are some fundamental
  things that need to be understood
• Data have different structures, which affect
  how they can be interpreted
• In the Vaske paper, scores were 1 to 5
• So, what does 3.2 mean?
• Is the distance from 1-2 the same as 4-5?
• In the Muoio paper, scores were 90 min
• 80-90 is the same distance as 60-70 min
• 85.5 min is a meaningful number

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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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Practical Example

• Generating a frequency distribution is the most
  common way of looking at data
• What can you learn from this dataset?
• This is a group of 30 total energy expenditure
  values from doubly labeled water
• 238.9 kcals 1 MJ (mega joule)
• 10 MJ/d 2389.0 kcals/d

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Drawing a frequency distribution

• Figure out the number of "groupings" you want to
  have
• If you have a large range of values you may want
  to group them
• ________/ groups ____
• __________________
• Plot the groupings by the number of tallies
  observed

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________________________
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________________________
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Descriptive Values

• After data has been collected, what is the best
  way to condense, or summarize the results?
• Measures of _____________________
• Where are most of the scores condensed?
• Where is the "center" of the data?
• Mean, median, mode
• Measures of _____________________
• 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
• Easiest to re-order the data
• In this case, the mode is ___
• What if 1 more people had a TEE of _____?

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Median

• Order the scores from low to high
• Median (n 1)/2 where n the of scores

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Mean

• Generally the most appropriate, esp. with
  interval and ratio data
• Mean ( ) ?X/ n
• ?X sum of all scores
• 321 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 (ordinal 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 total energy expenditures from
  participants different from each other?
• Mean and median of groups 1 and 2 are equal
• Does this imply that the groups have equal energy
  expenditures?
• Clearly group 1 are much less "____ _________"
  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 (14 7) 7
• Group 2 (19 5) 14
• Range of 2 is double!
• 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

• s for group 2 is 3.87 (more variable)

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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 2.65, mean 10

• This means that _____ of the scores varied by
  26.5
• Scores within this group were very different from
  each other
• CV for group 2 is 38.7

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Confidence Interval

• Tells you how variable a certain percentage of
  scores are
• In most cases, it is 2 SD (95)

Therefore the 95th confidence interval is 8.43 to
11.57