Statistics

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Statistics

• Evaluating Data in Research

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Percentile Ranks

• Joey finished at the 74th percentile on his EOC
  Algebra test.
• 74th percentile means
• Above 74 of test takers
• Actual 75, there is no 100th percentile

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How do we interpret our data?

• We look for..

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Central Tendencies

• A measure of central tendency is a single score
  that represents a whole set of scores.
• Mean
• Average
• most easily skewed by outliers (extreme numbers)
• Median
• Middle value (midpoint, or 50th percentile)
• (Place in sequential order and find middle
  number)
• Mode
• Most frequently occurring score

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Statistical Reasoning

• A Skewed Distribution

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Calculate the Mean
HISTOGRAM a bar graph depicting a frequency
distribution, where the height of the bars
indicates the frequency of a group of scores.
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Calculate the Median
MEAN
7 6 5 4 3 2 1
1 2 3 4 5 6
7 8 9 10 11 12
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Calculate the Mode
MEDIAN
MEAN
7 6 5 4 3 2 1
1 2 3 4 5 6
7 8 9 10 11 12
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MODE
MEDIAN
MEAN
7 6 5 4 3 2 1
1 2 3 4 5 6
7 8 9 10 11 12
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Measures of variability RANGE difference
between the highest and lowest scores (can be
deceptive due to outliers)
MEAN
7 6 5 4 3 2 1
1 11
1 2 3 4 5 6
7 8 9 10 11 12
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measures of variability STANDARD DEVIATION how
much any given score differs from the average, or
mean score
MEAN
1 sd
-1 sd
7 6 5 4 3 2 1
1 2 3 4 5 6
7 8 9 10 11 12
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The more spread out the scores, the larger the
STANDARD DEVIATION.
MEAN
1 sd
-1 sd
7 6 5 4 3 2 1
1 2 3 4 5 6
7 8 9 10 11 12
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Standard Deviation

• How much does the data deviate from the mean?
• Uses bell curve distribution
• For ex IQ average 100
• 1sd 15 (85 115) 68 of the pop.
• 2sd 30 (70 130 95 of the pop.

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The equation for standard deviation is (You
wont have to know this.)
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Bell CurveA graph of normal distribution

• 1 SD 68 of scores
• 2 SD 95 of scores
• 3 SD 99.7 of scores

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Weighing the odds

• 2 High School punters
• Kicker A
• mean distance 39.8 yds
• Standard deviation 14 yds.
• Kicker B
• mean distance 34.5 yds.
• Standard deviation 4 yds.
• Which player do you play?

• Player B team will know where to run

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Standard Deviation

• Z score
• number that represents how many SDs a particular
  score differs from the mean
• The mean score for the class was 80, with a SD of
  10.
• Joey scored 60 on his test. Whats his z score?
• Betsy scored a 95. what is her z score?

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When is an observed difference reliable?

1. Representative samples are better than biased
   samples.
2. Less-variable observations are more reliable than
   those that are more variable.
3. More cases are better than fewer.

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Statistical Significance

• When is a studys data significant?
• When there is a significant difference between
  the results (data) for the control group and
  experimental group.
• When the data is reliable (consistent)

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Statistical Practice

• 1. What is the mean of the following
  distribution of scores 2, 3, 7, 6, 1, 4, 9, 5,
  8, 2?
• A. 5
• B. 4
• C. 4.7
• D. 3.7
• E. 6
• Answer c

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Statistical Practice

• What is the median of the following distribution
  of scores 1, 3, 7, 7, 2, 8, 4?
• a. 1
• b. 2
• c. 3
• d. 4
• Answer d

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Statistical Practice

• What is the mode of the following distribution
  8, 2, 1, 1, 3, 7, 6, 2, 0, 2?
• a. 1
• b. 2
• c. 3
• d. 7
• Answer b

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One for the record

• Seven members of a Girl Scout troop report the
  following individual earnings from their sale of
  candy 4, 1, 7, 6, 8, 2, and 7. In this
  distribution of individual earnings
• The mean is equal to the mode and equal to the
  median
• The mean is less than the mode and equal to the
  median
• The mean is equal to the mode and greater than
  the median
• The mean is greater than the mode and greater
  than the median
• The mean is less than the mode and less than the
  median
• Mean5, median6, mode7
• Answere

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Ethics in Research

• APA Ethical Guidelines
• Informed Consent
• No harm to patients
• Confidentiality
• Debriefing

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Animal Testing

• Statistics to consider
• 30,000,000 animals used for research each year
  constitutes 1 of animals killed each year to
  eat.
• 200,000 dogs and cats researched annually /
  animal shelters euthanize 50x that each year
• Is it morally acceptable to place the well- being
  of humans above other animals regarding research?