Statistical Reasoning

1
Statistical Reasoning Descriptive Statistics

• Measures of Central Tendency
• Measures of Variability

2
Statistical ReasoningDescribing Data

• Statistical analysis helps us see what the naked
  eye misses.
• Simplest type of graphical analysis is a BAR
  GRAPH
• Problems can be manipulated to show what the
  researcher wants it to show.  

3
Frequency Distribution

• Shows the frequency of given response/behavior
  within the sample.
• Plotted on a frequency histogram it gives a
  pictorial representation of the data.
• While helpful, it doesnt tell the whole story

4
Measures of Central Tendency

• Summarizes the data into an easily readable form.
  Three types
• MODE Most frequently occurring score
•  MEAN Arithmetic average of all the scores.
• MEDIAN The score in the exact middle exactly ½
  of the scores are above and ½ below.

5
Mean v. Median

• Median is often more accurate than the mean
  because of extremes than can skew the scores up
  or down.

6
If you performed below the mean, which group
would you want to be in? If you performed above
the mean, which group would you want to be in?
Median v. MeanEffect of Outliers

• Group 1
• 55
• 58
• 60
• 62
• 63
• 70
• 70
• 70
• 77
• 78
• 80
• 82
• 85
•  
• Mean 70

• Group 2
• 55
• 64
• 68
• 69
• 69
• 70
• 70
• 70
• 71
• 71
• 72
• 76
• 85
• 70
• Mean 70

7
Median v. Mean Effect of Outliers
Mean 46,636
Median 40,000
Mode 30,000
8
Normal Curve
99.72
95.46
.14
.14
68.26
34.1
13.6
2.2
The normal or Bell curve is a statistical model
of how scores within a random sample should occur.
9
Normal Curve

• If scores in a set tend toward very high or very
  low, it will create a skewed curve.
• Skewed to the rightcalled a positive skew (there
  are fewer frequencies at the higher end of the
  scale).
• Skewed to the left called a negative skew (fewer
  frequencies at the lower end of the scale).

10
Measures of Central Tendency do not give us a
complete picture of the data.
11
Measures of Variability

• Variabilitythe way scores are distributed around
  the center (median/mean).
• The easiest way to check variability is by using
  the range.
• Range Highest score lowest score.

12
Range
What is the range of each set of scores? Is this
helpful? Why or why not?
Group 1 55 58 60 62 63 70 70 70 77 78 80 82 85   M
ean 70
Group 2 55 64 68 69 69 70 70 70 71 71 72 76 85 70
Mean 70
13
Problems with Range

• The range represents only the extremes
• To get more accurate data we have to have use a
  statistic that takes in to account ALL of the
  scores positions within the range.

14
Computing Standard Deviation

• Determine the mean of all the measurements in the
  distribution
• Subtract the mean from each measurement and
  square the difference
• Add the squares together
• Divide the sum of the squares by the number of
  measurements
• Take the square root of the value you obtained in
  step 4. This is the standard deviation.