- The document discusses determining whether distributions are normal or skewed
- A distribution is considered skewed if the skewness value divided by the standard error of skewness is less than -2 or greater than 2
- For the old car data set in the example, the skewness value of -4.26 divided by the standard error is less than -2, so this distribution is negatively skewed
- The new car data set skewness value of -1.69 divided by the standard error is between -2 and 2, so this distribution is normal
2. The Normal Distribution is a distribution that has most
of the data in the center with decreasing amounts
evenly distributed to the left and the right.
Skewed Distribution is distribution with data clumped
up on one side or the other with decreasing amounts
trailing off to the left or the right.
Central Tendency, Spread, or Symmetry?
3. The Normal Distribution is a distribution that has most
of the data in the center with decreasing amounts
evenly distributed to the left and the right.
The Skewed Distribution is distribution with data
clumped up on one side or the other with decreasing
amounts trailing off to the left or the right.
Central Tendency, Spread, or Symmetry?
Right skewed Left skewed
5. Why is this important to know?
Because the means and standard deviations of
samples with skewed distributions do not
generalize to the population well.
This is because the skewed distributions means
are pulled toward the tail of the distribution.
6. Why is this important to know?
Because the means and standard deviations of
samples with skewed distributions do not
generalize to the population well.
This is because the skewed distributions means
are pulled toward the tail of the distribution.
The Population
Skewed
Sample
7. Why is this important to know?
Because the means and standard deviations of
samples with skewed distributions do not
generalize to the population well.
This is because the skewed distributions means
are pulled toward the tail of the distribution.
The Population
Skewed
Sample
8. Why is this important to know?
Because the means and standard deviations of
samples with skewed distributions do not
generalize to the population well.
This is because the skewed distributions means
are pulled toward the tail of the distribution.
The Population
Skewed
Sample
9. Why is this important to know?
Because the means and standard deviations of
samples with skewed distributions do not
generalize to the population well.
This is because the skewed distributions means
are pulled toward the tail of the distribution.
The Population
Skewed
Sample
mean mean
10. How can you tell if a distribution is
• Normal?
11. How can you tell if a distribution is
• Normal?
or
• Skewed?
12. We will show you the answer to that question
within the context of a problem.
13. Problem
Is there a significant difference between drivers of
old cars and drivers of new cars in terms of average
freeway driving speed?
First let’s determine if the old and new car
distributions are normal or skewed.
14. Problem
Is there a significant difference between drivers of
old cars and drivers of new cars in terms of average
freeway driving speed?
First let’s determine if the old and new car
distributions are normal or skewed.
31. Let’s Interpret!
For the new car distribution the skewness is -.953.
If the skewness is below -2.0 or above +2.0 then
the distribution is considered skewed.
32. Let’s Interpret!
For the new car distribution the skewness is -.953.
Because -.953 is between -2.0 and +2.0 then the
distribution is considered Normal
35. We are NOT dealing with descriptive statistics.
We are dealing with inferential statistics.
Therefore, we must take a different approach.
Everyone in
the population
36. We are NOT dealing with descriptive statistics.
We are dealing with inferential statistics.
Therefore, we must take a different approach.
Everyone in
the population
Everyone in
the population
Sample
37. We are NOT dealing with descriptive statistics.
We are dealing with inferential statistics.
Therefore, we must take a different approach.
Everyone in
the population
Everyone in
the population
Sample
38. We must . . .
. . divide the skewness by the standard error of
skewness.
39. We must . . .
. . divide the skewness by the standard error of
skewness.
40. We must . . .
. . divide the skewness by the standard error of
skewness.
41. We must . . .
. . divide the skewness by the standard error of
skewness.
42. We must . . .
. . divide the skewness by the standard error of
skewness.
43. We must . . .
. . divide the skewness by the standard error of
skewness.
44. We must . . .
. . divide the skewness by the standard error of
skewness.
-1.69
45. We must . . .
The reason we do this will be explained later on in
the course.
-1.69
48. Let’s Interpret!
For the new car distribution the skewness is -1.69.
-1.69
If the skewness is below -2.0 or above +2.0 then
the distribution is considered skewed.
49. Let’s Interpret!
Because -1.69 is between -2.0 and +2.0 then the
distribution is considered Normal
For the new car distribution the skewness is -1.69.
-1.69
56. Let’s Interpret!
If the skewness is below -2.0 or above +2.0 then
the distribution is considered skewed.
-4.26
For the old car distribution the skewness is -4.26.
57. Let’s Interpret!
Because -4.26 is less than -2.0 then the
distribution is considered negatively skewed
-4.26
For the old car distribution the skewness is -4.26.
58. Let’s Interpret!
If the skewness had been positive +4.26 it would
have been positively or right skewed:
For the old car distribution the skewness is -4.26.
59. Let’s Interpret!
But in this case, the old car distribution is considered
negative or left skewed if we are dealing with
inferential statistics
-4.26
61. Old car / new car skew problem with
different data set.
62. Is the old car data set skewed or
normal (inferential study)?
63. Is the old car data set skewed or
normal?
Report
speed
new_old_car Mean N Std. Deviation Skewness
Std. Error of
Skewness
New car 72.81 16 6.595 -.953 .564
Old car 79.94 17 18.081 3.344 .550
Total 76.48 33 14.034 -1.832 .409
Normal? Skewed?
64. Report
speed
new_old_car Mean N Std. Deviation Skewness
Std. Error of
Skewness
New car 72.81 16 6.595 -.953 .564
Old car 79.94 17 18.081 3.344 .550
Total 76.48 33 14.034 -1.832 .409
Is the old car data set skewed or
normal?
+6.06
Normal? Skewed?
65. Report
speed
new_old_car Mean N Std. Deviation Skewness
Std. Error of
Skewness
New car 72.81 16 6.595 -.953 .564
Old car 79.94 17 18.081 3.344 .550
Total 76.48 33 14.034 -1.832 .409
Is the old car data set skewed or
normal?
+6.06
Normal? Skewed?
66. Report
speed
new_old_car Mean N Std. Deviation Skewness
Std. Error of
Skewness
New car 72.81 16 6.595 -.953 .564
Old car 79.94 17 18.081 3.344 .550
Total 76.48 33 14.034 -1.832 .409
Is the old car data set skewed or
normal?
+6.06
Normal? Skewed?
If the skewness is below -2.0 or above +2.0 then
the distribution is considered skewed.
67. Report
speed
new_old_car Mean N Std. Deviation Skewness
Std. Error of
Skewness
New car 72.81 16 6.595 -.953 .564
Old car 79.94 17 18.081 3.344 .550
Total 76.48 33 14.034 -1.832 .409
Is the old car data set skewed or
normal?
+6.06
Normal? Skewed?
Because +6.06 is greater than +2.0 then the
distribution is considered positively or right skewed.
68. Is the new car data set skewed or
normal?
Normal? Skewed?
69. Is the new car data set skewed or
normal?
Normal? Skewed?
Report
speed
new_old_car Mean N Std. Deviation Skewness
Std. Error of
Skewness
New car 72.81 16 6.595 1.813 .993
Old car 79.94 17 18.081 -2.344 .550
Total 76.48 33 14.034 -1.832 .409
70. Report
speed
new_old_car Mean N Std. Deviation Skewness
Std. Error of
Skewness
New car 72.81 16 6.595 1.813 .993
Old car 79.94 17 18.081 -2.344 .550
Total 76.48 33 14.034 -1.832 .409
Is the new car data set skewed or
normal?
Normal? Skewed?
1.83
71. Report
speed
new_old_car Mean N Std. Deviation Skewness
Std. Error of
Skewness
New car 72.81 16 6.595 1.813 .993
Old car 79.94 17 18.081 -2.344 .550
Total 76.48 33 14.034 -1.832 .409
Is the new car data set skewed or
normal?
Normal? Skewed?
1.83
72. Report
speed
new_old_car Mean N Std. Deviation Skewness
Std. Error of
Skewness
New car 72.81 16 6.595 1.813 .993
Old car 79.94 17 18.081 -2.344 .550
Total 76.48 33 14.034 -1.832 .409
Is the new car data set skewed or
normal?
Normal? Skewed?
1.83
If the skewness is between -2.0 and +2.0 then the
distribution is considered normal.
73. Report
speed
new_old_car Mean N Std. Deviation Skewness
Std. Error of
Skewness
New car 72.81 16 6.595 1.813 .993
Old car 79.94 17 18.081 -2.344 .550
Total 76.48 33 14.034 -1.832 .409
Is the new car data set skewed or
normal?
Normal? Skewed?
1.83
Because 1.83 is between -2.0 and +2.0 then the
distribution is considered normal.
74. After calculating the skew for the data set in your
original problem, determine if the distributions are
all normal or is there at least one that is skewed?
Normal? Skewed?