Inferential Statistics Descriptive Statistics just the s Mean average Median middle most data score Mode most frequently occurring data score Range max score min score Inter Quartile Range Q ID: 339158
Download Presentation The PPT/PDF document "(a brief over view)" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
(a brief over view)
Inferential StatisticsSlide2Slide3Slide4Slide5Slide6Slide7
Descriptive Statistics (just the #’
s
)
Mean = average
Median = middle most data score
Mode = most frequently occurring data score
Range = max score – min score
Inter Quartile Range = Q
3
– Q
1
Standard deviation = deviation (difference) from the meanSlide8Slide9Slide10Slide11
Standard deviation exampleSlide12Slide13
Example for grouped dataSlide14
INFERential Statistics
Putting it all together….what do the statistics
infer
?!Slide15
What do the numbers tell us?!Slide16
The “Normal” distributionSlide17
Matchboxes in
stavangerSlide18Slide19
Normal Distribution
Excel exampleSlide20
Significance tests: Is there a real difference???
Two tailed tests
One tailed testsSlide21
Matchboxes
40
S = 3
37
34
31
43
46
49Slide22
Frank
Wilcoxon
1892-1965
Chemist
Statistician
Inventor of…..
The
Wilcoxon
(T) signed ranks test!!!
(
yay
!)Slide23
Related Data: The
Wilcoxon
(T) Signed Ranks Test
Is for related ordinal data only
Ordinal data must be RANKED (1
st
, 2
nd
, 3
rd
, etc)
Lowest number always gets 1
Used to see if there is a real (statistical) difference in the data
examples of related ordinal data: Slide24
The Wilcoxon
(T) Signed Ranks Test
For ALL statistical significance tests:
1. State the null (H
o
) and alternative (H
a
or H
1
) hypothesis.
H
o
ALWAYS says no statistical difference
H
1
ALWAYS says there
IS
a statistical difference.
2. Pick a statistical test (
Wilcoxon
)
3. Calculate Statistic (T)
4. Decide whether to accept or reject H
o
based on alpha level Slide25
ExampleSlide26
The eye ball test
Does it
look
like there is a difference?!Slide27
The Wilcoxon
Test
……a slightly more accurate test that we all can agree on
Null Hypothesis: There is no
signifacant
difference between the two lessons.
Alternative Hypothesis: There IS a significant difference between the two lessons.
(Reject H
0
if T ≤ Critical Value)
Step 1: Calculate the difference (B-A)Slide28Slide29
2: Rank the data
Lowest difference is assigned a value of 1
Ignore sign differences (take absolute value of differences)
Ignore zero values
For tied scores, use the median rankSlide30Slide31
3 is the 2
nd
,
3
rd
, and 4
th
, rank therefore use the MEDIAN (middle) rank Slide32
8 is tied for the 9
th
and 10
th
rank so use the MEDIAN (middle) rank of 9.5Slide33Slide34
3. Sum up (+) vs
(-) ranks
Sum (+) = 12+9.5+3+5+
3+9.5+3+14+7+11+13= 90
Sum (-) = 1+6+8=15
Use the SMALLER of these two
values……this is your statistic
T!!!
So T = 15. Slide35
Find critical value:
(Remember N = 14
Since we dropped 0)Slide36
Significance tests: Is there a real difference???
Two tailed tests
One tailed testsSlide37
Average difference
T =15 ≤ 21 (alpha = 0.05)
T = 15 ≤ 15 (alpha =0.02)
98% of the time, you will not have this big of a difference by chance……the difference SHOULD be significant!Slide38
Reject H
0
.
Therefore we have sufficient evidence to accept H
1
and we conclude:
the difference between the lecture based class and investigation based class
is significant
according to our data!Slide39
Recap:
State Null and Alternative hypothesis
Choose confidence level (usually 0.05)
Take the differences and rank data
Sum up (+) and (-) differences and use
smaller
of two….this is your T-value.
Find the Critical Value from the table.
Reject H
0
if T ≤ C.V.
(note if T > all C.V. then there is no significant difference)Slide40
Some extra review…
http://www.social-science.co.uk/stats
/
http://www.youtube.com/watch?v=mbpGCxYya3M
http://www.khanacademy.org/video/statistics--standard-deviation?playlist=Statistics