Download Inferential Statistics

Inferential Statistics
(a brief over view)
Population
Sample
• Parameters
• Statistics
data
Qualitative
(nominal or
categorical)
Quantitative
(numerical)
Discrete
(think counting)
Continuous
(think measuring)
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 = Q3 – Q1
 Standard deviation = deviation (difference) from the mean
The middle
of the data set
The “spread”
of the data set
mean
Range
median
Inter-quartile
range
mode
Standard
deviation
Standard deviation example
Example for grouped data
INFERential Statistics
 Putting it all together….what do the statistics infer?!
What do the numbers tell us?!
The “Normal” distribution
Matchboxes in stavanger
Normal Distribution
 Excel example
Significance tests: Is there a real
difference???
 Two tailed tests
 One tailed tests
31
34
37
40
Matchboxes
S=3
43
46
49
Frank Wilcoxon
 1892-1965
 Chemist
 Statistician
 Inventor of…..
 The Wilcoxon (T) signed ranks test!!!
 (yay!)
Related Data: The Wilcoxon (T) Signed
Ranks Test
 Is for related ordinal data only
 Ordinal data must be RANKED (1st, 2nd, 3rd, etc)
 Lowest number always gets 1
 Used to see if there is a real (statistical) difference in the data
 examples of related ordinal data:
The Wilcoxon (T) Signed Ranks Test
For ALL statistical significance tests:
1. State the null (Ho) and alternative (Ha or H1) hypothesis.
 Ho ALWAYS says no statistical difference
 H1 ALWAYS says there IS a statistical difference.
2. Pick a statistical test (Wilcoxon)
3. Calculate Statistic (T)
4. Decide whether to accept or reject Ho based on alpha level
Example
The eye ball test
 Does it look like there is a difference?!
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 H0 if T ≤ Critical Value)
 Step 1: Calculate the difference (B-A)
2: Rank the data
Lowest difference is assigned a value of 1
2. Ignore sign differences (take absolute value of differences)
3. Ignore zero values
4. For tied scores, use the median rank
1.
3 is the 2nd, 3rd, and 4th, rank therefore use the MEDIAN (middle) rank
8 is tied for the 9th and 10th rank so use the MEDIAN (middle) rank of 9.5
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.
Find critical value:
(Remember N = 14
Since we dropped 0)
Significance tests: Is there a real
difference???
 Two tailed tests
 One tailed tests
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!
 Reject H0.
 Therefore we have sufficient evidence to accept H1 and we
conclude:
 the difference between the lecture based class and
investigation based class is significant according to our data!
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 H0 if T ≤ C.V.
 (note if T > all C.V. then there is no significant difference)
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