(a brief over view) Inferential Statistics

Parameters Population Statistics Sample

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 = Q 3 – Q 1 Standard deviation = deviation (difference) from the mean

The middle of the data set meanmedianmode The “spread” of the data set Range Inter-quartile range 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

Matchboxes 40 S =

Frank Wilcoxon 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 (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:

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

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 H 0 if T ≤ Critical Value) Step 1: Calculate the difference (B-A)

2: Rank the data 1. 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

3 is the 2 nd, 3 rd, and 4 th, rank therefore use the MEDIAN (middle) rank

8 is tied for the 9 th and 10 th rank so use the MEDIAN (middle) rank of 9.5

3. Sum up (+) vs (-) ranks Sum (+) = = 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 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!

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)

Some extra review… deviation?playlist=Statistics deviation?playlist=Statistics