Inferential Statistics

(a brief over view)Inferential Statistics

Descriptive Statistics (just the #s)

Mean = averageMedian = middle most data scoreMode = most frequently occurring data scoreRange = max score min scoreInter Quartile Range = Q3 Q1Standard deviation = deviation (difference) from the mean

Standard deviation example

Example for grouped data

INFERential StatisticsPutting it all together.what do the statistics infer?!

What do the numbers tell us?!

The Normal distribution

Matchboxes in stavanger

Normal DistributionExcel exampleSignificance tests: Is there a real difference???Two tailed tests

One tailed tests

Matchboxes

40S = 3373431434649Frank Wilcoxon1892-1965ChemistStatisticianInventor of..The Wilcoxon (T) signed ranks test!!!(yay!)

Related Data: The Wilcoxon (T) Signed Ranks TestIs for related ordinal data onlyOrdinal 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 dataexamples of related ordinal data:

The Wilcoxon (T) Signed Ranks TestFor ALL statistical significance tests:1. State the null (Ho) and alternative (Ha or H1) hypothesis.Ho ALWAYS says no statistical differenceH1 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 testDoes it look like there is a difference?!

The Wilcoxon Testa slightly more accurate test that we all can agree onNull 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 dataLowest difference is assigned a value of 1Ignore sign differences (take absolute value of differences)Ignore zero valuesFor tied scores, use the median rank

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 (-) ranksSum (+) = 12+9.5+3+5+3+9.5+3+14+7+11+13= 90

Sum (-) = 1+6+8=15

Use the SMALLER of these twovaluesthis is your statisticT!!!

So T = 15.

Find critical value:(Remember N = 14Since we dropped 0)

Significance tests: Is there a real difference???Two tailed tests

One tailed tests

Average differenceT =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 chancethe 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 hypothesisChoose confidence level (usually 0.05)Take the differences and rank dataSum 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 reviewhttp://www.social-science.co.uk/stats/http://www.youtube.com/watch?v=mbpGCxYya3Mhttp://www.khanacademy.org/video/statistics--standard-deviation?playlist=Statistics