1. Creating User Interfaces Review midterm Sampling Homework: User observation reports due next week

2. Sampling Basic technique when it is impossible or too expensive to measure everything/everybody Premise: possible to get random sample, meaning every member of whole population equally likely to be in sample NOTE: not a substitute for monitoring directly activity on / with interface

3. Source The Cartoon guide to Statistics by Larry Gonick and Woollcott Smith HarperResource Procedures (formulas) presented without proof, though, hopefully, motivated

4. Task Want to know the percentage (proportion) of some large group –adults in USA –television viewers –web users For a particular thing –think the president is doing a good job –watched specific program viewed specific commercial visited specific website

5. Strategy: Sampling Ask a small group –phone –solicitation at a mall –Follow-up or prelude to access to webpage –other? Monitor actions of a small group, group defined for this purpose Monitor actions of a panel chosen ahead of time ALL THESE: make assumption that those in group are similar to the whole population.

6. Two approaches Estimating with confidence interval c in general population based on proportion p hat in sample Hypothesis testing: H0 (null hypothesis) p = p0 versus Ha p > p0

7. Estimation process Construct a sample of size n and determine p hat –Ask who they are voting for (for now, let this be binomial choice) Use this as estimate for actual proportion p. … but the estimate has a margin of error. This means : The actual value is within a range centered at p hat …UNLESS the sample was really strange. The confidence value specifies what the chances are of the sample being that strange.

8. Statement I'm 95% sure that the actual proportion is in the following range…. p hat – m <= p <= p hat + m Notice: if you want to claim more confidence, you need to make the margin bigger.

9. Image from Cartoon book You are standing behind a target. An arrow is shot at the target, at a specific point in the target. The arrow comes through to your side. You draw a circle (more complex than +/- error) and say Chances are: the target point is in this circle unless shooter was 'way off'. Shooter would only be way off X percent of the time. (Typically X is 5% or 1%.)

10. Mathematical basis Samples are themselves normally distributed… –if sample and p satisfy certain conditions. Most samples produce p hat values that are close to the p value of the whole population. Only a small number of samples produce values that are way off. –Think of outliers of normal distribution

11. Actual (mathematical) process Can use these techniques when n*p>=5 and n*(1-p)>=5 The p hat values are distributed close to normal distribution with standard deviation sd(p) = Can estimate this using p hat in place of p in formula! Choose the level of confidence you want (again, typically 5% or 1%). For 5% (95% confident), look up (or learn by heart the value 1.96: this is the amount of standard deviations such that 95% of values fall in this area. So.95 is P(-1.96 <= (p-p hat )/sd(p) <=1.96) Sample size must be this big

12. Notes p is less than 1 so (1-p) is positive. Margin of error decreases as p varies from.5 in either direction. (Check using excel). –if sample produces a very high (close to 1) or very low value (close to 0), p * (1-p) gets smaller –(.9)*(.1) =.09; (.8)*(.2) =.16, (.6)*(.4) =.24; (.5)*.5)=.25

13. Notes Need to quadruple the n to halve the margin of error.

14. Formula Use a value called the z transform –95% confidence, the value is 1.96

15. Level of confidence 1-leg or 2-legStandard deviations (z- score) 80%.10 or.201.28 90%.05 or.101.64 95%.025 or.051.96 99%.005 or.012.58

16. Mechanics Process is Gather data (get p hat and n) choose confidence level Using table, calculate margin of error. Book example: 55% (.55 of sample of 1000) said they backed the politician) sd(p hat ) = square_root ((.55)*(.45)/1000) =.0157 Multiply by z-score (e.g., 1.96 for a 95% confidence) to get margin of error So p is within the range:.550 – (1.96)*(.0157) and.550 + (1.96)*(.0157).519 to.581 or 51.9% to 58.1%

17. Example, continued 51.9% to 58.1% may round to 52% to 58% or may say 55% plus or minus 3 percent. What is typically left out is that there is a 1/20 chance that the actual value is NOT in this range.

18. 95% confident means 95/100 probability that this is true 5/100 chance that this is not true 5/100 is the same as 1/20 so, There is only a 1/20 chance that this is not true. Only 1/20 truly random samples would give an answer that deviated more from the real –ASSUMING NO INTRINSIC QUALITY PROBLEMS –ASSUMING IT IS RANDOMLY CHOSEN

19. 99% confidence means [Give fraction positive] [Give fraction negative]

20. Why Confidence intervals given mainly for 95% and 99%?? History, tradition, doing others required more computing….

21. Let's ask a question How many of you watched the last Super Bowl? –Sample is whole class How many registered to vote? –Sample size is number in class 18 and older ????

22. Excel: columns A & B students watchers psample=B2/B1 sd=SQRT(B3*(1-B3)/B1) Ztransform for 95%=1.96 margin=B5*B4 lower=MAX(0,B3-B6) upper=MIN(B3+B6,1)

23. Variation of book problem Say sample was 300 (not 1000). sd(phat) = square_root ((.55)*(.45)/300) =.0287 Bigger number. The circle around the arrow is larger. The margin is larger because it was based on a smaller sample. Multiplying by 1.96 get.056, subtracting and adding from the.55 get.494 to.606 You/we are 95% sure that true value is in this range. Oops: may be better, but may be worse. The fact that the lower end is below.5 is significant for an election! Divisor smaller

24. Exercise size of sample is n proportion in sample is p hat confidence level produces factor called the z-score –Can be anything but common values are [80%], 90%, 95%, 99%) –Use table. For example, 95% value is 1.96; 99% is 2.58 Calculate margin of error m – m = zscore * sqrt((p hat )*(1-p hat )/n) Actual value is >= p hat – m and <= p hat + m

25. Opportunity sample Common situation –people assigned/asked to have a meter attached to their TVs –people asked/voluntarily sign up to have a meter (software) installed in their computers. –people asked during a Web session to participate in survey –students in a specific class! Practice is to determine categories (demographics) and project the sample results to the subpopulation to the population –For example, if actual population was 52% female and 48% male, and sample (panel) is 60% male and 40% female, use proportions to adjust result… But maybe this fact hides problem with the sample Has negative features of any opportunity sample –Are these folks different than others in their (sub)population?

26. Requirements Model / Categories must be well-defined and valid –Hispanic versus (Cuban, others) in Florida in 2000 Need independent analysis of subpopulations representation in general population The sample sizes are the individual Ns, making the margin of errors larger

27. Adjustment from panel data Panel of 10: 6 females, 4 males Population is 52% female and 48% male Female panelists: 5 liked interface, 1 didn't. Male panelists: 2 liked interface, 2 didn't. Estimate for whole population (size P) (5/6)*.52 * P + (2/4)*.48* P

28. Critical part of surveys and survey analysis: Understand the exact wording of question. Understand definition of categories of population. Don't make assumptions… Admire Michelle Obama example Belief in Holocaust example

29. Usability research Often aims for qualitative, not quantitative results –Ideas, critical factors Note: there are fields of study –Non-numeric statistics –Qualitative research Still necessary to be systematic. AD: consider taking Statistics!

30. Homework Continue work on user observation studies –This is qualitative work