Date post: | 30-Dec-2015 |
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Creating User InterfacesReview midterm SamplingHomework: User observation reports due next week
SamplingBasic technique when it is impossible or too expensive to measure everything/everybodyPremise: possible to get random sample, meaning every member of whole population equally likely to be in sampleNOTE: not a substitute for monitoring directly activity on / with interface
SourceThe Cartoon guide to Statistics by Larry Gonick and Woollcott Smith HarperResource
Procedures (formulas) presented without proof, though, hopefully, motivated
TaskWant to know the percentage (proportion) of some large groupadults in USAtelevision viewersweb usersFor a particular thingthink the president is doing a good jobwatched specific programviewed specific commercialvisited specific website
Strategy: SamplingAsk a small groupphonesolicitation at a mallFollow-up or prelude to access to webpageother?Monitor actions of a small group, group defined for this purposeMonitor actions of a panel chosen ahead of timeALL THESE: make assumption that those in group are similar to the whole population.
Two approachesEstimating with confidence interval c in general population based on proportion phat in sample Hypothesis testing: H0 (null hypothesis) p = p0 versus Ha p > p0
Estimation processConstruct a sample of size n and determine phatAsk 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 phat UNLESS the sample was really strange.The confidence value specifies what the chances are of the sample being that strange.
StatementI'm 95% sure that the actual proportion is in the following range.
phat m
Image from Cartoon bookYou 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%.)
Mathematical basisSamples are themselves normally distributedif sample and p satisfy certain conditions.Most samples produce phat 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
Actual (mathematical) processCan use these techniques when n*p>=5 and n*(1-p)>=5The phat values are distributed close to normal distribution with standard deviation sd(p) =
Can estimate this using phat 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
Notesp 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
NotesNeed to quadruple the n to halve the margin of error.
FormulaUse a value called the z transform95% confidence, the value is 1.96
MechanicsProcess is Gather data (get phat 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(phat) = square_root ((.55)*(.45)/1000) = .0157Multiply by z-score (e.g., 1.96 for a 95% confidence) to get margin of errorSo p is within the range: .550 (1.96)*(.0157) and .550 + (1.96)*(.0157) .519 to .581 or 51.9% to 58.1%
Example, continued51.9% 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.
95% confident means95/100 probability that this is true5/100 chance that this is not true5/100 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 PROBLEMSASSUMING IT IS RANDOMLY CHOSEN
99% confidence means[Give fraction positive][Give fraction negative]
WhyConfidence intervals given mainly for 95% and 99%??
History, tradition, doing others required more computing.
Let's ask a questionHow many of you watched the last Super Bowl?Sample is whole classHow many registered to vote?Sample size is number in class 18 and older
????
Excel: columns A & B
Variation of book problemSay sample was 300 (not 1000).sd(phat) = square_root ((.55)*(.45)/300) = .0287Bigger 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
Opportunity sampleCommon situationpeople assigned/asked to have a meter attached to their TVspeople asked/voluntarily sign up to have a meter (software) installed in their computers.people asked during a Web session to participate in surveystudents in a specific class!Practice is to determine categories (demographics) and project the sample results to the subpopulation to the populationFor example, if actual population was 52% female and 48% male, and sample (panel) is 60% male and 40% female, use proportions to adjust resultBut maybe this fact hides problem with the sampleHas negative features of any opportunity sampleAre these folks different than others in their (sub)population?
RequirementsModel / Categories must be well-defined and validHispanic versus (Cuban, others) in Florida in 2000Need independent analysis of subpopulations representation in general populationThe sample sizes are the individual Ns, making the margin of errors larger
Adjustment from panel dataPanel of 10: 6 females, 4 malesPopulation is 52% female and 48% maleFemale 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
Critical part of surveysand survey analysis:Understand the exact wording of question.Understand definition of categories of population.Don't make assumptionsAdmire Michelle Obama exampleBelief in Holocaust example
Usability researchOften aims for qualitative, not quantitative resultsIdeas, critical factors
Note: there are fields of studyNon-numeric statisticsQualitative researchStill necessary to be systematic.AD: consider taking Statistics!
HomeworkContinue work on user observation studiesThis is qualitative work