Prepare for STAT170 Exam

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Basic assumptions about you Many elementary concepts have been skipped. At this stage, it is assumed that you should know them well. In particular, you MUST know how to do HATPC for each of the 8½ hypothesis tests. Only important things, or those that inter-connect several topics together, are elaborated here. You have ABSOLUTELY NO hope of passing STAT170 if you do not know the 8½ HATPCs. This PP file will NOT push you from F to P. The contents of this file will only help the P or above student
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  11 Basic assumptions about you Many elementary concepts have been skipped. Atthis stage, it is assumed that you should knowthem well. In particular, you MUST know how todo HATPC for each of the 8½hypothesis tests.Only important things, or those that inter-connectseveral topics together, are elaborated here. You have ABSOLUTELY NO hope of passing STAT170if you do not know the 8½HATPCs. This PP filewill NOT push you from F to P. The contents of this file will only help the P or abovestudents, given the presumed basic knowledge. 22 Binding things together Review of:ã5 types of graphicsã5 types of research questionsã8½statistical testsã8 or MORE types of reports 33 Displaying Data: 5 types of graphics DATA  categoricalnumericalcategoricalnumerical clusteredbar chartcomparativebox plots bar chart orpie chart comparativebox plotsscatter plot histogram orstem-and-leaf plothistogram orstem-and-leaf plotbar chart orpie chart   44 Combination of variable(s)Graphic One categorical(Lecture 2, 11)ãBar chartãpie chartOne numerical(Lecture 2, 7)ãHistogramãstem-&-leaf Two categorical(Lecture 2, 11, 12) Clustered bar chartTwo numerical(Lectures 2, 9 & 10)Scatter plotOne categorical and one numerical(Lecture 2, 8) Comparative box plots Displaying Data: 5 types of graphics (The following table conveys the same information as theprevious slide.)  55 5 types of graphics STAT170 is restricted to only 5 types of combinations of variables, 5 different types of graphics, and 5 possibleresearch questions.The most important step is correctly identifying the typesof variables: NUMERICALvsCATERGORICAL.Surprisingly, many students have difficulty in this veryfirst step.The correct/wrongidentification of variables would leadyou to the correct/wrong:ãType of graphicãResearch question, andãStatistical test. 66 How to comment on graphics: 1.Comments on a single bar chart (seldom asked) Comment depends on whether variable is ordinal ornominalãOrdinal:comment similar to histogramãNominal: comment on which categories have the highestand lowest frequencies 050100150200250300350400meat vegetarian vegan dietcount Skewed to the right.This doesn’t make any sense!   77 1.Comment on shape (skewedleft/right, normal)2.Range fromxxxxtoxxxx3.Majority (high frequencies) of data aboutxxxx4.Comment outliers (if present)5.Comment on any unusual features (if present) 0 5 10 15 20 25 30 0100200300400500 Assessment Freq. 2. Comments on a single histogram(or stem-and-leaf plot)   8 036912 020406080100 Individual Days Freq. Example:ãU-shaped, high frequencies near both ends, lowestfrequencies near thecentreãU-shaped, but slightly skewed leftãRange from 0 to 12  99 3.Comments on comparativeboxplots ãCompare mediansãCompare spread (IRQ)ãCompare outliers(Even when there are nooutliers, say “no outliers”.) Class dayevening 15 20 25 30 35 AgeClass 1010 4. Comments on scatter plot ãComment on linear/curved?Positive or negative slope?ãComment on amount of scatter (big or small?)ãComment on outliers, if anyãComment on residuals –Sym on both sides of the line/normal? –Constant SD? 051015202530354045501015202530354045 Median AgeBirth Rate 1015202530354045505510 20 30 40 50 60 70 husband ageage marriage   102030405060708090100110-1012345 GPAUAI 1111 5. Comments on clustered bar charts Compare the shapes of the clusters, NOT the sizes. Shapes (not size) similar ⇒ The 2 variables independent(iehave no association)(since % are the same) Shapes (not size) notsimilar ⇒ The 2 variables not independent(iehave association)(because % are not the same)   12 Comments on clustered bar charts:explanation Never compare the actual frequencies (sizes).Only compare % (or proportions) (shapes).Since proportions are almost the same, ie about 1/3 and2/3 for smokers and non-smokers,smoking status is independent of Activity Level (noassociation)  13 Comments on clustered bar charts:explanation Never compare the actual frequencies (sizes).Only compare % (or proportions) (shapes).Since percentages of smokers and non-smokers areobviously different for males and females, there is anassociation between smoking status and gender. 1414 Different shape,(although same size)similar in shape(although differentsizes) 1515 The 8½hypothesis tests in STAT170 DATA  categoricalnumericalcategoricalnumerical ClusteredbarchartChi sq test of association + OR   comparativeboxplots2-sample t test   bar chartz-test of proportionor chi sq test of proportions   comparativeboxplots2-sample t test   scatter plotT-test of  ββββ   Histogram1-sample Z ort test   Histogram1-sample Z ort test   bar chartz-test of proportionor chi sq test of proportions Note: 7 tests above + paired t-test +”OR”= 8½tests in STAT170   1616 Determining numerical vs. categorical  You only need to be able to identify betweennumerical and categorical. No need to further classify into continuous ordiscrete(=integer), nor further classify intonominal or ordinal.If you cannot distinguish between nominal andordinal, you’ll only lose a few marks in Q.1.But how about numericalvscategorical ? Seenext slide.
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