Helen MacGillivray
Some Ghosts of Statistics Past
many great developments considerable progress teaching statistics past 2 3 decades even would wish greater penetration better understanding statistical literacy statistical thinking however statistics seems particularly susceptible type leftovers may appropriately tasty past hang around way past useby date susceptibility may part puzzle extensive discussion understanding nature statistical literacy thinking sufficiently widespread somewhat neglected rush embrace latest appellations including data literacy small examples statistical leftovers checked edibility either eaten sense correctly absorbed thrown focus topics popular school introductory tertiary level include received considerable ongoing attention elsewhere poor incorrect inappropriate graphical representations refer tangentially matters ongoing discussion pvalues effect sizes etc measure location necessarily measure centre particularly relevant considering myths modes mode viewed measure location albeit necessarily good one may poor measure centre discrete variable categorical count data one likely theoretical frequent data values key feature could poor measures centre distribution continuous variable mode local maximum probability density function could anywhere addition data continuous variable situation even complex almost always group observations classes bins called histogram obtain picture data pictorial estimate density function different groupings produce different pictures except large data sets data modal class property defined terms chosen groupings well poor measure centre hence mode taught measure centre case made restricting concept discrete variables data concept density function introduced mode come included measure centre likely goes back identification useful classes distributions important pearson 1895 subsequent papers system eventually covered many commonlyused continuous distributions many unimodal indeed two main ways producing new families continuous distributions one density function thus involving consideration modes transformations variables hence via quantile functions associated comment histograms especially school level appropriate histograms bar charts see humphrey et al 2014 discussion related points fact picture data given histogram dependent often heavily choice bins bin width starting point key emphasis played soon histograms introduced students see effects data picture changing groupings starting points quite startling also whether xaxis labelled midpoints starting points bins irrelevant certainly neither one correct provided always quite clear used another comment histograms trying infer sizes relationships measures standard deviation mean compared median etc futile meaningless classic example changing one observation hardly alters picture reverses order mean median leads another two myths meanmedian sign third central moment including 0 unimodal distributions mean median mode always occur reverse order neither statement true general whether distributions data statements arose early work distribution families tended hold particular erroneously generalised conditions hold easy find distributions course many many datasets dont skewness right left tendency distribution data set longer tail right left many possible measures refer measure centre example mean median adapted versions either signs always coincide even indeed especially distributions halfline signs measures separately reverse parameter values change data sometimes students say data appear asymmetric students forced choose skew left right symmetric indeed students enjoy challenge constructing data sets counter myths terminologies originally served purpose cause students confusion corrected retired term population used genuine population otherwise general situation datagenerating process discussed lu henning 2013 avoids lasting student misunderstandings confusion another confusing group terminologies students relating socalled different probabilities theoretical experimental subjective refer probabilities assigned assumptions models direct estimation subjective assignation combination assumption model estimation different types probabilities different pathways assigning probabilities sample space another term overdue makeover could turn improving understanding fundamental concepts results example emphasis beginning probabilities refer particular situation reference framework leads understanding probabilities conditional probabilities great care must taken working comparing probabilities akin ensuring absolute clarity handling percentages identifying percentages taken sir david spiegelhalter often commented involved learning support know handling percentages significant quantitative weakness many precisely able work different denominators conditional probabilities introduced gradually across educational levels always via conditioning language data relative frequencies whether one uses approach expected frequencies conditioning language percentages chance depending preferred particular context essential formula pab pabpb never term multiplication rule ever used never pab papb introduced conditional probability easier nothing could truth illustrated joerg meyers article issue sometimes independence assumed modelling situation sometimes far intuitive refers probability structure description events example result find often explain educated earlier eras normal approximation distribution sample proportion gives commonlyused approximate confidence intervals hypothesis tests theoretical proportion usually case word population appropriate normal approximation binomial follows students go confidence interval test p without going via normal approximation binomial never forget gruelling session senior mathematician insisted knew teaching statistics still really understand two hours confusion also associated need fundamental understanding different types variables data importance understanding statistics earliest graphs data storage handling challenges data science sophisticated statistical analyses two simple common misunderstandings bernoulli data data binomial variable first assumption many muchused statistical analyses response variable least continuous finally least long time statisticians urging use teaching manyvariabled real data sets real contexts moving quickly possible via technology understanding concepts assumptions application statistical exploration analysis including correct interpretation pvalues effect sizes debate pedagogy gets bogged one twosample mire wonder data science claim data science statistics