Summer 2020 Research Analysis and Statistics Presentation with: - PowerPoint PPT Presentation

Summer 2020 Research Analysis and Statistics Presentation with: Christopher P. Morley PhD Chair, Department of Public Health & Preventive Medicine July 30 , 20 20 1 PM Webinar

A QUICK INT RODUCT ION T O BASIC ST AT IST ICAL T E ST S Chr istophe r P. Mor le y PhD Cha ir , De pa r tme nt of Public He a lth & Pr e ve ntive Me dic ine

OBJE CT IVE S  Quic k ove r vie w of var iable type s  How Var iable type s ar e me asur e d  Re vie w of for BASIC but COMMON infe r e ntial statistic al te sts  Pe a rson Corre la tion  T - T e st  ANOVA e d” ( χ 2 )  “Chi- squar  SPSS – Statistic al Pac kage for the Soc ial Sc ie nc e s

VARIABL E DE F INIT ION Your r e se ar c h que stion(s) should inhe r e ntly imply your analytic appr oac h, var iable s e tc . Se e : https:/ / c irt.g c u.e du/ re se a rc h/ de ve lo pme ntre so urc e s/ tuto ria ls/ q ue stio n

VARIABL E T YPE S Continuous - • Inte r val – me asur able in a c ontinuum • Ratio – like an inte r val, but inte r val c ontains 0, and 0 implie s “none ” • Ca te g or ic a l – numbe r s de sc r ibe c a te g or ie s • Nominal – no implie d or de r (e .g. AA/ Asian/ White / AIAN e tc .) • Dic hotomous – a type of nominal that implie s only two state s (e .g. F e male / Male ) • A “Dummy Va ria ble ” is dic hotomize d into 1 a nd 0, with pre se nc e or a bse nc e of a sta te implie d • Or dinal – the r e is an implie d r anking in the or de r , but the r e lationship be twe e n r anks is not a r atio • (e .g. L ike r t Sc ale )

VARIABL E T YPE S, CONT INUE D • Nominal by Nominal (e .g. T r e atme nt ye s/ no by Cur e ye s/ no) e d” χ 2 “Chi-squa r • F ishe r ’s E xa c t T e st (whe n sa mple or c a te g or ie s a r e ve r y sma ll) • Continuous by Nominal • T -T e st - Compa r ing me a n of two g r oups • Ana lysis of Va r ia nc e – c ompa r ing me a ns a c r oss mor e tha t two g r oups • • Or dina l – c a n be tr e a te d like a c ontinuous va r ia ble in ma ny c a se s (a nd we ofte n do! T hink of L ike r t Sc a le s on sur ve ys) Continuous by Continuous • Cor r e la tion – T e sts the e xte nt to whic h one va r ia ble c ha ng e s with a nothe r • Pe a r son – be st for line a r r e la tionships • • Spe a r ma n – be tte r for or dina l or non-line a r r e la tionships

T ODAY’S DE MONST RAT ION • Continuous by Continuous - Pe a r son Cor r e la tion Continuous by Nomina l • T - T e st - Compar ing me an of two gr oups • Analysis of Var ianc e – c ompar ing me ans ac r oss mor e that two gr oups • e ” χ 2 Nomina l by Nomina l - “Chi-squa r •

F I RST – T HE DAT A SPSS  We will b e using SPSS – a va ila b le o n a ll (mo st? ) Upsta te c o mpute rs.  T he re a re a lso stude nt a nnua l lic e nse s a va ila b le .  GUI-drive n, b ut c a n a lso run o n c o de .  https:/ / www.ib m.c o m/ us-e n/ ma rke tpla c e / spss-sta tistic s-g ra dpa c k/ de ta ils# pro duc t-he a de r-to p Da ta Se t  F ro m Bio statistic s: An Applie d Intr o duc tio n fo r the Public He alth Pr ac titio ne r| 1st E ditio n |He athe r M. Bush  https:/ / www.c e ng a g e .c o m/ c / b io sta tistic s-a n-a pplie d-intro duc tio n-fo r-the -pub lic -he a lth- pra c titio ne r-1e -b ush/ 9781111035143/  995 pre g na nt wo me n fro m a la rg e fa rming c o mmunity  Se e wr ite -up and data se t

T ODAY’S DE MONST RAT ION Continuous by Continuous - Pe a r son Cor r e la tion • A Pearson correlation is a number between -1 and 1 that indicates the extent to which two variables are linearly related. The Pearson correlation is also known as the “product moment correlation coefficient” ( PMCC ) or simply “ correlation ”. Pearson correlations are suitable only for metric variables (which include dichotomous variables). •For ordinal variables , use the Spearman correlation or Kendall’s tau and •for nominal variables , use Cramér’s V. F ro m: https:/ / www.spss-tuto ria ls.c o m/ pe a rso n-c o rre la tio n-c o e ffic ie nt/

PE ARSON CORRE L AT ION Continuous by Continuous - Pe a r son Cor r e la tion •

PE ARSON CORRE L AT ION Continuous by Continuous - Pe a r son Cor r e la tion • Annua l Ho use ho ld We e k 9 He mg lo bin We e k 36 Ag e a t Initial Visit Inc o me (USD, Numb e r o f pre vio us E duc a tio nal (g / dL ) He mo g lo bin (g / dL ) (Yrs) b irths Atta inme nt T ho usa nds) We e k 9 He mg lo bin Pe a rso n Co rre latio n .766 ** .076 * .083 ** 1 .012 .015 (g / dL ) Sig . (2-ta ile d) .000 .017 .708 .641 .010 N 979 979 979 975 979 979 We e k 36 He mo g lo b in Pe a rso n Co rre latio n .766 ** .351 ** .078 * - .143 ** .340 ** 1 (g / dL ) Sig . (2-ta ile d) .000 .000 .015 .000 .000 N 979 979 979 975 979 979 Ag e a t Initial Visit (Yrs) Pe a rso n Co rre latio n .076 * .351 ** .083 ** .162 ** 1 - .052 Sig . (2-ta ile d) .017 .000 .010 .105 .000 N 979 979 979 975 979 979 Annua l Ho use ho ld Pe a rso n Co rre latio n .078 * .083 ** .273 ** .012 1 - .043 Inc o me (USD, Sig . (2-ta ile d) .708 .015 .010 .179 .000 N T ho usa nds) 975 975 975 975 975 975 Numb e r o f pre vio us Pe a rso n Co rre latio n - .143 ** .015 - .052 - .043 1 - .038 b irths Sig . (2-ta ile d) .641 .000 .105 .179 .241 N 979 979 979 975 979 979 E duc a tio nal Pe a rso n Co rre latio n .083 ** .340 ** .162 ** .273 ** - .038 1 Atta inme nt Sig . (2-ta ile d) .010 .000 .000 .000 .241 N 979 979 979 975 979 979 **. Co rre latio n is sig nific a nt a t the 0.01 le ve l (2-ta ile d). *. Co rre la tio n is sig nific a nt a t the 0.05 le ve l (2-ta ile d).

PE ARSON CORRE L AT ION • Continuous by Continuous - Pe arson Corre lation (What doe s this L OOK like , graphic ally?) r =.078, p<.015 r =.766, p<.001 r =.012, p=.708

COMPARISON OF ME ANS – T - T E ST Continuous by Nomina l • • T - T e st - Compar ing He moglobin at we e k 36 ac r oss pr e - pr e gnanc y smoking status • So your two gr oups have diffe r e nt me ans. Ar e the y RE AL L Y diffe r e nt, or simply diffe r e nt by c hanc e ?

COMPARISON OF ME ANS – T - T E ST Continuous by Nomina l • • T - T e st - Compar ing He moglobin at we e k 36 ac r oss pr e - pr e gnanc y smoking status • So your two gr oups have diffe r e nt me ans. Ar e the y RE AL L Y diffe r e nt, or simply diffe r e nt by c hanc e ? Gro up Sta tistic s Std . Std . E rro r Pr e - Pr e gnanc y N Me a n De via tio n Me a n Smoke r No 741 1.16342 .04274 We e k 36 He moglobin 8.3524 Ye s 238 1.09255 .07082 (g/ dL ) 7.8314 Inde pe nde nt Sa mple s T e st L e ve ne 's T e st fo r E q ua lity o f Va ria nc e s t-te st fo r E q ua lity o f Me a ns Sig . Me a n Std . E rro r 95% Co nfide nc e Inte rva l L o we r Uppe r F Sig . t d f (2-ta ile d ) Diffe re nc e Diffe re nc e .751 .386 977 .52095 .08543 .35330 .68860 We e k 36 He moglobin 6.098 .000 E q ua l va ria nc e s (g/ dL ) a ssume d 423.097 .52095 .08272 .35836 .68353 6.298 .000 E q ua l va ria nc e s no t a ssume d

COMPARISON OF ME ANS - ANOVA Continuous by Nominal - Analysis o f Var ianc e – c ompar ing me ans ac r oss mor e that two gr oups •

COMPARISON OF ME ANS - ANOVA Continuous by Nominal - Analysis o f Var ianc e – c ompar ing me ans ac r oss mor e that two gr oups • De sc riptive s We e k 36 He mo g lo b in (g / d L ) ANOVA 95% Co nfid e nc e Inte rva l We e k 36 He mo g lo b in (g / dL ) fo r Me a n Me a n Sum o f Std . Std . L o we r Uppe r df Sq ua re Sq ua re s F Sig . N Me a n De via tio n E rro r Bo und Bo und Min Max 2 353.943 Be twe e n 707.887 552.247 .000 T a p Wa te r Only 270 .85532 .05205 7.1571 7.3620 5.31 10.08 7.2596 Gro ups Bo ttle d / F ilte re d 315 .75322 .04244 9.3069 9.4739 7.09 11.69 9.3904 976 .641 Within 625.533 Wa te r Only Gro ups 978 Co mb ina tio n o f T a b 394 .79853 .04023 7.8776 8.0357 5.13 9.86 T o ta l 1333.420 7.9566 a nd Bo ttle d / F ilte re d T o ta l 979 1.16765 .03732 8.1525 8.2990 5.13 11.69 8.2257 Post Hoc Tests - Multiple Co mpa riso ns - T uke y HSD De p e nd e nt Va ria b le : We e k 36 He mo g lo b in (g / d L ) 95% Co nfid e nc e I nte rva l (I ) Wa te r Co nsump tio n Gro up (J) Wa te r Co nsump tio n Gro up Me a n Diffe re nc e (I -J) Std . E rro r Sig . L o we r Bo und Up p e r Bo und -2.13089 * T a p Wa te r Only Bo ttle d / F ilte re d Wa te r Only .06640 .000 -2.2867 -1.9750 -.69709 * Co mb ina tio n o f T a b a nd .06325 .000 -.8456 -.5486 Bo ttle d / F ilte re d 2.13089 * Bo ttle d / F ilte re d Wa te r Only T a p Wa te r Only .06640 .000 1.9750 2.2867 1.43379 * Co mb ina tio n o f T a b a nd .06051 .000 1.2918 1.5758 Bo ttle d / F ilte re d .69709 * Co mb ina tio n o f T a b a nd T a p Wa te r Only .06325 .000 .5486 .8456 -1.43379 * Bo ttle d / F ilte re d Bo ttle d / F ilte re d Wa te r Only .06051 .000 -1.5758 -1.2918 *. T he me a n d iffe re nc e is sig nific a nt a t the 0.05 le ve l.

T ODAY’S DE MONST RAT ION e ” χ 2 Nomina l by Nomina l - “Chi-squa r •