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, 2020 1PM 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

 “Chi- squar

e d” (χ2)

 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

• ac 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)

• “Chi-squa r

e d” χ2

• 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

• ups
• Ana lysis of Va r

ia nc e – c ompa r ing me a ns a c r

• ss mor

e tha t two g r

• ups
• 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

• r

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

• ups
• Analysis of Var

ianc e – c ompar ing me ans ac r

• ss mor

e that two gr

• ups
• Nomina l by Nomina l - “Chi-squa r

e ” χ2

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

• 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

We e k 9 He mg lo bin (g / dL ) We e k 36 He mo g lo bin (g / dL ) Ag e a t Initial Visit (Yrs) Annua l Ho use ho ld Inc o me (USD, T ho usa nds) Numb e r o f pre vio us b irths E duc a tio nal Atta inme nt We e k 9 He mg lo bin (g / dL ) Pe a rso n Co rre latio n

1 .766** .076* .012 .015 .083**

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 (g / dL ) Pe a rso n Co rre latio n

.766** 1 .351** .078*

• .143**

.340**

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** 1 .083**

• .052

.162**

Sig . (2-ta ile d)

.017 .000 .010 .105 .000

N

979 979 979 975 979 979

Annua l Ho use ho ld Inc o me (USD, T ho usa nds) Pe a rso n Co rre latio n

.012 .078* .083** 1

• .043

.273**

Sig . (2-ta ile d)

.708 .015 .010 .179 .000

N

975 975 975 975 975 975

Numb e r o f pre vio us b irths Pe a rso n Co rre latio n

.015

• .143**
• .052
• .043

1

• .038

Sig . (2-ta ile d)

.641 .000 .105 .179 .241

N

979 979 979 975 979 979

E duc a tio nal Atta inme nt Pe a rso n Co rre latio n

.083** .340** .162** .273**

• .038

1

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 =.766, p<.001 r =.078, p<.015 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

• ss pr

e - pr e gnanc y smoking status

• So your

two gr

• ups 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

• ss pr

e - pr e gnanc y smoking status

• So your

two gr

• ups 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

Pr e - Pr e gnanc y Smoke r

N Me a n Std . De via tio n Std . E rro r Me a n

We e k 36 He moglobin (g/ dL )

No 741

8.3524

1.16342 .04274 Ye s 238

7.8314

1.09255 .07082

Inde pe nde nt Sa mple s T e st

L e ve ne 's T e st fo r E q ua lity

• f Va ria nc e s

t-te st fo r E q ua lity o f Me a ns

F Sig . t d f Sig . (2-ta ile d ) Me a n Diffe re nc e Std . E rro r Diffe re nc e

95% Co nfide nc e Inte rva l

L

• we r

Uppe r

We e k 36 He moglobin (g/ dL )

E q ua l va ria nc e s a ssume d

.751 .386

6.098

977

.000

.52095 .08543 .35330 .68860

E q ua l va ria nc e s no t a ssume d

6.298

423.097

.000

.52095 .08272 .35836 .68353

COMPARISON OF ME ANS - ANOVA

• Continuous by Nominal - Analysis o f Var

ianc e – c ompar ing me ans ac r

• ss mor

e that two gr

• ups

COMPARISON OF ME ANS - ANOVA

• Continuous by Nominal - Analysis o f Var

ianc e – c ompar ing me ans ac r

• ss mor

e that two gr

• ups

De sc riptive s

We e k 36 He mo g lo b in (g / d L ) N Me a n Std . De via tio n Std . E rro r 95% Co nfid e nc e Inte rva l fo r Me a n Min

Max

L

• we r

Bo und Uppe r Bo und T a p Wa te r Only 270

7.2596

.85532 .05205 7.1571 7.3620 5.31 10.08 Bo ttle d / F ilte re d Wa te r Only 315

9.3904

.75322 .04244 9.3069 9.4739 7.09 11.69 Co mb ina tio n o f T a b a nd Bo ttle d / F ilte re d 394

7.9566

.79853 .04023 7.8776 8.0357 5.13 9.86 T

• ta l

979

8.2257

1.16765 .03732 8.1525 8.2990 5.13 11.69

ANOVA

We e k 36 He mo g lo b in (g / dL )

Sum o f Sq ua re s

df Me a n Sq ua re

F Sig . Be twe e n Gro ups 707.887

2 353.943

552.247 .000 Within Gro ups 625.533

976 .641

T

• ta l

1333.420

978

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 ) (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 . 95% Co nfid e nc e I nte rva l L

• we r Bo und

Up p e r Bo und T a p Wa te r Only Bo ttle d / F ilte re d Wa te r Only

• 2.13089*

.06640 .000

• 2.2867
• 1.9750

Co mb ina tio n o f T a b a nd Bo ttle d / F ilte re d

• .69709*

.06325 .000

• .8456
• .5486

Bo ttle d / F ilte re d Wa te r Only T a p Wa te r Only 2.13089* .06640 .000 1.9750 2.2867 Co mb ina tio n o f T a b a nd Bo ttle d / F ilte re d 1.43379* .06051 .000 1.2918 1.5758 Co mb ina tio n o f T a b a nd Bo ttle d / F ilte re d T a p Wa te r Only .69709* .06325 .000 .5486 .8456 Bo ttle d / F ilte re d Wa te r Only

• 1.43379*

.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

• Nomina l by Nomina l - “Chi-squa r

e ” χ2

T ODAY’S DE MONST RAT ION

• Nomina l by Nomina l - “Chi-squa r

e ” χ2

• Compar

ison of pr

• po r

tio ns ac r

• ss c ate gor

ie s

• Be st use d in 2 x 2, as that is e asie st to inte r

pr e t

Cro ssta b

Pre -Pre g na nc y Smo ke r T

• ta l

No Ye s T a p Wa te r Only .00 Co unt 558 151 709 % within T a p Wa te r Only 78.7% 21.3% 100.0% 1.00 Co unt 183 87 270 % within T a p Wa te r Only 67.8% 32.2% 100.0% T

• ta l

Co unt 741 238 979 % within T a p Wa te r Only 75.7% 24.3% 100.0%

Chi-Sq ua re T e sts

Va lue d f Asymp to tic Sig nific a nc e (2-sid e d ) E xa c t Sig . (2-sid e d ) E xa c t Sig . (1-sid e d ) Pe a rso n Chi-Sq ua re 12.683a 1 .000 Co ntinuity Co rre c tio nb 12.096 1 .001 L ike liho o d Ra tio 12.219 1 .000 F ishe r's E xa c t T e st .000 .000 L ine a r-b y-L ine a r Asso c ia tio n 12.670 1 .000 N o f Va lid Ca se s 979 a . 0 c e lls (0.0%) ha ve e xp e c te d c o unt le ss tha n 5. T he minimum e xp e c te d c o unt is 65.64. b . Co mp ute d o nly fo r a 2x2 ta b le

F OR DE E PE R ST UDY

 "SPSS T

utor ials" site he r e : https:/ / www.spss- tutor ials.c om/

 I c an't r

e ally vouc h for what it is or who r uns it (some ads ar e bloc ke d by Mc Afe e ). As an intr

• to SPSS, it's a plac e to star
• t. I would r

e c omme nd pe ople c an ope n the le ssons (anywhe r e it says "Re ad"), but be c ar e ful about ope ning any links. I would ONL Y c lic k on the links that le ad to the le ssons - NOT HING that looks like an adve r tise me nt or a link off the site . A fe w pointe r s:



• - T

ype s of va ria ble s



• - How to se t up a ra w da ta ta ble for a na lysis



• - A hypothe sis (sig nific a nc e ) te st



• - Corre la tions (mostly Pe a rson)



• - T
• te st (le a rn the z- te st if you must, but the t- te st is fa r more wide ly use d)



• - Ana lysis of Va ria nc e (ANOVA) - ba sic a lly a n e xte nsion of the t- te st



• - Chi squa re - for a na lyzing c a te g oric a l by c a te g oric a l va ria ble s

 T

hose fe e ling adve ntur

• us c an star

t looking at r e gr e ssion, but most le ar ne r s c an ge t to poste r stage if the y c an r un, inte r pr e t, and e xplain the var iable s above

F OR DE E PE R ST UDY

Khan Ac ade my:

 https:/ / www.kha na c a d e my.o rg / ma th/ sta tistic s-pro b a b ility  A fr

e e online statistic s c our se

Sta tistic a l Solutions Inc :

 https:/ / www.sta tistic sso lutio ns.c o m/ dire c to ry-o f-sta tistic a l-a na lyse s/  De signe d to offe r

disse r tation c onsultation, but lots of fr e e and VE RY str aightfor war d dir e c tions

Soc ia l Re se a rc h Me thods:

 http:/ / so c ia lre se a rc hme tho ds.  Not statistic s, but a gr

e at guide for study de sign, foundations of r e se ar c h me thods, e tc .

F I NAL T I PS

Pa rtne r with pe o ple who c o mple me nt yo ur skills I

f funding a va ila b le : c o nsult with the Ce nte r fo r Re se a rc h & E va lua tio n (CRE )

http:/ / www.upsta te .e du/ pub lic he a lth/ re se a rc h/ c re / inde x.php Ple a se b e a wa re the re a re c ha rg e s ($110/ hr a fte r c o nsulta tio n)

– spe a k w/ fa c ulty a b o ut funding