keys statistical terms

7/27/2019 KEYS Statistical Terms

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Prepared for KEYS 2.0 Data Analysis and Interpretation, May 8-11, 2007!lled "y #a$%!es &a$son fro' (ario!s Internet )e"sites.

Definition of Statisti$al *er's

Standard Deviation

)+A* IS S*A&DAD DEIA*I&/ *e standard de(iation is te 'ost fre%!ently$al$!lated 'eas!re of (aria"ility or dispersion in a set of data points. *e standard

de(iation (al!e represents te a(erae distan$e of a set of s$ores fro' te 'ean or

a(erae s$ore.

Standard deviation and the normal curve

Knoin te standard de(iation elps $reate a 'ore a$$!rate pi$t!re of te distri"!tionalon te nor'al $!r(e. A s'aller standard de(iation represents a data set ere s$ores

are (ery $lose to te 'ean s$ore 3a s'aller rane4. A data set it a larer standard

de(iation as s$ores it 'ore (arian$e 3a larer rane4. 5or e6a'ple, if te a(erae

s$ore on a test as 80 and te standard de(iation as 2, te s$ores o!ld "e 'ore$l!stered aro!nd te 'ean tan if te standard de(iation as 10.

Figure 1. The normal curve. Standard deviation is a constant interval from the mean.Roll the mouse over the curve to discover the percentage each portion represents.

Calculating the standard deviation

*e fi!re "elo displays te for'!la for $al$!latin te standard de(iation. 3It is '!$easier tan it loos4

1
http://coe.sdsu.edu/eet/Articles/standarddev/start.htm#%23


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S 9 standard de(iation

: 9 s!' of

; 9 indi(id!al s$oreM 9 'ean of all s$ores

n 9 sa'ple si


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Descriptive Statistics

True Mean! Con"idence #ntervals and $evels o" Signi"icance

Pro"a"ly te 'ost often !sed des$ripti(e statisti$ is te 'ean or a(erae s$ore in a set of

data. *e 'ean is a parti$!larly infor'ati(e 'eas!re of te C$entral tenden$yC ofte (aria"le 3set of s$ores4 if it is reported alon it its $onfiden$e inter(als3related to te (aria"ility a'on te s$ores4 .

Bs!ally e are interested in statisti$s 3s!$ as te 'ean4 fro' o!r sa'ple only en tey

$an elp !s infer infor'ation a"o!t te pop!lation. *e $onfiden$e inter(als for

te 'ean i(e !s a rane of (al!es aro!nd te 'ean ere e e6pe$t to find te

Ctr!eC 3pop!lation4 'ean 3it a i(en le(el of $ertainty4. 5or e6a'ple, if te'ean in a sa'ple is 2=, and te loer and !pper li'its of te p9.0? $onfiden$e

inter(al are 1 and 27 respe$ti(ely 32 standard de(iations on eiter side of te 'ean

!nder te "ellF $!r(e4, ten yo! $an $on$l!de tat tere is a ?G pro"a"ility tat

te pop!lation 'ean is reater tan 1 and loer tan 27. If yo! set te p-le(el to as'aller (al!e, ten te inter(al o!ld "e$o'e ider tere"y in$reasin te

C$ertaintyC of te esti'ate, and (i$e (ersa. *is $on$ept is also !sef!l to!nderstand resear$ers en tey point to le(els of sinifi$an$eF "eteen to or

'ore 'eans.

As e all no fro' te eater fore$ast, te 'ore C(a!eC te predi$tion 3i.e., ider

te $onfiden$e inter(al4, te 'ore liely it ill 'ateriali


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orrelation Analysis

orrelation is a 'eas!re of te relation "eteen to or 'ore (aria"les. orrelation

$oeffi$ients $an rane fro' -1.00 to H1.00. *e (al!e of -1.00 represents a perfe$tnegative $orrelation ile a (al!e of H1.00 represents a perfe$tpositive $orrelation. A

(al!e of 0.00 represents a la$ of $orrelation.

*e 'ost idely-!sed type of $orrelation $oeffi$ient isPearson r, also $alled linearor

product- moment$orrelation.

Pearson $orrelation deter'ines te e6tent to i$ (al!es of te to (aria"les areCproportionalC to ea$ oter. *e (al!e of $orrelation 3i.e., $orrelation $oeffi$ient4 does

not depend on te spe$ifi$ 'eas!re'ent !nits !sed for e6a'ple, te $orrelation "eteen

eit and eit ill "e identi$al reardless of eter inchesandpounds, orcentimetersand kilogramsare !sed as 'eas!re'ent !nits.Proportional'eans linearly

related tat is, te $orrelation is i if it $an "e Cs!''ari


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*is line is $alled te regression lineor least squares line (related to Regression

Analysis).

As 'entioned a"o(e, te $orrelation $oeffi$ient 3r4 represents te linear relationsip

"eteen to (aria"les. If te $orrelation $oeffi$ient is s%!ared, ten te res!ltin r2 (al!e3$alled te $oeffi$ient of deter'ination4 ill represent te proportion of $o''on

(ariation in te to (aria"les 3i.e., te CstrentC or C'anit!deC of te relationsip4.

eardless of te strent or 'anit!deF of a $orrelation, it is risy and inappropriate to

infer a $a!sal or $a!se-effe$t relationsip "eteen te to (aria"les. So'eti'es a$orrelation 'ay "e sp!rio!sF tat is, a $orrelation tat is d!e 'ostly to te infl!en$es of

CoterC (aria"les. 5or e6a'ple, tere is a $orrelation "eteen te total a'o!nt of losses

in a fire and te n!'"er of fire'en tat ere p!ttin o!t te fire. If e ere to infer a$a!sal relationsip, ten one o!ld say tat feer fire'en o!ld res!lt in loer losses.

+oe(er, tere is a tird (aria"le 3te initialsizeof te fire4 tat infl!en$es "ot te

a'o!nt of losses and te n!'"er of fire'en. If yo! C$ontrolC for tis (aria"le 3e..,$onsider only fires of a fi6ed si


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%actor &nal'sis

*e p!rpose of fa$tor analysis is to dis$o(er patterns of relationsips a'on 'any

(aria"les. In parti$!lar, it sees to dis$o(er if te o"ser(ed (aria"les $an "e e6plainedlarely or entirely in ter's of a '!$ s'aller n!'"er of (aria"les $alledfactors. It is a

statisti$al pro$ed!re, in(ol(in $orrelation analysis, !sed to !n$o(er relationsips a'on

'any (aria"les. *is allos n!'ero!s inter-$orrelated (aria"les to "e $ondensed into

feer di'ensions, $alled fa$tors, or indi$ators as in KEYS 2.0.

Many statisti$al 'etods are !sed to st!dy te relation "eteen independent and

dependent (aria"les. 5a$tor analysis is different it is !sed to st!dy te patterns ofrelationsip a'on 'any dependent (aria"les, it te oal of dis$o(erin so'etin

a"o!t te nat!re of te independent (aria"les tat affe$t te', e(en to! tose

independent (aria"les ere not 'eas!red dire$tly. *!s ansers o"tained "y fa$toranalysis are ne$essarily 'ore ypoteti$al and tentati(e tan is tr!e en independent

(aria"les are o"ser(ed dire$tly. *e inferred independent (aria"les are $alled factors. Atypi$al fa$tor analysis s!ests ansers to fo!r 'aJor %!estions

1. +o 'any different fa$tors are needed to e6plain te pattern of relationsips

a'on tese (aria"les/

2. )at is te nat!re of tose fa$tors/

=. +o ell do te ypotesi


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Regression Analysis

*e 'ost $o''on type of reression analysis is linear reression. *ere are to inds of

linear reression 14 si'ple linear reression, and 24 '!ltiple linear reressions3also non as '!lti(ariate linear reression4. Si'ple linear reression is en

yo! a(e one dependent (aria"le 3also non as an o!t$o'e, or response

(aria"le4 and one independent (aria"le 3also non as a predi$tor or

e6planatory (aria"le4. M!ltiple linear reressions are en yo! a(e onedependent (aria"le and to or 'ore independent (aria"les.

ne p!rpose of linear reression analysis is to predi$t a dependent (aria"le.S!ppose yo! a(e a data set $onsistin of te ender, eit and ae of $ildren

"eteen te aes of ? and 10 years. In si'ple linear reression, yo!r oal 'it

"e to predi$t te eit of a $ild, i(en is or er ae. In '!ltiple linearreressions, yo! 'it ant to predi$t te eit of a $ild i(en ae and

ender. In te KEYS 2.0 analysis, after te fa$tor analysis tat elped !s

identify te >2 indi$ators 3fa$tors4, e ran a series of reression analyses todeter'ine te e6tent to i$ ea$ indi$ator as $orrelated to to different'eas!res of st!dent a$ie(e'ent.

5or tose of yo! o o!ld lie to no a "it 'ore a"o!t reression analysis, read on.

*e linear reression 'odel is a 'ate'ati$al e%!ation for a line. *e para'eters of te

e%!ation are esti'ated !sin 'ate'ati$al for'!las tat are applied to te dataset of ender, eit and ae of te $ildren aes ?-10. In oter ords, te

linear reression 'odel is fittedF to te sa'ple data. *is $an "e (is!ali


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%reuenc' tales

5re%!en$y or one-ay ta"les represent te si'plest 'etod for analy4"ever interested.

In pra$ti$ally e(ery resear$ 3in$l!din a$tion resear$ $ond!$ted "y s$ool staff4

proJe$t, a first ClooC at te data !s!ally in$l!des fre%!en$y ta"les. 5or e6a'ple, if e

ere to s!r(ey s$ool parents, fre%!en$y ta"les $an so te n!'"er of 'ales andfe'ales o parti$ipated in te s!r(ey, te n!'"er of respondents fro' parti$!lar etni$

and ra$ial "a$ro!nds, and so on. esponses on so'e la"eled attit!de 'eas!re'ent

s$ales 3e.., interest in (ol!nteerin in so'e s$ool a$ti(ity4 $an also "e ni$ely

s!''ari

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