chapter 11 quantitative data

8/18/2019 Chapter 11 Quantitative Data

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QUANTITATIVE DATA

ANALYSIS

Chapter 11



LEVELS OF MEASUREMENT

• Variable attributes the !hara!teristi!s "r

#ualities that $es!ribe a %ariable

•Variable attributes !a& be $e'i&e$ at '"ur$i''ere&t le%els "' (easure(e&t

) N"(i&al

) Or$i&al

) I&ter%al

) Rati"



N"(i&al Measure(e&t

• The l"*est le%el "' (easure(e&t

• Attributes "r resp"&se !ate+"ries "' a

%ariable are ) mutually exclusive



Or$i&al Measure(e&t

• Se!"&$ hi+hest le%el "' (easure(e&t

• Attributes "r resp"&ses !ate+"ries "r a

%ariable are ) Mutuall, e-!lusi%e

) Rank ordered



I&ter%al Measure(e&t

• Thir$ hi+hest le%el "' (easure(e&t



) Ra&. "r$ere$

) Equal distance from each other



Rati" Measure(e&t

• /i+hest le%el "' (easure(e&t



) Ra&. "r$ere$

) E#ual $ista&!e 'r"( ea!h "ther

) Based on a true 0 point



COM0UTER A00LICATIONS

• Variables (ust be !"$e$ assi+&e$ a

$isti&!t %alue2 '"r $ata t" be pr"!esse$ b,

!"(puter s"'t*are

• The resear!her (ust .&"* the le%el "'

(easure(e&t '"r ea!h %ariable t"

$eter(i&e *hi!h statisti!al tests t" use



DESCRI0TIVE STATISTICS

• Su((ari3e a %ariable "' i&terest a&$

p"rtra, h"* that parti!ular %ariable is

$istribute$ i& the sa(ple "r p"pulati"&

) Fre#ue&!, $istributi"&s

) Measures "' Ce&tral Te&$e&!,

) Measures "' Variabilit,



Fre#ue&!, Distributi"&s

• A !"u&ti&+ "' the "!!urre&!es "' ea!h

resp"&se %alue "' a %ariable4 *hi!h !a& be

prese&te$ i&

) Table '"r(

) 5raphi! '"r( Fre#ue&!, 0"l,+"&2



Measures "' Ce&tral Te&$e&!,

• The %alue that represe&ts the t,pi!al "r

a%era+e s!"re i& a sa(ple "r p"pulati"&

• Three t,pes

) Mode, Median, and Mean

• N"r(al Cur%e a bell6shape$ 're#ue&!,

p"l,+"& i& *hi!h the (ea&4 (e$ia&4 a&$

("$e represe&t the a%era+e e#uall, See

Fi+ure 17892



Mode

• The s!"re "r resp"&se %alue that "!!urs

("st "'te& i8e84 has the hi+hest

're#ue&!,2 i& a sa(ple "r p"pulati"&

• Mi&i(u( le%el "' (easure(e&t is &"(i&al



Median

• The s!"re "r resp"&se %alue that $i%i$es

the a $istributi"& i&t" t*" e#ual hal%es

• Mi&i(u( le%el "' (easure(e&t is "r$i&al



Mean

• Cal!ulate$ b, su((i&+ i&$i%i$ual s!"res

a&$ $i%i$i&+ b, the t"tal &u(ber "' s!"res

• The ("st s"phisti!ate$ (easure "' !e&tral

te&$e&!,

• Mi&i(u( le%el "' (easure(e&t is i&ter%al



Measures "' Variabilit,

• A %alue "r %alues that i&$i!ate$ h"*

*i$el, s!"res are $istribute$ i& a sa(ple

"r p"pulati"&: a (easure "' $ispersi"&

• T*" !"(("& t,pes

) Range

) Standard Deviation



Range

• The $ista&!e bet*ee& the (i&i(u( a&$

(a-i(u( s!"re i& a $istributi"&

• The lar+er the ra&+e4 the +reater the

a("u&t "' %ariati"& "' s!"res i& a

$istributi"&

• Mi&i(u( le%el "' (easure(e&t is "r$i&al



Standard Deviation

• A (athe(ati!all, !al!ulate$ %alue that

i&$i!ates the $e+ree t" *hi!h s!"res i& a

$istributi"& are s!attere$ "r $isperse$

ab"ut the (ea&

• The (ea& a&$ sta&$ar$ $e%iati"& $e'i&e

the basi! pr"perties "' the &"r(al !ur%e

• Mi&i(u( le%el "' (easure(e&t is i&ter%al



INFERENTIAL STATISTICS

• Ma.e it p"ssible t" stu$, a sa(ple a&$

;i&'er< the 'i&$i&+s "' that stu$, t" the

p"pulati"& 'r"( *hi!h the sa(ple *as

ra&$"(l, $ra*&

• =ase$ "& !ha&!e "r pr"babilit, "' err"r

) C"(("&l, a!!epte$ le%els "' !ha&!e are

p > 8?1 1 i& 1??2 a&$ p > 8?@ @ i& 1??2



Statisti!s that Deter(i&e

Ass"!iati"&s

• Statisti!s that $eter(i&e *hether "r &"t a

relati"&ship e-ists bet*ee& t*" %ariables

• The %alues "' "&e %ariable !"6%ar, *ith

the %alues "' a&"ther %ariable

) Chi-square χ 2 2

) Correlation r 2



Chi-Square χ 2 2

• Use$ *ith &"(i&al "r "r$i&al le%els "'

(easure(e&t

• 0r"%i$es a (easure "' ass"!iati"& base$

"& "bser%e$ a!tual s!"res2 a&$ e-pe!te$

statisti!all, esti(ate$2 're#ue&!ies

• The $ire!ti"& "r stre&+th "' the

relati"&ship bet*ee& the t*" %ariables is

&"t spe!i'ie$



Correlation r 2

• T,pi!all, use$ *ith i&ter%al a&$ rati" le%els

"' (easure(e&t

• A (easure "' ass"!iati"& bet*ee& t*"

%ariables that als" i&$i!ates $ire!ti"& a&$

stre&+th "' the relati"&ship

) r ? &" relati"&ship24 r 18?? per'e!t

relati"&ship2

) A Br %alue a $ire!t relati"&ship24 6r %alue a&

i&%erse relati"&ship2



Statisti!s that Deter(i&e

Di''ere&!es

• Statisti!s use$ t" $eter(i&e *hether

+r"up $i''ere&!es e-ist "& a spe!i'ie$

%ariable

• Di''ere&!es bet*ee&

) T*" relate$ +r"ups Dependent t-test

) T*" u&relate$ +r"ups Independent t-test

) M"re tha& t*" +r"ups ANOVA



Dependent t-test

• Use$ t" !"(pare t*" sets "' s!"res

pr"%i$e$ b, "&e +r"up "' i&$i%i$uals

) E-a(ple pretest a&$ p"sttest s!"res



Independent t-test

• Use$ t" !"(pare t*" sets "' s!"res4 ea!h

pr"%i$e$ b, a $i''ere&t +r"up "' i&$i%i$uals

) E-a(ple Fathers a&$ M"thers



One-Wa Analsis o! Varian"e

• Use$ t" !"(pare three "r ("re sets "'

s!"res4 ea!h pr"%i$e$ b, a $i''ere&t +r"up

"' i&$i%i$uals

) E-a(ple Fathers4 M"thers4 a&$ Chil$re&



SUMMARY

• Statisti!s are use$ t" a&al,3e #ua&titati%e

$ata

• The le%el "' (easure(e&t (ust be

spe!i'ie$ '"r ea!h %ariable

• Des!ripti%e a&$ I&'ere&tial statisti!s are

use$ t" buil$ .&"*le$+e ab"ut a sa(ple

"r p"pulati"&

chapter 11 quantitative data

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