Chapter 11 Quantitative Data
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Transcript of Chapter 11 Quantitative Data
8/18/2019 Chapter 11 Quantitative Data
http://slidepdf.com/reader/full/chapter-11-quantitative-data 1/25
QUANTITATIVE DATA
ANALYSIS
Chapter 11
8/18/2019 Chapter 11 Quantitative Data
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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"
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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
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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
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I&ter%al Measure(e&t
• Thir$ hi+hest le%el "' (easure(e&t
• Attributes "r resp"&ses !ate+"ries "r a
%ariable are ) Mutuall, e-!lusi%e
) Ra&. "r$ere$
) Equal distance from each other
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Rati" Measure(e&t
• /i+hest le%el "' (easure(e&t
• Attributes "r resp"&ses !ate+"ries "r a
%ariable are ) Mutuall, e-!lusi%e
) Ra&. "r$ere$
) E#ual $ista&!e 'r"( ea!h "ther
) Based on a true 0 point
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COM0UTER A00LICATIONS
• Variables (ust be !"$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"
$eter(i&e *hi!h statisti!al tests t" use
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DESCRI0TIVE STATISTICS
• Su((ari3e a %ariable "' i&terest a&$
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,
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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
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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
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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
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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
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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&$e&!,
• Mi&i(u( le%el "' (easure(e&t is i&ter%al
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Measures "' Variabilit,
• A %alue "r %alues that i&$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
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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
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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"& $e'i&e
the basi! pr"perties "' the &"r(al !ur%e
• Mi&i(u( le%el "' (easure(e&t is i&ter%al
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INFERENTIAL STATISTICS
• Ma.e it p"ssible t" stu$, 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
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Statisti!s that Deter(i&e
Ass"!iati"&s
• Statisti!s that $eter(i&e *hether "r &"t a
relati"&ship e-ists bet*ee& t*" %ariables
• The %alues "' "&e %ariable !"6%ar, *ith
the %alues "' a&"ther %ariable
) Chi-square χ 2 2
) Correlation r 2
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Chi-Square χ 2 2
• Use$ *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 $ire!ti"& "r stre&+th "' the
relati"&ship bet*ee& the t*" %ariables is
&"t spe!i'ie$
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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 $ire!t relati"&ship24 6r %alue a&
i&%erse relati"&ship2
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Statisti!s that Deter(i&e
Di''ere&!es
• Statisti!s use$ 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
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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
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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
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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$re&
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SUMMARY
• Statisti!s are use$ 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"&