Small Business Framework - Research - The Legal Services Board
Small Business Framework - Research - The Legal Services Board
Small Business Framework - Research - The Legal Services Board
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Based"on"an"alpha"level"of"0.05"(which"equates"to"a"Z'value"of"1.96"in"equation"<br />
1 11 )," Table" 5.2" sets" out" some" example" sample" sizes" that" would" be" required" to"<br />
measure" a" key" statistic," in" this" case" the" percentage" of" businesses" using" legal"<br />
services,"with"varying"levels"of"precision"and"for"varying"estimated"percentages."<br />
For"example,"if"one"estimates"that"40%"of"businesses"use"legal"services,"a"margin"<br />
of"error"of"2%"(i.e."d'="0.02"above)"would"involve"level"of"precision"between"38%"<br />
and"42%."In"this"instance,"using"simple"random"sampling,"with"an"alpha"level"of"<br />
0.05,"a"sample"of"2,304"businesses"would"be"required."<br />
!<br />
Table'5.2.'Example'sample'size'calculations'using'equation'1'<br />
Margin! of!<br />
Percentage!using!legal!services!<br />
error!! 10%" 20%" 30%" 40%" 50%" 60%" 70%" 80%" 90%"<br />
1! 3,455" 6,137" 8,050" 9,197" 9,579" 9,197" 8.050" 6,137" 3,455"<br />
2! 865" 1,536" 2,016" 2,304" 2,400" 2,304" 2,016" 1,536" 865"<br />
3! 385" 683" 897" 1,025" 1,067" 1,025" 897" 683" 385"<br />
4! 217" 385" 505" 577" 601" 577" 505" 385" 217"<br />
!!<br />
Other'Considerations'<br />
In" reality," relatively" few" surveys" follow" simple" random" sampling," or" for" that"<br />
matter"(as"in"the"current"context)"can"be"reduced"to"a"single"key"statistic."With"<br />
regard" to" final" calculation" of" sample" size," stratification," clustering" and"<br />
assignment"of"selection"probabilities"should"all"be"considered"jointly"as"they"all"<br />
have" a" bearing." With" regard" to" key" statistics," surveys" of" this" type" are" typically"<br />
designed" to" answer" a" variety" of" questions," with" a" variety" of" statistics." Each"<br />
statistic"is"likely"to"have"different"requirements"for"precision"and"may"only"apply"<br />
to"subsets"of"the"survey"(as"a"consequence"of"the"statistic"only"applying"to"some"<br />
businesses"or"only"some"businesses"being"of"interest)."As"a"result,"compromises"<br />
are"likely"to"need"to"be"made"on"the"sample"design"and"sample"size"required"to"<br />
address" research" questions" within" budgetary" constraints." Precision" and" power"<br />
can"diminish"quickly.""""<br />
" Moreover,"in"practice,"rather"than"determine"the"predetermined"standard"<br />
error"for"a"key"statistic,"the"survey"may"be"constrained"by"the"money"available."<br />
In"this"case,"the"calculation"is"likely"to"estimate"what"standard"error"is"possible"<br />
(for"what"key"statistics)"given"the"constraints"(Groves"et"al."2009)"<br />
" Where" surveys" do" not" follow" simple" random" sampling," for" example,"<br />
where"cluster"or"multistage"sampling"is"used,"a"larger"sample"size"is"required"to"<br />
achieve"the"same"precision."Put"simply,"this"involves"multiplying"equation"1"by"a"<br />
design" effect" (e.g." see" Cochran" 1977" or" Groves" et" al." 2009)." <strong>The</strong>" design" effect"<br />
should"be"considered"if"the"sampling"method"progresses"beyond"simple"random"<br />
or"systematic"random"sampling.""<br />
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!<br />
11"Note,"if"you"wanted"to"be"more"confident,"for"example,"applying"an"alpha"level"of"0.01,"a"Z'of"2.58"would"<br />
be"required"in"Equation"1.""<br />
! 39!