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V(FKG7aK˵Ri'pHCZeU(0xL!=85BNd tY3y"~'*@ K/AK[Wf.ي\r@tlA9iظS7fqNݩ !xjmltBgdnVk _ѿ2cFZmJ lkkeo@:o5o@6^XkxMf:n 9ᅯ|ç(Ȇ2Cy\t +"5m@P=$rfHυd(h{WϟWϟ<|vGN~ou97p: ߿?ew~ TԢ?ٓ_|7=mUx&D|3ĸ8D?ƴ*$Nţb}{Ze^?p b;݌9kqeᦞBsqo6NvNSَcé#;~@:Ppɇ ݧ>84Ag fjqzH < sh '>}*ᷰ&":鴡Gqԉ>;&w$̬ΰژ*cd>􏦱<h+|!8{8>ܥ#Ǥ7uj;:޽p[<7Nuy}EDmz=1Vot{C{'6[d|H #لKX. j9s$,᧮d62HpUq/lV2Dpp4^e@b;jGvxERjdD+Z\ɕoo2Y]lucil˚bs@K`dv7DpDw",& Mr#1 3\anbWЌ=#cd H;gA SAt5Z[,EG`cuy5@!Κ3 hR1Q3k VcN8e vm ͫ4=JޜNV.-fp^BoibOW?+oċ5~1%5p|74aڎ5jaDqc,3!T~ jCoE /5}ɤUYjfX/xZ{lm">'&ʝΩŋ$;gڎͥ"{DahXCL`G)>xށ1dO=akIIڬgd>"珒 [BSIE6h-\\EjY /-\JeRͧ>[oZWK e {Y2{P|mހ2uzrăOѫg/,:6MnPK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-!pO[Content_Types].xmlPK-!֧6 -_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-! mutheme/theme/theme1.xmlPK-! ѐ' theme/theme/_rels/themeManager.xml.relsPK] :  I   ` ( _ 0 `/ `  p H0e0e?Title 1 /    k#Quantitative Statistics: Chi-Square$ $  $y  `  vh`U0e0e ?Subtitle 2"PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*ŀӚܠ7#KOiʰ!}F' drs/shapexml.xmlVMo7 x-}K`) -B Gc˕[H}$WbP$z3ÙyofJ4z{ﺜI-L^<\]s<霔rOgfpnVz8w؊L&’5քF]R]jtSb֫(ž@9g0UM~׵>:9~"[ (=j t>[Content_Types].xmlPK-!]  ,_rels/.relsPK-!}F' (drs/shapexml.xmlPK-!{ˣdrs/downrev.xmlPK'    6ScWk 242  Session 7 Slides u @` ï+-f3f3B_u80___PPT10.#J ,$d (  d' d  pX?R0e0e?Title 11:   cChi-Square Test of Independence     d   S0e0e?,Content Placeholder 2"U O PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*ŀӚܠ7#KOiʰ!V!drs/shapexml.xmlYmo6>`!umD)ǀX Ej$8{b0.)[|#=㏛B06*#&T\닃KD=}@]H62'9!M~lٖ8Y#l4b+pE[ru:hN%P $ FjY-#$p3P G_L"P2wD"+n=%hc2!WsSG$? wWyhi uy>Gd[zPf$>w&Y&wxEe-BXv)ٕ.ٕ$~)ԁ#= abqJ `LJo%ĒF ]/Idcǻ؟{-m .66ބ-hs m֥穣շ#(4_+) L';C|Ug@'6Pn =l91qI8ݥ&{4iS]{SM$' @GǸ;@ UnһSE9`[R)Yy?K*Pjus4AyU!'(;Ύ~t*s>_'|mL_x D#:<PK!\drs/downrev.xmlDQK0C/cKu8GA*M|6wmY$koAjЍIMaUmJu<E5paՂRe{.SBBhS)}Q&?-btT׍OTPQ/Fl~[Content_Types].xmlPK-!]  ,_rels/.relsPK-!V!(drs/shapexml.xmlPK-!\?drs/downrev.xmlPKD_:}   bChi-Square (X2) is a statistical test used to determine whether your experimentally observed results are consistent with your hypothesis. Test statistics measure the agreement between actual counts and expected counts assuming the null hypothesis. It is a non-parametric test. The chi-square test of independence can be used for any variable; the group (independent) and the test variable (dependent) can be nominal, dichotomous, ordinal, or grouped interval. Z Z c  c  @` ï+-f3f3B_u80___PPT10.nO J ) ! h (  h& h  pU0e0e?Title 11:   bChi-Square Limits & Problems    h  (U0e0e?,Content Placeholder 2" PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*ŀӚܠ7#KOiʰ!#drs/shapexml.xmlZYo6~/@BE mojYゖX E$8bmzl[ 1C'owb[il^r&uR˃cά:2~sREb@6bqld!웲sYi 5H+j05?RzZviX|̙(&[*MRi؈(@͢LlCx Ij.7`6xzZ4(M |2OG| ٱ-2S|-i'"*lDαh:.@Lp:DJVe9h] )It¢"I  -Ժ^=>81 3P *%RYds)\%G0ԍ0V}1X~4RQeE^?Am̥>xB䆞Ɛ gkRcs &\gwҐ%{\$o*B] +UNǂ[|;͍C^J̕ [<5VQ4("Z#hU?!zp'ygde2q8녾yʹ]{v]Bw!EBH4g&hԝ _ 3 U0k aDr/_op:] #3>b^S3>x5>dh25sm2 f4!' Osb>aꀿ t|쳁>賁rBB_Hx,`PNpFCE_m?7Wr_tj+= L\(~H% \~4Npi_PK!b2drs/downrev.xmlDKK0!\Z|P Vq^͝6L$v.b4,4rJay"YEpɌ ~k 6RaCa:9o(k< nZye7Ґ顡Alv,w dx~6>܃[Content_Types].xmlPK-!]  ,_rels/.relsPK-!#(drs/shapexml.xmlPK-!b2drs/downrev.xmlPKg:   Implying cause rather than association Overestimating the importance of a finding, especially with large sample sizes Failure to recognize spurious relationships Nominal variables only (both IV and DV)  P Z(ccOc c ,cc(c @` ï+-f3f3B_u80___PPT10. J l( q l l  pHT0e0e?Title 1M:   [Chi-Square Attributes  { l  U0e0e?,Content Placeholder 2" PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*ŀӚܠ7#KOiʰ!by3drs/shapexml.xml[mO8~+_OlK_"8#rSp_N'A$yf&f2ZmBvĄJY^ČjeD }:rdJfeFeͭ-GI"CQ 9Vrr[9TtGI9Jnƚe8FLKʂ%Oļ3Y'jj!i\ H3Ϳa0U]ZDS-oGΰ78 iGT`4ep7G6ݽn$#,oݽv2zAƼd.-qOq=OW B7͡KuSA4:L3j`J=W #[5-z"/=U2!VX~dtVLߜKhiS [Y iJ\]9*/z&\)f;h­ˈDz hj#:N)бphh•U˜+8x,U/ ϔ8m X8iEkE(5ajtq,X@?' V_QM{"`ޖ"E/&Gssm{Fp}NiAcL  л^Y^y̠8jtzIq):bbZb9 !Ee݉?\wʍv77E,D*V'~~2(.,򿊙W>ťXF8sFѭ+Kn, T$RT],-HvvYPgF*.x\J̽c2{(Vq}3 2c)8,A] J׸%\rKi M5 d/|o07 +we:ݲw٨yC1?(Qu5/|t.p"ӾnY7PTia#1nR)U6N\~]/ӛJ?Q|[u ub $Xݶb.ݿ` >[AWnl@uΫHK.^/RM}tY}\oק +|X|.ڄa꺹79w5h7{|8gְ".CT٘k~޼_aMV˵.jҟR9Kݩ** 8TܽL wu@&*;"֔C?ll2?y&Q ujCWeg(up ^M+GأwDZ_F- ШMS PK!#T,drs/downrev.xmlDMK@Eaxb'Z;-*Alf^̛83MB{93[ 9_[Vp;N@V\*mn |@X&g_^0ն眺M(EOQABJ鋊 mcw`ѕR;#4.IC-VT7'`˶:pߓgwRW@CZV0q_9@NAtPK-!2<>[Content_Types].xmlPK-!]  ,_rels/.relsPK-!by3(drs/shapexml.xmlPK-!#T,drs/downrev.xmlPKO:  ___PPT9 A chi-square analysis is not used to prove a hypothesis; it can, however, refute one. As the chi-square value increases, the probability that the experimental outcome could occur by random chance decreases. The results of a chi-square analysis tell you: Whether the difference between what you observe and the level of difference is due to sampling error. The greater the deviation of what we observe to what we would expect by chance, the greater the probability that the difference is NOT due to chance.  q %CC C C tC CC-c  # @` ï+-f3f3B_u80___PPT10.HJ p( q p$ p  pV0e0e?Title 11:   `Critical Chi-Square Values  ( p  V0e0e?,Content Placeholder 2"V P PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*ŀӚܠ7#KOiʰ!h,drs/shapexml.xmlZ[O8~_iRZaHEي2G&8Y~~Nh)H ʤėc2Wl! w]Τ$xysșuB'BZFVZ矎ʑ-k;*#>wu:6\wE)5¡j;Vj'Uwri~bZN aY=δȱYF*xYĈ/7LK tӹ('u:-԰ߓi昢)/dRd_Ӡ8[%Uƿ /=ͅG;p]x]L'4B]CBY"K1ՠ1Rp?D@YNn } 7T:"Mbϖ$vl!0pM2mH FaEpM5wV)x2p%Q 8Y5nU;۬:ݖ2Ed'HIrVf.i*cר˥w8L%;,"tv#nLhؐ4bXiQ#>Ͷ ;SR["`@ۈ#>|r=bIi9 WOd&$6t u|Oďr~Z۰zncrWcCL{%]Y1CB ߐ;~t@olq۩07%>V$[dRB{j5Zsu A)wRhmnSgg= /(R}[k_%_!G} KoCblSμ/jh~quo71QY \ϯ jnl)<PK!q3drs/downrev.xmlDMK@Eax7NX%kA"+.=3Ihf&L;˽Y݈A$ VզDO | aZPloB)"TJ_TOl&v4])>u#&5&>ű<۟L?mЍ77y".u}zSSj%!Dh-A.PK-!2<>[Content_Types].xmlPK-!]  ,_rels/.relsPK-!h,(drs/shapexml.xmlPK-!q3?drs/downrev.xmlPKE:   Critical values for chi-square are found on tables, sorted by degrees of freedom and probability levels. Be sure to use p < 0.05. If your calculated chi-square value is greater than the critical value calculated, you reject the null hypothesis. If your chi-square value is less than the critical value, you fail to reject the null hypothesis|Y PcZ c Cx     =      @` ï+-f3f3B_u80___PPT10.`%UJ v n tV (  t: t  p V0e0e?Title 1:   vHypothesis Testing with X2.    t  x V0e0e?,Content Placeholder 2"PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*ŀӚܠ7#KOiʰ!p~drs/shapexml.xmlXmk8~pAM杺K[A.(*K>IN{Fdpe{,GH%~ܔu ?LdO۫1g eLtٯVSW1k7v:.]RcNe JuN) 0^/Vz[Vd ?LK^!JreT&-N5*Y;ana1- ihFV+Ix7OdFYbm^N9'h TS,h0e `75 Eժ\쉤cP߃&٣pVr.~F=trwDQf M by#MY ?Ӌ*%2n[1jBn6d`;/$7yᙢ)odVitI(I:1Dw"X덇_5 B3+G-PPqV,M)f>yp f"+yS,cI*tB-wu>fxa8׬;|貾T@2r%щ4"򁆖kY/:0#1\p*2% 8 DY(\ $+LJ '\Gzy(6)IUGL |ˢ41m¥>@Fzc 2%Xʸ-6AZd8PFHB] 'UA06䡝nҤ6WRрHqFxi.?,WhU9i(e¶s֝LnjҠi4 mQJǮ#1h"o>"F+u;~6FΟ;v^@F#"=Ͼ-#Žħ5ߛ+NRcR%?  [XS?a 0W]v]@$?. @E-"'^l)ww{_C maϹ{N8Abܷٞeh[zyE%$n15ᾧK8n' \Z΄PGx'µ#oۮ%H"u$KBg Th_PK!ku#rdrs/downrev.xmlDMK@EB nԢi)Dg5 ̋3$.tys9eojђ[qlκnkJS͝P STPФR$~ ؝ 1Bj]Z'ɣ4XPbC/%(>ٳh=1Ei*A)n4܂\ʰ-!2<>[Content_Types].xmlPK-!]  ,_rels/.relsPK-!p~(drs/shapexml.xmlPK-!ku#rdrs/downrev.xmlPKY:   qTo test the null hypothesis, compare the frequencies which were observed with the frequencies we expect to observe if the null hypothesis is true If the differences between the observed and the expected are small, that supports the null hypothesis If the differences between the observed and the expected are large, we will be inclined to reject the null hypothesis \q P Zacc c  @` ï+-f3f3B_u80___PPT10.xJ x( q x$ x  px&V0e0e?Title 11:   `Chi-Square Use Assumptions  q x  hRV0e0e?,Content Placeholder 2") # PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*ŀӚܠ7#KOiʰ!P27drs/shapexml.xml[[o6~@uHvu4@Yg)k(R'~!XJdmj7i|Ƌ޼]] mBMW I.dzUe4&z{/oʉ)+3)rx)rn^P(K sW}+0BYn1P.{~LEJ]˙TjYLS<ǐDžhfbYDh6zumߐ"45IhlQTƄvi'@ Z.Aj xo0u}4ZOǸi*cI;|'E2z|0E`&'beYhoLp4^;"=%nfrbWZ/{P& &b53Ϳ"bOexw8iֽ GfɢYV$scidC&\%j^ԆUjcV.%lz_̗:5n֥ {T",K!Kxx+i"biǯg%!k)Voиo\:~!% f*$X"3^TӗБk3 ]Wu1,*{c!dx[vA DZBúQjVmԫKձBcpZ/S7PPkQoni܇:N0qfK@MO%O2癄 Kê:h-_x)LI6O]Vyd3t q+ x]Hduv T1w] MRKƃŤuEds݈?!3rl"u$C^IE$Bf e|%*ٲ tr:dCoo!tZ@mmuVQP6 -W;6)NAlj4{/322M< Rep֠>GH;UBU 6wNtJf\szm}(nځ2V#!P BɇDľ(C#h/ ]8o?~ѺCx¯eoȏw/ov ^FwaU6;'CHF4r})=a3FnL`c &ܖV޺`m΢>=w+ըm줱7w;Sׯ;bF90~|(^<f`cW|!=.vWm{:m NAZ7[NeQ =L%ora]6Z),?٤vS:vf>׷.p;.llٲNs3ݳ٦6ڇNYWB"LVS9t„밭Yײ/=豫ѱG!=p劅4ʰ!;R/Ƿɲ԰.泾ُM1![Content_Types].xmlPK-!]  ,_rels/.relsPK-!P27(drs/shapexml.xmlPK-!;Rdrs/downrev.xmlPK :  ___PPT9 Normally requires sufficiently large sample size: In general N > 20. No one accepted cutoff  the general rules are No cells with observed frequency = 0 No cells with the expected frequency < 5 Applying chi-square to very small samples exposes the researcher to an unacceptable rate of Type II errors. Note: chi-square must be calculated on actual count data, not substituting percentages, which would have the effect of pretending the sample size is 100. 3 FC F F nF Z2C    {  $$((` ï+-f3f3B_u80___PPT10.J \T|<( q |J |  pnV0e0e?Title 1:   Using SPSS for Calculating X2 : ff ffff   |  sV0e0e?,Content Placeholder 2"> 8 PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*ŀӚܠ7#KOiʰ!EL drs/shapexml.xmlYO6>iRZ Hl[E9G&pv_c筰NwZ"<69y{f1gRE黈;: -#(-O'– .ʈo+72]QJ ^Z\8nTiva\&(J?ʥ!(4,K"~9(&[*Mi؄j(`U$-&%F|:wa`A4ӘaMZn`6p>9ղAJr_XlSi'bQ)g0`: b!g!1x#%~erEHk ypFr~6)Ls Y9/ Ea)B^D5F .R+*cҡeƺgaJF এj#JÕu,ijY4sLѐ2b`ipi(VQufS_ zD4*!k+FB;PqFWOu x)qIQg^EY3\llC-+cM2ϖ2vAPɥM%e:d?I hO殫 Rԯ$0c8">ʡZW9ʏHX9sLњ"ˤi9+3o.E)TyJw.?8(q׉uHD㯗Ij;b~*,΍{Vhw [ wS7=CKC XHZ RD/T$ZX27_oPK!%drs/downrev.xmlDMK@EB nԢ-R b3fęi{˹Ū7hʲ8A[]qYcm\j9Z`m[jw>*ϰ2Ƕ!:!±p$+%6Xڝ!۟M澧ѷ6԰{_Գ0.Ұ􁜂ѣ%ʰ-!2<>[Content_Types].xmlPK-!]  ,_rels/.relsPK-!EL (drs/shapexml.xmlPK-!%'drs/downrev.xmlPK-Q:   ,Conceptually, the chi-square test of independence statistic is computed by summing the difference between the expected and observed frequencies for each cell in the table divided by the expected frequencies for the cell. We identify the value and probability for this test statistic from the SPSS statistical output. If the probability of the test statistic is less than or equal to the probability of the alpha error rate, we reject the null hypothesis and conclude that our data supports the research hypothesis. We conclude that there is a relationship between the variables. If the probability of the test statistic is greater than the probability of the alpha error rate, we fail to reject the null hypothesis. We conclude that there is no relationship between the variables, i.e. they are independent. 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