{"text_format":"2","workbook":"xls","n_sheets":3,"sheets":["ChiSq","Regression","ANOVA"],"not_rendered":{"charts":0,"images":1,"macros":0,"external_links":1,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"run_cost":"one","rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"ChiSq","index":0,"n_rows":37,"n_cols":13,"rows_kept":37,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["In this activity we demonstrate the equivalence of two methods for testing for equality of  "]
["population proportions: "]
[]
["Method 1 involves a chi-square test for homogeneity and method 2 is a classical test of hypothesis"]
["for two the difference between two population proportions "]
[]
["Pressing the F9 key generates new data in the observed frequency table and recomputes both the"]
["Chi-Square and z values.  "]
[]
["Observe that in each case the Chi-Square value is the square of the z-value. "]
[]
["Note also that the critical value of Chi-Square is 3.841455 and critical value of z is 1.959963. "]
["Again, the Chi-Square value is equal to the square of the z value"]
[]
[]
[]
[]
["The chi-square test",{"$nulls":5},"The difference of proportions test"]
[]
[null,"A","B",null,null,null,"p-bar 1","p-bar 2","Difference",null,null,"Pooled Estimate of proportion"]
["X",49,39,88,null,null,0.6282051282051282,0.5735294117647058,0.05467571644042235,"=TS",null,null,0.6027397260273972]
["Y",29,29,58]
[null,78,68,146,null,null,null,"z* = ",0.6734685742272505,1.9599627874084047]
[{"$nulls":7},"(z*)^2 =",0.4535599204716856,3.8414541280257235]
[]
[null,"A","B"]
["X",47.013698630136986,40.986301369863014]
["Y",30.986301369863014,27.013698630136986]
[]
[null,0.08392007535843156,0.09626126291114208]
[null,0.12732701088865478,0.14605157131345695]
[]
["ChiSq",0.45355992047168536]
[null,3.841455338005062]
[]
[]
[{"$nulls":4},0.003932186653317262]

{"sheet":"Regression","index":1,"n_rows":32,"n_cols":10,"rows_kept":32,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["In this activity we demonstrate the equivalence of the t-test for the regession coefficient in SLR"]
["and the corresponding F-test."]
[]
["Note that F = 284.24 and t = 16.86. Clearly t^2 = F."]
[]
["Similarly, the critical value of F = 7.7086 and the critical value of t = 2.7764. Again, we see that"]
["F = t^2, subject to minor rounding error."]
[]
["X","Y",null,"SUMMARY OUTPUT"]
[12,21]
[21,33,null,"Regression Statistics"]
[14,25,null,"Multiple R",0.9930370678183715]
[17,27,null,"R Square",0.9861226180613091]
[20,32,null,"Adjusted R Square",0.9826532725766364]
[24,38,null,"Standard Error",0.8104706935466809]
[null,null,null,"Observations",6]
[]
[null,null,null,"ANOVA"]
[{"$nulls":4},"df","SS","MS","F","Significance F"]
[null,null,null,"Regression",1,186.7058823529412,186.7058823529412,284.2388059701498,7.255484692576942e-05]
[null,null,null,"Residual",4,2.627450980392152,0.656862745098038]
[null,null,null,"Total",5,189.33333333333334]
[]
[{"$nulls":4},"Coefficients","Standard Error","t Stat","P-value","Lower 95%","Upper 95%"]
[null,null,null,"Intercept",4.980392156862734,1.4818847170054845,3.360849936374842,0.02828253905115431,0.8660120660021171,9.09477224772335]
[null,null,null,"X",1.3529411764705888,0.08024855658698479,16.859383321170128,7.25548469257697e-05,1.1301350028506945,1.575747350090483]
[]
[]
[null,null,null,"=FINV(0.05,1,4)","=TINV(.05,4)"]
[null,null,null,7.7086497185518965,2.776450855890289,7.708679355173918]
[]
[null,null,null,"FINV(.05,1,4) = TINV(.05,4)^2"]

{"sheet":"ANOVA","index":2,"n_rows":38,"n_cols":10,"rows_kept":38,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["In this activity we demonstrate the equivalence of the independent sampes t-test for"]
["the equality of two population means and one-way ANOVA"]
[]
[]
["A","B",null,"Anova: Single Factor"]
[21,32]
[32,53,null,"SUMMARY"]
[24,48,null,"Groups","Count","Sum","Average","Variance"]
[41,42,null,"A",7,213,30.428571428571427,46.952380952380885]
[36,51,null,"B",5,226,45.2,71.69999999999982]
[28]
[31]
[null,null,null,"ANOVA"]
[null,null,null,"Source of Variation","SS","df","MS","F","P-value","F crit"]
[null,null,null,"Between Groups",636.4023809523809,1,636.4023809523809,11.194131738533187,0.007418101765847479,4.96459051646525]
[null,null,null,"Within Groups",568.5142857142856,10,56.85142857142856]
[]
[null,null,null,"Total",1204.9166666666665,11]
[]
[]
[]
[]
[]
[]
[null,null,null,"t-Test: Two-Sample Assuming Equal Variances"]
[]
[{"$nulls":4},"A","B"]
[null,null,null,"Mean",30.428571428571427,45.2]
[null,null,null,"Variance",46.952380952380885,71.69999999999982]
[null,null,null,"Observations",7,5]
[null,null,null,"Pooled Variance",56.85142857142846]
[null,null,null,"Hypothesized Mean Difference",0]
[null,null,null,"df",10]
[null,null,null,"t Stat",-3.3457632520148843]
[null,null,null,"P(T<=t) one-tail",0.003709050882923714]
[null,null,null,"t Critical one-tail",1.8124615053238813]
[null,null,null,"P(T<=t) two-tail",0.007418101765847428]
[null,null,null,"t Critical two-tail",2.228139237558935]