The large sample approximation leads to the following estimate for its standard deviation: σ, σ One can find several ways to compute the z statistic in the statistical literature. The number of observations is large enough, and the proportions are neither too close to 0 nor to 1.The probability p of having the property in question is identical for all observations,.The observations are mutually independent,.This z-test is based on the following assumptions: In the left-tailed test, the following hypotheses are used: In the one-tailed case, you need to distinguish the left-tailed (or lower-tailed or lower one-sided) test and the right-tailed (or right-sided or upper one-sided) test. The two-tailed (or two-sided) test corresponds to testing the difference between p – p0 and D, using the null (H0) and alternative (Ha) hypotheses shown below: Let D be the assumed difference (exact, minimum or maximum) between the two proportions p and p0. Let p0 be a known proportion with which we wish to compare p. The proportion of the sample verifying the property is defined by p = n / N. Let n be the number of observations verifying a certain property among a sample of size N. XLSTAT uses the z-test to to compare one empirical proportion to a theoretical proportion. We find that, if overall Anova result is significant, we can work further in Excel to run Post Hoc Test e.g.Test for the comparison of one proportion However, we can calculate the ‘Lower Bound’ and ‘ Upper Bound’ of the 95% confidence interval for counter checking with those on SPSS printout!!Ĥ5 Proving that same figures would be found in using Excel and in using SPSSĤ6 Conclusion After activating the ‘Analysis TookPak’ Add-in in Excel, we can have useful statistical tests to use including different Anova tests. Group 1 vs Group 2, Group 1 vs Group 4, Group 2 vs Group 3 & Group 3 vs Group 4 are found to be significantly different in their group mean respectively!!Ĥ2 The overall results are identical with that in Excel output previously:-Ĥ3 95% confidence interval Lower Bound Upper BoundĤ4 Proving that the Excel result are exactly equal to that in SPSS!!Īlthough the Excel result for the Fisher’s LSD test well matched that in SPSS, this might not be enough to prove the figures they got are absolutely being the same!. LSD = t0.05/2,DFW □□□ 1 □2 + 1 □4 = t0.025, ( ) = X = I Mean Group 2 – Mean Group 4 I = >1.4078 Significance is found on Mean difference between Group 2 & Group 4!!ġ4 Calculation of LSD (Lease Significant Difference) For Group 3 vs Group 4 LSD = t0.05/2,DFW □□□ 1 □2 + 1 □3 = t0.025, ( ) = X = I Mean Group 2 – Mean Group 3 I = > Significance is found on Mean difference between Group 2 & Group 3!!ġ3 Calculation of LSD (Lease Significant Difference) For Group 2 vs Group 4 LSD = t0.05/2,DFW □□□ 1 □1 + 1 □4 = t0.025, ( ) = X = I Mean Group 1 – Mean Group 4 I = > Significance is found on Mean difference between Group 1 & Group 4!!ġ2 Calculation of LSD (Lease Significant Difference) For Group 2 vs Group 3 LSD = t0.05/2,DFW □□□ 1 □1 + 1 □2 = t0.025, = X = I Mean Group 1 – Mean Group 2 I = Significance is found on Mean difference between Group 1 & Group 3!!ġ1 Calculation of LSD (Lease Significant Difference) For Group 1 vs Group 4 The overall Anova result reject the null hypothesis that all group means are equal! For finding exactly where the differences exist, we proceed to run Scheffe’s Test!! N Group Means to be used later Within Degree of Freedom DFw Within Group Variance MSw to be used laterĩ Calculation of LSD (Lease Significant Difference) For Group 1 vs Group 2 Please find any significant different increase of weight among the 4 groups.ĥ In Excel with ‘Analysis ToolPak’ Add-In activated, click Data, Data Analysis :-Ħ Choose ‘Anova: Single Factor’ = One-way Anova However, some chickens have died during the experiment, especially in groups with higher dosage. Completely Randomized Design Unequal Sample SizeĪn experiment with Completely Randomized Design has been started with 10 equal weight chickens in each group of Treatment A (Control), Treatment B, Treatment C and Treatment D, with increasing dosage of a new drug that might increase growing rate. But the chance of committing Type I error - It can be used in either Equal or Unequal Sample size conditionsĤ e.g. (Post Hoc = unplanned before experiment) It is the most ‘sensitive’ Post Hoc Test and most unlikely to miss sign. 1 Running Fisher’s LSD Multiple Comparison Test in Excelįor finding Inter-Groups Differences after getting significant results in overall ANOVA testĢ Fisher’s LSD Test It is also a popular Post Hoc Test.
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