Part 2. MM4XL Tools > 2. Analytical Tools > Proportion Analyst > Technicalities

Proportion Analyst

Technicalities

Proportion Analyst applies the Z test for homogeneity of two proportions when investigating whether a significant difference exists. It tests equality running a two-tailed test that determines whether there is any difference in the proportion of successes in the two samples. A one-tailed test is needed when determining if successes are higher in one of the two groups.

The null ( Significance Test of Difference of Proportion Software) and alternative (  Significance Test of Difference of Proportion Software) hypotheses Proportion Analyst sets are:

 Significance Test of Difference of Proportion Software:  Significance Test of Difference of Proportion Software or the difference

 Significance Test of Difference of Proportion Software:  Significance Test of Difference of Proportion Softwareor the difference  Significance Test of Difference of Proportion Software

The test statistic, Z, is approximated by a standard normal distribution:

 Significance Test of Difference of Proportion Software

Where:

 Significance Test of Difference of Proportion Software = Proportion of successes in sample 1;

 Significance Test of Difference of Proportion Software = Proportion of successes in sample 2;

 Significance Test of Difference of Proportion Software Sample proportion from population I;

 Significance Test of Difference of Proportion Software = Size sample I;

 Significance Test of Difference of Proportion Software = Pooled estimate for population proportion.

The probability of accepting or rejecting Ho, called p Value in the output report, is approximated by a standard normal distribution with mean 0 and standard deviation 1 (see formula NORMSDIST in Excel). The equation for the standard normal density function is:

 Significance Test of Difference of Proportion Software

The null hypothesis is rejected if the Z value lies outside the critical values from the standard normal distribution. This means, when the achieved is higher that the user stated probability the two proportions are recognized as significantly different and the alternative hypothesis( Significance Test of Difference of Proportion Software) is accepted.

 Significance Test of Difference of Proportion Software

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