ZSTAT() calculates the standard Z-statistic for use in many problem-solving tasks, including digital analysis. It returns an answer to three decimal places.
Use ZSTAT() to evaluate the likely frequency of occurrence of a given result in a specified period or category. The larger the resulting Z-statistic, the more unlikely the occurrence. For example, a Z-statistic of 1.96 has a significance of 0.05, representing the likelihood of a one time in 20 occurrence, whereas a Z-statistic of 2.57 has a significance of 0.01, representing the likelihood of a one time in 100 occurrence. For information on the Z-statistic, consult a statistics textbook.
You can specify the parameters for ZSTAT() as either numbers or proportions:
| • | When you specify both parameters as numbers, the function computes the Z-statistic using floating-point arithmetic. |
| • | When you specify both parameters as proportions, the function computes the Z-statistic using fixed-point arithmetic and you need to use a decimal multiplier to control rounding. |
The function format when parameters are expressed as numbers is:
ZSTAT(v1,v2,v3)
| • | v1 represents the actual count, such as a leading digit or a leading digit combination. |
| • | v2 represents the expected count, such as a leading digit or a leading digit combination. |
| • | v3 represents the total number of items being tested and must be a positive whole number greater than 0. |
The function format when parameters are expressed as proportions is:
ZSTAT(v1,v2,v3)
| • | v1 represents the actual proportion of the value being tested and must be between 0 and 1 inclusive. |
| • | v2 represents the expected proportion of the value being tested and must be between 0 and 1 exclusive. |
| • | v3 represents the total number of items being tested and must be a positive whole number greater than 0. |
Analyzer typically evaluates expressions using fixed point arithmetic and rounds the result. When using an expression within an expression for v1 and v2, you must specify the level of precision you want in the result by using a decimal multiplier. Analyzer has a precision of 8 digits, therefore a multiplier of 1.00000000 will return the greatest precision attainable. For more information, see Fixed-point Arithmetic.
Based on 10 years of previous data, you know that the distribution of worker disability claims per month is normally highly uniform. In April, May and June of this year, claims were higher by about 10 percent, averaging 220 per month instead of 200. Claims in July and August were slightly low, at 193 and 197. The total claims for the year were 2,450. To test whether these high and low results were significant, use the Z-statistic.
High Results:
The actual number of claims for April to June is 660. The expected number of claims for this period is 25 percent of the 2,450 annual claims or 612.5. The Z-statistic for these counts is:
ZSTAT(660,612.5,2450) = 2.193
A Z-statistic of 1.96 has a significance of 0.05 and 2.57 has a significance of 0.01. Thus, the probability that the higher rates of claims are due to chance is between 1:20 and 1:100.
Low Results:
The actual number of claims for July and August is 390. The expected number of claims for this period is one sixth of the 2,450 annual claims or 408.33. The Z-statistic for these proportions is:
ZSTAT(390,408.33,2450) = 0.967
This is not a very significant result. Z-statistics of 1.000 and less are very common and can typically be ignored.
Based on 10 years of previous data, you know that the distribution of worker disability claims per month is normally highly uniform. In April, May and June of this year, claims were higher by about 10 percent, averaging 220 per month instead of 200. Claims in July and August were slightly low, at 193 and 197. The total claims for the year were 2,450. To test whether these high and low results were significant, use the Z-statistic.
High Results:
The actual number of claims for April to June is represented by the proportion 660/2450. The expected number of claims for this period should be 25 percent of the 2,450 annual claims. The Z-statistic for these proportions is:
ZSTAT((1.00000000*660/2450),0.25,2450) = 2.193
A Z-statistic of 1.96 has a significance of 0.05 and 2.57 has a significance of 0.01. Thus, the probability that the higher rates of claims are due to chance is between 1:20 and 1:100.
Low Results:
The actual number of claims for July and August is 390. The expected number of claims for this period should be one sixth or 16.6667 percent of the 2,450 annual claims. The Z-statistic for these proportions is:
ZSTAT((1.00000000*390/2450),0.16667,2450) = 0.967
This is not a very significant result. Z-statistics of 1.000 and less are very common and can typically be ignored.