Difference between revisions of "Documentation/How Tos/Calc: ZTEST function"
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− | __NOTOC__ | + | {{DISPLAYTITLE:ZTEST function}} |
+ | {{Documentation/CalcFunc StatisticalTOC | ||
+ | |ShowPrevNext=block | ||
+ | |PrevPage=Documentation/How_Tos/Calc:_WEIBULL_function | ||
+ | |NextPage=Documentation/How_Tos/Calc:_CORREL_function | ||
+ | }}__NOTOC__ | ||
== ZTEST == | == ZTEST == | ||
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=== Syntax: === | === Syntax: === | ||
<tt>'''ZTEST(data; μ σ)'''</tt> | <tt>'''ZTEST(data; μ σ)'''</tt> | ||
− | : <tt>'''data'''</tt> is a range or array | + | : <tt>'''data'''</tt> is a range or array containing a random sample from a population (population assumed to have a normal distribution). |
: <tt>'''μ'''</tt> is the (known) mean of the population. | : <tt>'''μ'''</tt> is the (known) mean of the population. | ||
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: <tt>'''σ'''</tt> is the (known) standard deviation of the population. If omitted, it is estimated from the sample data by <tt>'''STDEV(data)'''</tt>. | : <tt>'''σ'''</tt> is the (known) standard deviation of the population. If omitted, it is estimated from the sample data by <tt>'''STDEV(data)'''</tt>. | ||
− | : <tt>'''ZTEST'''</tt> calculates the z statistic | + | : <tt>'''ZTEST'''</tt> calculates the z statistic: |
:: [[Image:Calc_z_formula.png]] | :: [[Image:Calc_z_formula.png]] | ||
− | : and | + | : where ''m'' is the sample mean and ''n'' the number in the sample. When the mean and standard deviation of the population are known, the z statistic forms a standard normal distribution - that is, a normal distribution with mean=0 and standard deviation=1. |
+ | |||
+ | : <tt>'''ZTEST'''</tt> returns the '''one-sided''' cumulative probability - the area under the standard normal curve to the right of the z value (shaded blue here): | ||
+ | <center>[[Image:Calc_ztest_graph2.png]] [[Image:Calc_ztest_graph1.png]] </center> | ||
=== Example: === | === Example: === | ||
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: returns the result of a z-test on a sample A2:A20 drawn from a population with known mean 9 and known standard deviation 2. | : returns the result of a z-test on a sample A2:A20 drawn from a population with known mean 9 and known standard deviation 2. | ||
− | === | + | === Issues: === |
− | + | * Excel has referred to this as both a one-tailed and a two-tailed test. Neither is correct - the test is '''one-sided''' as described above. For example, when z = -1.5 part of the left tail and all parts of the right tail are included. This is an unconventional measure, but can be used. | |
+ | * As with all statistics, a good understanding is needed for reliable results. | ||
− | [[Documentation/How_Tos/Calc: | + | {{SeeAlso|EN| |
+ | * [[Documentation/How_Tos/Calc: TTEST function|TTEST]] | ||
− | + | * [[Documentation/How_Tos/Calc: Statistical functions|Statistical functions]] | |
− | + | ||
− | * Calc | + | * [[Documentation/How_Tos/Calc: Functions listed alphabetically|Functions listed alphabetically]] |
+ | * [[Documentation/How_Tos/Calc: Functions listed by category|Functions listed by category]]}} | ||
+ | [[Category: Documentation/Reference/Calc/Statistical functions]] |