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TEST STDEV

Calculates the p-value of the statistical test for the population standard deviation.

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Syntax

TEST_STDEV(X, sigma, Return_type, Alpha)

X   is the input data sample (one/two dimensional array of cells (e.g. rows or columns)).

Sigma   is the assumed population standard devation. If missing, the default value of one is assumed.

Return_type   is a switch to select the return output (1 = P-Value (default), 2 = Test Stats, 3 = Critical Value.

MethodDescription
1P-Value
2Test Statistics (e.g. Z-score)
3Critical Value

Alpha   is the statistical significance of the test (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.

Remarks

  1. The data sample may include missing values (e.g. #N/A).
  2. The test hypothesis for the population standard deviation:

    $H_{o}: \sigma =\sigma_o$

    $H_{1}: \sigma \neq \sigma_o$

    Where:
    • $H_{o}$ is the null hypothesis.
    • $H_{1}$ is the alternate hypothesis.
    • $\sigma_o$ is the assumed population standard deviation.
    • $\sigma$ is the actual (real) population standard deviation.
  3. For the case in which the underlying population distribution is normal, the sample standard deviation has a Chi-square sampling distribution:

    $ \hat \sigma \sim \chi_{\nu=T-1}^2 $

    Where:
    • $\hat \sigma $ is the sample standard deviation.
    • $\chi_{\nu}^2()$ is the Chi-square probability distribution function.
    • $\nu$ is the degrees of freedom for the Chi-square distribution.
    • $T$ is the number of non-missing values in the sample data.
  4. Using a given data sample, the sample data standard deviation is computed as:

    $ \hat \sigma(x) = \sqrt{\frac{\sum_{t=1}^T(x_t-\bar x)^2}{T-1}}$

    Where:
    • $\hat \sigma(x)$ is the sample standard deviation.
    • $\bar x$ is the sample average.
    • $T$ is the number of non-missing values in the data sample.
  5. The underlying population distribution is assumed normal (gaussian).
  6. This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level ($\alpha/2$).

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