# One Sample Tests - Proportions

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Significance Tests on Grids | |

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The significance tests used for proportions is determined by whether or not the data is weighted and by the **Proportions** setting and the **Weights and significance** setting in Statistical Assumptions.

If Proportions = **Non-parametric**: One Sample Score Test of a Proportion

If Proportions = **z-Test**:

- Data is not weighted: Z-Test of a Proportion
- Data is weighted: Complex Samples Z-Test of a Proportion

If Proportions = **t-Test**:

- Data is not weighted: t-Test of a Proportion
- Data is weighted: Complex Samples t-Test of a Proportion

If Proportions = **Quantum Proportions** or **Survey Reporter Proportions**: Quantum and Survey Reporter t-Test of a Proportion

Each of these tests has an expected value,[math]\displaystyle{ e }[/math], as an input. It is computed as follows:

- For Pick One and Date questions: [math]\displaystyle{ e=1/k }[/math], where [math]\displaystyle{ k }[/math] is the number of cells for which Not Duplicate is 1 (i.e., all the non-NET and duplicated cells).
- For Pick Any questions: [math]\displaystyle{ e=k^{-1}\sum^k_{i=1}p_i }[/math], where [math]\displaystyle{ p_i }[/math] is the proportion of observed in the
*i*th cell for which Not Duplicate is 1. - For Pick Any - Grid questions: [math]\displaystyle{ e }[/math] is the fitted value from a log-linear model fitted to the observed proportions, with additive main effects for rows and columns.
- For Pick One - Multi questions: [math]\displaystyle{ e }[/math] is the average of the proportions for the same category in all the variables (e.g., the [math]\displaystyle{ e }[/math] for
`Very dissatisfied`is the average of all the proportions for`dissatisfied`).