# 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,$e$, as an input. It is computed as follows:

• For Pick One and Date questions: $e=1/k$, where $k$ is the number of cells for which Not Duplicate is 1 (i.e., all the non-NET and duplicated cells).
• For Pick Any questions: $e=k^{-1}\sum^k_{i=1}p_i$, where $p_i$ is the proportion of observed in the ith cell for which Not Duplicate is 1.
• For Pick Any - Grid questions: $e$ 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: $e$ is the average of the proportions for the same category in all the variables (e.g., the $e$ for Very dissatisfied is the average of all the proportions for dissatisfied).