Sign test - overview
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Sign test | Multilevel ordinal logistic regression |
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Independent variable | Independent variables | |
2 paired groups | One or more quantitative of interval or ratio level and/or one or more categorical with independent groups, transformed into code variables, plus at least one random factor | |
Dependent variable | Dependent variable | |
One of ordinal level | One of ordinal level | |
Null hypothesis | THIS TABLE IS YET TO BE COMPLETED | |
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Alternative hypothesis | n.a. | |
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Assumptions | n.a. | |
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Test statistic | n.a. | |
$W = $ number of difference scores that is larger than 0 | - | |
Sampling distribution of $W$ if H0 were true | n.a. | |
The exact distribution of $W$ under the null hypothesis is the Binomial($n$, $P$) distribution, with $n =$ number of positive differences $+$ number of negative differences, and $P = 0.5$.
If $n$ is large, $W$ is approximately normally distributed under the null hypothesis, with mean $nP = n \times 0.5$ and standard deviation $\sqrt{nP(1-P)} = \sqrt{n \times 0.5(1 - 0.5)}$. Hence, if $n$ is large, the standardized test statistic $$z = \frac{W - n \times 0.5}{\sqrt{n \times 0.5(1 - 0.5)}}$$ follows approximately the standard normal distribution if the null hypothesis were true. | - | |
Significant? | n.a. | |
If $n$ is small, the table for the binomial distribution should be used: Two sided:
If $n$ is large, the table for standard normal probabilities can be used: Two sided:
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Equivalent to | n.a. | |
Two sided sign test is equivalent to
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Example context | n.a. | |
Do people tend to score higher on mental health after a mindfulness course? | - | |
SPSS | n.a. | |
Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples...
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Jamovi | n.a. | |
Jamovi does not have a specific option for the sign test. However, you can do the Friedman test instead. The $p$ value resulting from this Friedman test is equivalent to the two sided $p$ value that would have resulted from the sign test. Go to:
ANOVA > Repeated Measures ANOVA - Friedman
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Practice questions | Practice questions | |