Chi-squared Sign Test


Chi-squared (x²) sign test of two independent samples

This test is also known as the "median test" as it compares the medians of two independent samples.

The null hypothesis is that there is no difference between the medians of the populations from which the samples were drawn.

The data consist of two independent samples with N1 and N2 observations. The median of the combined observations is calculated, and in each sample observations above and below the combined median are assigned either a "+" or a "-". The number of "positive" and "negative" signs is calculated and the Chi-square test is used to determine whether the observed frequencies of + and - signs depart significantly from the null hypothesis.

Script operation

This tool operates in much the same way as most of the others with no specific departures from the usual methods needed.

Click here for information about general script usage.

Raw sample data must be entered as multiple samples, the data being arranged in columns. Note that sample titles may be included within the output by inclusion within the input range.

 Raw data:      	   Spreadsheet output:

 Sample I   Sample II      Chi-Square Non-Parametric Sign Test
       10           6      of Two Independent Samples
       10           7   		      Positive  Negative
       10           8      Sample_I     	     7         5
       12           8      Sample_II    	     3         6
       15          12
       17          16      Median:      	    16
       17          19      Count:       	    21
       19          19      Chi-Square:  	0.4813
       20          22      d.f.:		     1
       22       	   P(CHI<=chi):       0.512143
       25       	   Chi-Critical(95%)    3.8431
       26       	   Chi-Critical(99%)     6.637

Interpretation

The calculated Chi-square probability of 0.512 includes the Yates correction for continuity. This value is below the value of 3.84 required for significance at the 5% level indicating that we have no grounds for rejecting the null hypothesis.



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