# Manuals/calci/SIGNTEST

SIGNTEST(Array,Median,AlternateHypothesis,NewTableFlag)

• is the set of values to find the statistic value.
• is the median of the array of values.
• is the alternate hypothesis of the array.
• is either TRUE or FALSE.

## Description

• This function gives the test statistic of the Sign test.
• The Sign Test is ued to test the Hypothesis that there is no difference between two continuous distributions X and Y.
• This test is one type of the Non parametric Test.
• The sign test is designed to test a hypothesis about the location of a population distribution.
• The Sign test does not require the assumption that the population is normally distributed.
• The normality of the distribution is doubtable, then Sign test is used to find the statitic instead of one sample T-test.
• The sign test uses the sign of the differences, unlike the paired t test which uses the sign and magnitude of the differences.
• To perform this test, Consider the independent pairs of sample data from the populations .
• From this pair,it must be omitted with no differences .
• The Sign test data are having the following properties:
• 1.The differences of pairs are assumed to be independent.
• 2.Each pairs comes from the same continuous population.
• 3.The values and represent are ordered , so the comparisons "greater than", "less than", and "equal to" are meaningful.
• The test statistic is expected to follow a binomial distribution, the standard binomial test is used to calculate significance.
• The sign test can also be viewed as testing the hypothesis that the median of the differences is zero.
• The sign test Hypothesis is having the following steps:
• Step1:State Null and Alternative Hypothesis
• Two ways to state these: One sample or sample of differences, want to test specific value for the population median M.
• Null: H0:p=1/2is equivalent to M = M0.
• Alternative: Ha:p<1/2 is equivalent to or is equivalent to or Ha:p not equal to 1/2 is equivalent to
• Step2:Test statistic (no data conditions needed)
• S+ = Number of observations greater than or Number of observations with .
• S− = Number of observations less than or Number of observations with .
• Ties are not used, so use n = S+ + S−.
• Step3: Finding the p-value
• Remember, p-value is:
• Probability of observing a test statistic as large as or larger than that observed
• in the direction that supports Ha
• if the null hypothesis is true.
• Step 4:Use tables of the binomial distribution to find the probability of observing a value of

r or higher assuming p = 1/2 and .

• If the test is one-sided, this is your p-value.
• Step5: If the test is a two-sided test, double the probability to obtain the p-value.

## Example

A B
1 15 10
2 19 17
3 32 35
4 42 38
5 24 16
• =SIGNTEST(A1:B5,5,10,true)
TEST STATISTICS SIGN TEST
X Range Y Range Difference
15 10 5
19 17 2
32 35 -3
42 38 4
24 16 8
 P-Value 0.375

Sign Test