Runs Test of Randomness


Posted June 3, 2009

Run test of randomness is a statistical test that is used to know the randomness in data. Run test of randomness is sometimes called the Geary test, and it is a nonparametric test. Run test of randomness is an alternative test to test autocorrelation in the data. Autocorrelation means that the data has correlation with its lagged value. To confirm whether or not the data has correlation with the lagged value, run test of randomness is applied. In the stock market, run test of randomness is applied to know if the stock price of a particular company is behaving randomly, or if there is any pattern. Run test of randomness is basically based on the run. Run is basically a sequence of one symbol such as + or -. Run test of randomness assumes that the mean and variance are constant and the probability is independent.

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Procedure for run test for randomness:

Hypothesis: To test the run test of randomness, first set up the null and alternative hypothesis. In run test of randomness, null hypothesis assumes that the distributions of the two continuous populations are the same. The alternative hypothesis will be the opposite of the null hypothesis.

Calculation of statistics: In the run test of randomness, the second step is the calculation of the mean and variance. The mean and variance in run test of randomness is calculated by using the following formula:

Mean:

Variance:

Where N= Total number of observations =N1+N2
N1=Number of + symbols
N2=Number of – symbols
R= number of runs
If the run test of randomness is sustainable with the null hypothesis, then we can expect the following properties of normal distribution:

Decision run, in run test of randomness: If the calculated value of the run test of randomness lies within the preceding confidence interval, then do not reject the null hypothesis. If the calculated value of the run test of randomness lies outside the preceding confidence interval, then reject the null hypothesis.

Assumptions in run test of randomness:

1. Data level: In run test of randomness, it is assumed that the data is recorded in order and not in a group. If data is not in order, then we have to assign the mean, median or mode value to the data.

2. Data Scale: In run test of randomness it is assumed that data is in numeric form. This condition is compulsory in run test of randomness, because in numeric data, it is easy to assign run to the numeric data.

3. Distribution: Run test of randomness is a nonparametric test, so it does not assume any assumption about the distribution.

4. In run test of randomness, the probability of run is independent.

Run test of randomness and SPSS: These days, statistical software makes very easy calculations of the run test. Statistical software performs the run test of randomness. In SPSS, run test of randomness can be performed by selecting the “run test” option from the nonparametric options available in the analysis menu. As we select the run test option, a window appears with the variable list. Select the variable for the run test from this window and drag it into the test variable list. If data is not in order, then select the “cut if” point. Select the “significance level” and “descriptive statistics,” from the option menu. After selecting these options, click on the “ok” button. Results of the run test of randomness appear in the SPSS result window. In SPSS, the output probability value is used for making the decision of whether we are going to accept or reject the null hypothesis. If the probability value of the run test of randomness is greater than the predetermined significance value, then we will accept the null hypothesis. If the calculated probability value is less than the predetermined significance value, then we will reject the null hypothesis.


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