Statistical test, like mean, standard deviation, variance, Z, t and F-tests are termed as parametric tests. This is because such suppositions are governed by the distribution of the sampled population or populations which is/or are at least approximately normal. However when the population in a specific hypothesis-testing condition is not normally distributed, then the non-parametric or distribution-free tests is employed.
Non parametric test can as well be employed to test hypothesis which don't comprise specific population parameters like μ, σ or P.
Merits of Non-parametric test:
There are five merits that non parametric processes have over parametric methods.
1) They can be employed to test population if the variable is not normally distributed.
2) They can be employed if the data are nominal or ordinal.
3) Can be employed to test hypothesis which don't comprise population parameters.
4) In most cases, calculation is simpler than in the parametric.
5) They are simpler to comprehend.
Demerits of non-parametric test:
1) They are less sensitive than in parametric that are; bigger differences are required before the null hypothesis can be refused.
2) They tend to employ less information than the parametric tests.
3) They are less proficient than their parametric complements if the suppositions of the parametric are met.
Difference between non-parametric and parametric tests:
a) Might be employed by real observations or by observations transformed to ranks.
Are employed merely by real observations.
b) Might be employed by observations on nominal, ordinal & interval scales.
Usually limited to observations on the interval scales.
c) Compare medians
Compare means and variances
d) Are appropriate for data that are counts
Counts should be transformed
e) Data are 'distributed in free' that is, should not be normally distributed.
Data are needed to be normally distributed and to encompass similar variances
f) Are appropriate for derived data example: proportions and indices.
Derived data might first be transformed.
The Sign test:
The simplest non-parametric test is the sign test for the single samples. It is employed to test the value of a median for a particular sample. In the Sign test, you:
a) Hypothesize the particular value for the median of a population.
b) Choose a sample of data and compare each and every value by the conjectured median.
c) Allocate plus sign when the data value is over the conjectured median.
d) Allocate minus sign when the data value is beneath the conjecture median.
e) And zero (0) when it is similar as the conjecture median.
f) Compare the number of plus and minus signs and avoid the zeros.
g) When the null hypothesis (Ho) is true, the number of plus signs must be approximately equivalent to the number of minus signs.
h) However if Ho is not true, there will be disproportionate number of plus or the minus signs.
Kruskal - Wallis Test:
The Kruskal - Wallis test, at times termed as the H - test is a non- parametric test that can be employed to compare three or more means, where the suppositions for the ANOVA test: populations are normally distributed and the population variances are equivalent and can't be met. In Kruskal - Wallis test, each and every sample size should be 5 or more with M-1 degrees of freedom, where m = number of groups.
The distribution in kruskal - Wallis can be estimated by the chi-square distribution.
Formula for Kruskal-Wallis Test:
H = 12 [(R12/n1+ R22/n2 + ........ + Rk2/nk) - 3 (N + 1)]/N(N+1)
R1: Sum of ranks of sample 1
n1: Size of sample 1
R2: Sum of ranks of sample 2
n2: Size of sample 2
Rk: Sum of ranks of sample K
Nk: Size of sample k
N: n1 + n2 + ..... nk
K: number of samples
Spearman Rank Correlation:
The spearman rank correlation coefficient, symbolized by rs, is the non- parametric equivalent of the Pearson coefficient employed for testing hypothesis if samples acquired are not normally distributed. It can be employed if the data are ranked. When the two sets of data encompass the similar ranks, rs will be +1. When the ranks are in precisely the opposite way, rs will be -1. When there is no relationship among the rankings, then rs will be near 0.
The formula for spear rank correlation is represented as:
rs = 1 -[(6∑d2)/n(n2-1)]
Where: d is the difference in ranks and n is the number of data pairs.
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