Research Methodology - Dr. Krishan K. Pandey

164 Research Methodology
Table 8.1: Criteria for Judging Significance at Various Important Levels
Significance Confidence Critical Sampling Confidence Difference Difference
level level value error limits Significant if Insignificant if
5.0% 95.0% 1.96 196 . σ ±196 . σ > 196 . σ < 196 . σ
1.0% 99.0% 2.5758 2. 5758 σ ± 2. 5758 σ > 25758 . σ < 25758 . σ
2.7% 99.73% 3 3 σ ± 3 σ > 3 σ < 3 σ
4.55% 95.45% 2 2 σ ± 2 σ > 2 σ < 2 σ
σ = Standard Error.
2. The standard error gives an idea about the reliability and precision of a sample. The smaller the
S.E., the greater the uniformity of sampling distribution and hence, greater is the reliability of sample.
Conversely, the greater the S.E., the greater the difference between observed and expected
frequencies. In such a situation the unreliability of the sample is greater. The size of S.E., depends
upon the sample size to a great extent and it varies inversely with the size of the sample. If double
reliability is required i.e., reducing S.E. to 1/2 of its existing magnitude, the sample size should be
increased four-fold.
3. The standard error enables us to specify the limits within which the parameters of the population
are expected to lie with a specified degree of confidence. Such an interval is usually known as
confidence interval. The following table gives the percentage of samples having their mean values
within a range of population mean bg μ ±S.E.
Table 8.2
Range Per cent Values
μ ± 1S.E. 68.27%
μ ± 2S.E. 95.45%
μ ± 3S.E. 99.73%
μ ± 196 . S.E. 95.00%
μ ± 2. 5758 S.E. 99.00%
Important formulae for computing the standard errors concerning various measures based on
samples are as under:
(a) In case of sampling of attributes:
(i) Standard error of number of successes = n⋅ p ⋅ q
where n = number of events in each sample,
p = probability of success in each event,
q = probability of failure in each event.