How to Interprete Significant Difference


By Anthony M. Wanjohi:

More often than not, students of research are confused between  “Significant Relationship and/or Significant Difference” when making conclusion upon testing an hypothesis.

When do we conclude that there is a statistical significant relationship  between variables? and / or when do we conclude that there is a statistical significant difference between population means?

In order to answer these questions, let us first understand the rule of thumb as guided by the following:

95% Confidence level; Significance level 5%

Significance level is the probability value (p value) that forms the boundary between rejecting or not rejecting the null hypothesis (Ogula, 1998 p. 104).  The most commonly used level of significance is .05, which means that there is a 5% probability that the  observed relationship is due to chance (confidence level of 95%).

Decision Rule

  • If probability value (p value) is  SMALLER than or equal to to .05;  REJECT the null hypothesis; there is evidence against null hypothesis. Conclude that there is a statistical significant difference, there is evidence to conclude effect.
  • If P value is GREATER than .05;  DO NOT REJECT the null hypothesis; there is NO evidence against null hypothesis; there is no effect.

If the p value is equal to or smaller than .05, we conclude that there is a statistical significant difference between parameters (H0: µ1 – µ2 = 0);  that  there is evidence to conclude that a statistical significant difference exists.

If the p value is greater than .05, we conclude that there is  no statistical  significant difference between parameters (H1: µ1 – µ2  is not equal to 0); that  there is no evidence to conclude that a statistical significant difference exists.

Note:
  • A strong statistical association does not show cause!
  • Every time we reject the null hypothesis we risk being wrong and
  • Every time we fail to reject the null hypothesis we risk being wrong

Conclusion

Thus,  ‘significant difference’ are often used when testing whether there is difference between the means of the two or more populations. Can be used with t test or ANOVA.

Significant relationship or significant association is used in situations where one is examining the association between any two sets of variables (King’oriah, 2004).

References

Easton, V.J. & McColl, J.H. (n.d). Glossary of Terms. Available online at  http://www.stats.gla.ac.uk/steps/glossary/confidence_intervals.html

King’oriah, G.K. (2004).  Fundamentals of applied statistics. Nairobi: Jomo Kenyatta Foundation.

Ogula P.A.  (1998). A Handbook on Educational Research. Nairobi: New Kemit  Publishers.

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