Discuss the fundamental concepts in determining the significance of the difference between means.
Answer – For some time in the field of psychology we are interested in testing the importance of the difference between two sample means.
Fundamental Concepts in Determining the Significance of the Difference between Means –
1 Null Hypothesis
2 Standard Error
3 Degrees of Freedom
4 Level of Significance
5 Two Tailed and One Tailed Tests of Significance
6 Errors in Making Inferences
1 Null hypothesis – It is a useful tool in testing the importance of differences. The null hypothesis claims that there is no real difference between the two population instruments, and the difference found between the sample means are therefore accidental or unimportant (Garrett 1981). During a study or an experiment, the null hypothesis has been explained so that it can be tested for possible rejection.
2 standard error – The primary purpose of statistical estimates is to generalize the population from a sample to some population, from which the sample is part. Standard error measurement (1) error of sampling and (2) error of measurement. Suppose we have information about the real meaning of the population, the instrument, we randomly choose 100 representative samples from the population and calculate their means and standard deviation. Standard deviation obtained from this representative sample is known as standard error of means.
3 Degrees of Freedom – When a parameter is used to estimate a parameter, the number of degrees of freedom available (d.f) depends on the restriction imposed on the observations.
4 levels of Significance – Depending on the likelihood that the difference between the instrument is to be taken as a statistically significant, the difference may be “coincidentally”. The researcher must decide on the level of Significance on which he will test his hypothesis.
5 Two Tailed and One Tailed Tests of Significance – In many situations, we are interested in finding the difference between means and population means. Our null hypothesis shows that M1 and M2 does not vary and the difference between them is zero. (i, e..: M1-M2 = 0). Whether this difference is positive or negative, we are not interested in the direction of such a difference. We are all interested whether there is any difference. For example, we hypothesized that two groups would be different from each other, we do not know which group will have high means scores and which group will be less. This is a non-directional hypothesis and it gives birth to a two-tailed hypothesis test. In other words, the difference may be in either direction and thus it is called non-directional.
6 Errors in Making Inferences – If the null hypothesis is true and we keep it or if it is wrong then we reject it, we made a right decision. But sometimes we do errors. There are two types of errors: type I error and type II error.