Advanced Research Q3 Essay Example

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Statistical power
Statistical power according to Cohen is the probability of rejecting a null hypothesis illustrated as 1-β. This occurs when given the population effect size is not equal to zero hence the null hypothesis is false; the failure to reject it leads to a type II error. The probability of it occurring in a given population effect size, sample size and significance criterion is what is referred to as β. (Cohen 1992).According to the Neyman-Pearson theory, power (1-β) is the long-run frequency of accepting the alternative hypothesis is its true. (WC 89)

The three components that influence power

Sample size influences the statistical power as the larger the sample size the higher the power, though the large sample size leads to a decrease in the effect size and significance. (Cohen 1992). When the number of observations increase the standard deviations between the two hypotheses reduces, hence the distribution will reduce overlapping and this results in increase in the power

The effect size expresses the difference between the null hypothesis and the alternate hypothesis. When all the other factors are kept constant, the greater the effect size the greater the power. According to Cohen (1992) the degree to which the null hypothesis is false is indexed as the discrepancy between the alternative and null hypothesis and is referred to as the effect size.

The level of significance (α) is the frequency of rejecting the null hypothesis when it is true. The smaller the level of significance the lower the statistical power ,if all other factors are kept constant (Sedlemeier & Gigerenzer 1989).

If one mistakenly rejects the null hypothesis, he commits a type I error and as such the value of significance is put lower so as to reduce false rejections of the null hypothesis, this leads to a low statistical power as the probability of rejecting a null hypothesis reduces (Cohen 1992; Sedlemeier & Gigerenzer 1989). (WC 218)

Two types of a priori power analysis

These two types of power analysis are used to determine the effect size. The first one is determining how many
participants one needs. This can be determined through previous studies or by use of a pilot study. The sample size also depends on the desired power hence it is important to estimate a higher desired power so as to increase the chance of capturing the effects. The second type is “what to do with what I am going to get”. In this case the sample size has been determined and hence the need is to determine the statistical power at the different effect sizes, that is the small, medium and large population effect sizes. (Cohen 1992). The higher the effect size the higher the statistical power, though according to Chase and his colleague this should be done with caution due to procedural discrepancies (1976). A statistical power of 0.8 is considered adequate for detecting or capturing the desired effects (Cohen 2002). (WC 168)

(d) Power can be calculated post-hoc. How can this figure be used?

Post-hoc analysis involves the use of past published data to inform the present study whose variables are almost similar to the variables of interest in the present study. (Hasse 1982). Post hoc power is also known as observer power and determines the fixed level of significance, the sample size used in the study and an effect size observed in the study. The post-hoc power can be used to estimate the probability that replication of the previous data will yield a significant result. This figure can be important for the researchers when their calculated means are in the direction of the hypothesis. (WC 101)


Chase BR., & Chase JL (1976) A Statistical Power Analysis of Applied Psychological Research Journal of Applied Psychology , Vol. 61(2), 234-237

Cohen, J. (2002). A power primer. Psychological Bulletin, 112(1); 155159.

Cohen, J. (1992). A power primer. Psychological bulletin112(1), 155.

Haase RF (1982) How Significant Is a Significant Difference? Average Effect Size of Research in Counseling Psychology Journal of Counseling Psychology , Vol. 29(1);58-65

Sedlemeier P., & Gigerenzer,G (1989) Do studies of statistical power have an effect on the power of studies, Psychological bulletin, PA. 105 (2);309-316.