Inferential Statistics, Statistics Problem Example

Activity 1

P=0.5 means the standard probability of a given finding. Conventionally, a <0.5 value is always considered significant. P=0.5 would, therefore mean that if the study is to be conducted several times or done randomly, then the results would get similar reduction in 5% of the time. The p- value has been interpreted in several wrong ways making unreliable conclusions. The p-value has no probability that the null hypothesis is true or the alternative hypothesis is false. Frequentist statistics does not show any connection between probabilities and hypothesis (Levine, 2011).

The p-value is not a probability that a finding is based on chances but on assumption that every finding is based on chances. Therefore, the probability of a finding to be a chance is 100%

The p-value is not the probability of false rejection of the null hypothesis. This error is a version of the prosecutor’s fallacy- a statistical reasoning used in court by the prosecutor to argue for the guilt of a defendant.

The p-value is not the probability that when the same test is repeated the results will be the same. Measuring the degree of replicability of an experiment was done through the concept of p-rep (Levine et al., 2008).

Activity 2

Effect size is measured by comparing the mean difference between the two classes divided by the standard deviation of the control group. Statistical significance helps one to know how likely it is that these changes occur randomly and do not show differences as a result of the program. These tests provide one with evidence to either accept or reject the null hypothesis to determine whether the program had an effect. Effect size is when a difference is significant irrespective of its specific size, importance or helpful in making a decision (Sun & Fan, 2010).

Statistically significant results and clinically significant results differ. Statistical difference is the measure of any apparent difference in result between treatment and control groups are real and not due to chances. The p values and the confidence interval (C1) are the most commonly applied measures of statistical significance. The p values give the assumptions that any particular results would have arisen by chance and that with the assumptions that the new and the new and the control treatments are the same in effect as the null hypothesis. CI measures the deviation in which the actual results will fall if the trial is conducted many times. Therefore 95% of the difference would indicate the range in which the difference will fall on 95% of the occasions if the experiment is repeated severally. Clinical significance determines how large the differences in clinical effects are in clinical practice. Different measures have been devised to calculate this. Relative risk is the measure of the prevalence of the disease and can be used on populations with difference prevalence of the disease.A relative risk is the comparison of the dangers in the treatment class to the event rate in the control group. However, it has a disadvantage because it does not clarify the size of the absolute risk.The measures of absolute risk reduction (ARR) and numbers needed to treat (NNT) differ with the prevalence of the disease.ARR is the difference in the absolute risks between the treatment class and the control group.NNT is the number of patients required to treat to prevent of adverse event, and its numerical equal to 1/ARR. The level of clinical regarded as clinically significance also depend on the severeness of the disease and any potential side effect of the treatment (Weber & Popova, 2012).

NHST is the researchers’ work platform for making inductive inferences. However, this technique has encountered various discrepancies. These discrepancies can be explained in two different ways. Most text -books were revised in before 1990 when NHST was not very much controversial. The revision author only based their revisions on updating the contents about the studies and methods they cited. Another possible explanation for the failure of NHST issues in textbooks concerns the le level of depth difficulty of concepts and student’s prior knowledge. The textbooks that were reviewed were intended for master’s- or doc- toral-level students in education. Oftenly, this was as a first course in research or statistics or one taken many years after having an earlier such course (Levine, 2011). The third possible explanation is that although there is general acknowledgement that each of the topics we explored should be covered in research and statistics textbooks, there is not general agreement about how it should be covered. In this case, it is especially the case in regard on how to decide whether statistically significant information has a practical importance. There is also controversy about best practice for hypothesis significance testing (Harlow, Mulaik, & Steiger, 1997) and effect size reporting (Levin & Robinson, 2000; Robinson & Levin, 1997). Textbook authors are in most cases reluctant to put their best practice in print that may be used in the future.

Effect size statistics. This alternative is based on reporting the effect and the size observed together with the confidence interval. Confidence intervals are much better than standard errors despite the difficulty in interpreting the information. This is so happens when errors are not symmetrically distributed around the point estimate. Confidence variables can be computed for nonparametric tests including a randomization tests although the test can be very tedious. Effect size and confidence interval are basically the best choice of descriptive studies which are the most common in management of wildlife science.The confidence interval would exhibit whether the data is consistent with (a) no effect and/or (b) an effect large enough to have biological importance

Another method is the information theoretical method. This relies on the measure of relative discrepancies of a proposed model from the truth. Although the actual distance is unknown, the (AIC) and its deviations allow a relative distance for the set of candidate to be estimated (Weber & Popova, 2012).

Information theoretical method would be best in answering the question in activity 1 because it goes further to examine the deviations from the truth. The perception that the p- value would exhibit almost equal results when a test is repeated several times indicates that the probability of getting the actual figure depends on the deviations. This method employs the ability the ability to compare multiple models and to produce estimated averages over several models.

References

Levine, T. R. (2011). Quantitative Social Science Methods of Inquiry. Handbook of interpersonal communication, pp. 25-58.

Levine, T. R., Weber, R., Park, H. S., & Hullett, C. R. (2008). A Communication Researchers’ Guide to Null Hypothesis Significance Testing and Alternatives. Human Communication Research, Vol.34 no. 2, pp. 188-209.

Sun, S., & Fan, X. (2010). Effect Size Reporting Practices in Communication Research. Communication Methods and Measures, Vol. 4 no.4, pp.331-340.

Weber, R., & Popova, L. (2012). Testing Equivalence in Communication Research: Theory and Application. Communication Methods and Measures, Vol. 6 no. 3,  pp.190-213.