Posted: August 5th, 2015
nferential statistics are used to determine how confident we can be that the descriptive statistics obtained from the sample can be inferred to the population. It usually is not practical to study an entire population. As a result, inferential statistical tests were developed to determine the probability that the findings from the sample in a study can be inferred to the population. In other words, inferential statistical tests determine whether the same differences or similarities in descriptive statistics obtained from the sample would be found in the population if the entire population were studied. Thus, inferential statistics help us infer from the sample to the population.
All significance tests have five components: assumptions, hypothesis, p-value, level of significance, and test statistics.
he hypothesis is the scientific method used to make a prediction about a population parameter. A parameter can be a mean, median, or proportion. The tentative prediction is tested based on the measure of the variable obtained from a sample. Once the hypothesis is identified, the researcher will perform experiments to either prove or disprove the hypothesis.
The null hypothesis is symbolized by Ho. The null hypothesis is the hypothesis that an intervention does not affect an outcome or that a relationship does not exist. The decision based on inferential testing is either to reject the null hypothesis or fail to reject the null hypothesis. An example of a null hypothesis is, “Nurses working at Magnet hospitals do not score higher on job satisfaction than nurses working at non-Magnet hospitals.” Researchers typically do not believe their null hypotheses but state their hypotheses negatively because proving that something is true is never possible.
The alternative hypothesis is symbolized by Ha. It is the hypothesis that contradicts the null hypothesis and is also known as the research hypothesis. An example of an alternative hypothesis is, “Nurses working at Magnet hospitals score higher on job satisfaction than nurses working at non-Magnet hospitals.” The decision as to whether to use a null or an alternative hypothesis, or both, belongs to the researcher.
The level of significance is represented by the Greek letter alpha (α). The two most common alpha levels are 0.05 and 0.01. Of these alpha levels, 0.05 is the more commonly used. If an alpha level is not specified in a published research article, then it is assumed to be 0.05.
Going back to the normal distribution, the area under the curve of a probability distribution is the probability of any value falling in that area. If the test statistic falls in the critical region beyond the tails (p≤ 0.05 or 0.01), the probability of that happening by error is acceptably small and the findings of the analysis are statistically significant. (See the above normal distribution illustration.)
The p-value summarizes the evidence in the data about the null hypothesis. The p-value is the probability, if Ho is true, that the test statistics would fall in this value.
For example, a p-value of 0.26 indicates that the observed data would not be unusual if Ho were true. However, if the p-value equaled .01, then the data would be very unlikely and would provide strong evidence against Ho.
Thus, if a p-value in the hypothesis example is .01, then the alternative hypothesis would be true. Using the previous example, with a p-value of .01, nurses at Magnet hospitals would score higher on a job satisfaction survey in comparison to nurses at non-Magnet Magnet hospitals, and the higher scores are not likely due to chance.
he test statistic is the statistical calculation from the sample data to test the null hypothesis (e.g., t-test, chi square tests). Researchers have developed hundreds of test statistics designed to detect relationships or differences in their data. We will cover the most common test statistics in the following section.
Assumptions refer to suppositions about the type of data included in a study, the population distribution, characteristics of the population, the randomness of the sample, sample size, and the underlying theory being tested. We tend to assume that the sample represents the population in inferential statistics.
Below is the question:
Describe the inferential tests that were used in the article that you used in the first discussion (in other words, t-tests and chi-squares). Given the p-values related to the tests, how do you interpret the results? Are statistically significant findings also clinically significant? What are the recommendations based on this paper? Share some alternate explanations (mediating or intervening variables) for the results of the study.
Article: Grenier, T., Deckelbaum, D., Boulva, K., Drudi, L., Feyz, M., & Rodrigue, N. (2013). A descriptive study of bicycle helmet use in Montreal, 2011. Journal Article, 104(5), 400- 404.
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