Question: This module focuses on inferential statistics. As a reminder, inferential statistics are used to determine the probability that a conclusion based on analysis of data from a sample is true (Norman & Streiner, 2008). The purpose of this discussion is to show the various types of hypotheses, how to identify them in an article and the importance of "significance" and a p-value.
For this discussion, use a peer-reviewed article (focused on a health study) of your choice to:
- Identify the Ho and H1
- Identify and explain what "significance" is in a general sense and in your chosen article. Be sure to discuss the p-value.
In this module, we shift gears from descriptive statistics to inferential statistics. Inferential statistics are used to determine the probability that a conclusion based on analysis of data from a sample is true (Norman &Streiner, 2008). As statisticians, we keep in mind that when gathering data on a sample of people there is a possibility for random error. In other words, measurements drawn at random from a population of individuals of interest will differ by some amount as a result of random processes.
We start by formulating a null hypothesis. A null hypothesis is an assumption that there is no significant difference between a sample mean and a population mean. We then formulate an alternate hypothesis that is mutually exclusive.
The primary goal of a statistical test is to determine whether an observed data set is sufficiently different from what we would expect under the null hypothesis that we should reject the null hypothesis.
A Health Scientist may carry out an experiment to attempt to test a particular null hypothesis, so that it cannot be rejected unless the evidence against it is sufficiently strong.
For example,
Ho: there is no difference in likelihood of heart attack between patients who took Medication A compared to those who took Medication B
H1: there is a difference in likelihood of heart attack between patients who took Medication A compared to those who took Medication B One of the most important concepts to grasp in this course is the term "Significance". Significant (in the statistical sense) means the likelihood of a particular result is probably not due to chance.
In the example above, we estimate the probability of getting the observed data assuming that the null hypothesis is true. One useful statistic commonly used across disciplines is the p-value.
The p-value may be defined as the probability of getting the observed result, or one more extreme, given that the null hypothesis is true. Researchers commonly choose in advance (i.e. a priori) a probability of less than 5% as their criterion for statistical significance. So in other words, a test result reported as p<.05 means that the likelihood of obtaining that result due to chance alone is less than .05.
Remember, we assume that the null hypothesis is true and then perform a statistical test of comparison as basis for our decision about whether to reject. There are one sided tests and two sided tests.
H0: μ1 = μ2
HA: μ1 ≠ μ2 (Two-sided test)
H0: μ1 = μ2
HA: μ1 > μ2 (One-sided test)
In the next module we will actually perform inferential statistical tests to compare sample means to population means.
Sources: Norman, G., and Streiner, D. (2008). Biostatistics the bare essentials (3rd ed.). BC Decker Inc. PMPH USA, Ltd. Shelton, CT. eISBN: 9781607950585 pISBN: 9781550093476. Available in e-Brary, accessed via Trident's Online Library.