Hypothesis Testing
Hypothesis testing using a one sample t-test
Defining hypothesis testing
Hypothesis testing can be simple defined as an act in statistical analysis where the researcher tests the applicability/ accuracy of an assumption made about a certain population parameter. It is used to examine the plausibility of proposed hypothesis in an effort to reject or accept certain assumptions statistically.
Hypothesis testing using a one-sample t-test
A one sample t-test is used to test a hypothesis between the population mean. It is specifically used to determine whether an observed population mean parameter is statistically significantly different from a specific value. For example, a one-sample t-test would be used to determine whether the average weight of Americans is statistically different from a given average weight maybe, 70kgs or for instance the average weight of the world population, let’s say (75kgs). Hypothesis testing using a one-sample t-test involve different steps. The commonly used steps are;
- Step 1: Specifying a null hypothesis. A null hypothesis is a proposal that assumes there is no difference between given population parameters. In the case of a one-sample t-test, the null hypothesis is denoted as H0: µ = X, where X is the test specific value and µ is the mean of the population being tested.
- Step 2: Specifying an alternative hypothesis. An alternative hypothesis is a proposal; that assumes there is a difference between the given population parameter. In the case of a one-sample t-test, the null hypothesis is denoted as H1: µ ≠ X, where X is the test specific value and µ is the mean of the population being tested
- Step 3: Setting the significance levels. This is the probability that the difference in the parameters being observed might have occurred just by chance.
- Step 4: Computing the one sample t-test statistics and its corresponding p-value.
- Step 5: Determining the conclusion from the findings.
Assumptions of the one-sample t-test
When you decide that you are going to conduct a hypothesis test suing a one-sample t-test, the first step to determine whether the data being used for the analysis can actually be used to conduct an ANOVA test. This involves checking for various assumptions that are required to get valid and accurate results. These assumptions are;
- The dependent variables being examined should be measured as an interval or ratio variables (this means that they are scale of continuous variables).
- There should be independence of observations. This means that neither the groups nor individual observations should be related to one another (there is no correlation).
- The data being utilized, i.e., both variables should not have significant and extreme outliers. Outliers my end up distorting the results.
- The variables being tested should be nearly normally distributed. This is tested in a histogram, where it shows almost a bell-shaped curve for approximately normally distributed variables.
Computing the one sample t-test test
When computing a t-test’s test statistic, one will require the sample size (n), the standard deviation (σ), and the mean of the sample size (µ). Furthermore, one will require the test Parmenter the sample mean is being compared to (X). from these, you will computer the standard error using;
Difference = µ - X
Standard error of the mean = σ/ √n
Test statistic (t) = Difference / standard error
To make a conclusion about the test statistic; you will need to compare it to a value from the t-distribution table. If the test statistic is greater than t-value from the t-distribution table, we will reject the null hypothesis.
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