Type-I Error Definition in Hypothesis Testing
In statistical hypothesis testing, we evaluate a null hypothesis ($H_0$). Decisions made during this process can lead to errors. Understanding these errors is crucial for drawing accurate statistical inferences.
Understanding Hypothesis Testing Errors
There are two primary types of errors that can occur when testing a null hypothesis ($H_0$):
- Type-I Error: This error occurs when the null hypothesis ($H_0$) is actually true, but we decide to reject it. It is also known as an alpha error or a false positive.
- Type-II Error: This error occurs when the null hypothesis ($H_0$) is actually false, but we fail to reject it. It is also known as a beta error or a false negative.
Decision Outcomes in Hypothesis Testing
The relationship between the actual state of the null hypothesis ($H_0$) and the decision made based on sample data determines the outcome. The table below summarizes the possibilities:
| Actual State of $H_0$ | Decision Based on Data | Outcome |
|---|---|---|
| $H_0$ is True | Reject $H_0$ | Type-I Error |
| $H_0$ is True | Fail to Reject $H_0$ | Correct Decision |
| $H_0$ is False | Reject $H_0$ | Correct Decision |
| $H_0$ is False | Fail to Reject $H_0$ | Type-II Error |
The question asks specifically about the definition of a Type-I error. Based on the standard definitions in statistical inference, a Type-I error is precisely the scenario where we reject the null hypothesis ($H_0$) when it is, in fact, true.
Important Questions from Hypothesis testing
- Assertion (A) : When sample size is small and/or data are badly skewed (so that assumption of normality is doubtful) parametric methods are not applicable.
Reason (R) : In parametric tests we can assume that scores upon which our statistics are based are normally distributed in the population.
Code : - Arrange in order the steps in testing for statistical significance :
(i) Select the statistical test to be applied
(ii) State the research question
(iii) Compute the test statistic
(iv) State the null and alternate hypothesis
(v) Compare the test statistic with the critical value
(vi) Interpret the results.
Code : - When Ho is rejected and infact it is true, the researcher is committing a :
- Assertion (A) : Assumption free tests are some what less powerful than parametric techniques when assumption for the latter are met.
Reason (R) : Assumption free tests are less powerful because the researchers do not use scientific sampling methods.
Code : - Arrange in order the steps in hypothesis testing about a single population mean using the normal curve model :
(a) Decide of n and draw a random sample
(b) Reject/retain Ho on basis of z calculated
(c) Calculate $\bar{\text{x}}$ and $\sigma_{\bar{\text{x}}}$
(d) Identify $\alpha$ level
(e) Define the target population
(f) Specify Ho and HA
(g) Calculate z-score
Code :
