Our previous discussion covered the prerequisite knowledge base for hypothesis testing and introduced the hypothesis test for a single population mean, along with some data examples.
For more information about perquisition knowledge, please refer to:
2.2 Parameter Estimation_Inferential Statistics (1)
2.3 Probabilities and Significance level_Inferential Statistics (2)
2.4 Sample vs. Population: Inferential Statistics (3) (σ² Known)
2.6 How to identify a one-tailed or two-tailed test?
These templates explain some fundamental concepts for hypothesis testing.
For more information about a single population mean hypothesis test, please refer to :
Template 2.4, "Sample vs. Population: Inferential Statistics (3),"
Template 2.5, "Type I and Type II Errors in Hypothesis Testing."
These templates illustrate scenarios involving known and unknown population variances ( σ² known vs. σ² unknown).
1.Review of Hypothesis Testing prerequisite knowledge:
In prior discussions, we thoroughly examined key concepts related to hypothesis testing for one population and expanded our focus to methodologies relevant to two populations. Below, I summarize the key points covered with this perquisition knowledge and one population hypothesis testing example; you can find the details in the related template:
2.Parameter estimation
Point Estimation
Interval Estimation
Hypothesis testing relies on parameter estimation, but we must clarify its specific objectives and grasp some fundamental definitions related to parameter estimation.
From “2.2 Parameter Estimation_Inferential Statistics (1)”, you can find these related key concepts there:
parameter to be estimated
estimator
estimated value
parameter estimation
point estimation
interval estimation
confidence level
confidence interval
Unbiased estimator
Effective estimator
consistent estimator
Fully estimator
3.Low probability event and Significance level
Random sampling error is consistently a consideration in statistical analysis. Based on this principle, we have detailed both Two-tailed and One-tailed tests. Also, seven needed concepts :
Low Probability Event
Region for acceptance
Region for rejection
Significance level
Two-tailed test
Left-tailed test
Right-tailed test
You can obtain it from “2.3 Probabilities and Significance level_Inferential Statistics (2)”; all the aforementioned information is depicted there precisely.
4.Comparison of parametric and non-parametric hypothesis testing
We can make different assumptions about data distribution depending on the various data qualities.
I must admit that I overlooked this segment. I will illustrate it in the next blog and provide easy-to-understand examples in the related template.
However, before that, we can identify the main pillars of the distinction rules between parametric and non-parametric testing by referring to”2.4 Sample vs. Population: Inferential Statistics (3) (σ² Known).”
In short, with the parametric test, the data adheres to a specific distribution assumption, such as :
Normal distribution curve X~N(u, σ²), T-distribution, F-distribution, Chi-Squared distribution, and so forth, but not with non-parametric testing.
Given the length and scope of this post, I will continue in the next blog entry. Each segment is intended to be digestible in approximately 10 minutes. Stay tuned for more!
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