Math, asked by StudiousStudent1332, 1 year ago

Discuss the characteristics of hypothesis.explain type i and ii errors in the context of testing of hypothesis.

Answers

Answered by adilmalik1
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Answered by brmishra89
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Answer:

Step-by-step explanation:

Type I error

A Type I error means rejecting the null hypothesis when it’s actually true. It means concluding that results are statistically significant when, in reality, they came about purely by chance or because of unrelated factors.

The risk of committing this error is the significance level (alpha or α) you choose. That’s a value that you set at the beginning of your study to assess the statistical probability of obtaining your results (p value).

The significance level is usually set at 0.05 or 5%. This means that your results only have a 5% chance of occurring, or less, if the null hypothesis is actually true.

If the p value of your test is lower than the significance level, it means your results are statistically significant and consistent with the alternative hypothesis. If your p value is higher than the significance level, then your results are considered statistically non-significant.

Example: Statistical significance and Type I errorIn your clinical study, you compare the symptoms of patients who received the new drug intervention or a control treatment. Using a t test, you obtain a p value of .035. This p value is lower than your alpha of .05, so you consider your results statistically significant and reject the null hypothesis.

However, the p value means that there is a 3.5% chance of your results occurring if the null hypothesis is true. Therefore, there is still a risk of making a Type I error.

To reduce the Type I error probability, you can simply set a lower significance level.

Type II error

A Type II error means not rejecting the null hypothesis when it’s actually false. This is not quite the same as “accepting” the null hypothesis, because hypothesis testing can only tell you whether to reject the null hypothesis.

Instead, a Type II error means failing to conclude there was an effect when there actually was. In reality, your study may not have had enough statistical power to detect an effect of a certain size.

Power is the extent to which a test can correctly detect a real effect when there is one. A power level of 80% or higher is usually considered acceptable.

The risk of a Type II error is inversely related to the statistical power of a study. The higher the statistical power, the lower the probability of making a Type II error.

Example: Statistical power and Type II error When preparing your clinical study, you complete a power analysis and determine that with your sample size, you have an 80% chance of detecting an effect size of 20% or greater. An effect size of 20% means that the drug intervention reduces symptoms by 20% more than the control treatment.

However, a Type II may occur if an effect that’s smaller than this size. A smaller effect size is unlikely to be detected in your study due to inadequate statistical power.

Statistical power is determined by:

Size of the effect: Larger effects are more easily detected.

Measurement error: Systematic and random errors in recorded data reduce power.

Sample size: Larger samples reduce sampling error and increase power.

Significance level: Increasing the significance level increases power.

To (indirectly) reduce the risk of a Type II error, you can increase the sample size or the significance level.

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