HYPOTHESIS.pdf
- 1. HYPOTHESIS TYPE I AND TYPE II ERROR NEETHU SUSAN ABRAHAM ROLL NO: 23
- 2. HYPOTHESIS TESTING Hypothesis testing refers to – Making an assumption, called hypothesis, about a population parameter. – Collecting sample data. – Calculating a sample statistic. – Using the sample statistic to evaluate the hypothesis (how likely is it that our hypothesized parameter is correct. To test the validity of our assumption we determine the difference between the hypothesized parameter value and the sample value.)
- 3. NULL HYPOTHESIS The null hypothesis H0 represents a theory that has been put forward either because it is believed to be true or because it is used as a basis for an argument and has not been proven. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug. We would write H0: there is no difference between the two drugs on an average.
- 4. ALTERNATIVE HYPOTHESIS The alternative hypothesis, HA, is a statement of what a statistical hypothesis test is set up to establish. For example, in the clinical trial of a new drug, the alternative hypothesis might be that the new drug has a different effect, on average, compared to that of the current drug. We would write HA: the two drugs have different effects, on average. or HA: the new drug is better than the current drug, on average.
- 5. TYPE I AND TYPE II ERROR Type I error refers to the situation when we reject the null hypothesis when it is true (H0 is wrongly rejected). • e.g. H0: there is no difference between the two drugs on average. • Type I error will occur if we conclude that the two drugs produce different effects when actually there isn’t a difference. • Prob(Type I error) = significance level = α Type II error refers to the situation when we accept the null hypothesis when it is false. • H0: there is no difference between the two drugs on average. • Type II error will occur if we conclude that the two drugs produce the same effect when actually there is a difference. • Prob(Type II error) = ß
- 6. EXAMPLE 1 – Hypothesis: "Adding water to toothpaste protects against cavities." – Null hypothesis: "Adding water to toothpaste has no effect on cavities." – This null hypothesis is tested against experimental data with a view to nullifying it with evidence to the contrary. – A type I occurs when detecting an effect (adding water to toothpaste protects against cavities) that is not present. The null hypothesis is true (i.e., it is true that adding water to toothpaste has no effect on cavities), but this null hypothesis is rejected based on bad experimental data.
- 7. EXAMPLE 2 – Hypothesis: "Adding fluoride to toothpaste protects against cavities." – Null hypothesis: "Adding fluoride to toothpaste has no effect on cavities." – This null hypothesis is tested against experimental data with a view to nullifying it with evidence to the contrary. – A type II error occurs when failing to detect an effect (adding fluoride to toothpaste protects against cavities) that is present. The null hypothesis is false (i.e., adding fluoride is actually effective against cavities), but the experimental data is such that the null hypothesis cannot be rejected.