Flashcards
Hypothesis Testing Procedures
Flashcards do conjunto (21)
- 1Ho [Null hypothesis]The mean of population proportion is the same as the mean of the sampled population. The mean weight of the population is the same as the current (sample) mean weight. There is no difference.
- 2H1 [Alternative hypothesis]Something is happening and is different from the old one; reflects new belief or new results; the mean weight is now lower or higher or equal to the old mean weight
- 3Critical level1) threshold or cutoff to decide when to believe the null hypothesis and when to believe the alternative hypothesis
2. it is a point where one accept or rejects hypothesis.
3. You select critical value form the z-score or t-score. - 4Level of significance1) It is the probability of rejecting the null (in favor of alternative hypothesis) hypothesis when it is true.
2) alpha or α
3) could be 0.05, 0.01, 1 - 5Upper-tailed, Lower-tailed, Two-tailed TestsH1: μ > μ 0 , where μ0 is the comparator or null value (e.g., μ0 =191 in our example about weight in men in 2006) and an increase is hypothesized - this type of test is called an upper-tailed test;
H1: μ < μ0 , where a decrease is hypothesized and this is called a lower-tailed test; or
H1: μ ≠ μ 0, where a difference is hypothesized and this is called a two-tailed test. - 6Steps of hypothesis testing (1)a) Set up hypothesis (What is you H0 and what is your H1)
b) H1 could be upper-tailed, lower-tailed, two-tailed Tests.
c) your level of significance = 0.05 (if not given, always assume) - 7Steps of hypothesis testing (2)a. Select test statistic (what is test statistic?)
A single number that summarizes the sample information
b. What are the types of test statisctics?
1. z-statistic: used only when n = or > 30
2. t-statistic: used when n < 30 - 8Steps of hypothesis testing (3)a) set up decision rule (what is decision rule?): a statement that spells out the circumstances under which you would reject the null hypothesis.
b) example: Reject H0 if z > or = 1.645 or 0.05 or 50% - 9decision rule depends of 3 factors .... [Hint: Steps of hypothesis 1 and 2]1) Research hypothesis
2) test statistic
3) Level of significance - 10Steps of hypothesis testing (4)Compute the test statistic, either z or t
- 11Steps of hypothesis testing (5)Conclusion: either reject or accept null hypothesis.
- 12p-value, what is it and what is its significance?A p-value is calculated to assess whether trial results are likely to have occurred simply through chance (assuming that there is no real difference between new treatment and old, and assuming, of course, that the study was well conducted
- 13Interpreting p-value a) Reject Ho if p = or < α b. Do not reject Ho if p > αa) If p is a small value that is equal or less than alpha, the findings are less likely to arise from chance and we reject the findings or the null hypothesis .
b) If p is large, the observed difference is plausibly by chance and we accept the findings or do not reject the null hypothesis - 14Type 1 Error (α)1) occurs when the null hypothesis is true, but we reject it because of an usual sample result.
2) incorrectly reject Ho hypothesis when it is actually true
3) We incorrectly conclude that research hypothesis (H1) is true when it is not true
4) False positive
5) Example if Ho = 0.09; a mayor of a town conclude the unemployment rate is not 9% when it actually is [Khan Academy] - 15Type 2 Error (β)1) occurs when the Ho is false and we do not reject it [Failing to reject the null]
2) False negative: we fail to reject H0 when
in fact it is false
3) accepting that there is no difference, no change when the H1 is true (proof there is a change)
4) most common reason = small sample
5) Example: If Ho = 0.09; a mayor of a town conclude the unemployment rate is 9% when it actually is not [Khan Academy] - 16χ2 Test are based on -----1) χ2 tests are based on the agreement between expected (under Ho) and observed (sample frequencies)
2) if Ho is true, χ2 will be close to 0
3) If Ho is false, χ2 will be large
4) Reject Ho if χ2 > or = Critical value - 17When do you use χ2 statistical test1) for categorical and ordinal outcomes
- 18a) In χ2 , what does K stands for? b) how do you calculate the degree of freedom (df)? c) how do you determine the critical value in χ2?a) K = the number of response categories
b) df = K - 1
c) by using df and level of significance - 19W/n χ2 , what does the lower- or upper-tailed tests stand for?In χ2 , there are no upper- or lower-tail test
- 20in χ2 , the rejection region is ALWAYS on the right upper-tail (Y or N)Yes, it is always on the upper right region
- 21α = P(Type 1 Error); assuming α = 0.005, what does that mean?