Stats II 2

13 flashcards · Other · by Daniel F.

1. Central limit theorem

   under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution

2. 7 steps of essay hypothesis testing

   Define the random variables and consider which test you have to perform. Formulate the hypothesis and report the significance level . Formulate and calculate the test statistic Mention the distribution of the test statistic if is true. Determine the rejection region or calculate the p-value of the test (or the confidence interval if the test is two-sided). Conclusion: Determine whether the null hypothesis is rejected or not. Give a conclusion in words

3. One-tailed versus two-tailed tests

   one tailed tests can detect effect two tailed tests can miss directional effect

4. Nonparametric testing

   the distribution is not normal or the sample size is small

5. Goodness-of-Fit testing

   Does sample data conform to a hypothesized distribution Chi2 distribution K is the number of categories (not samples) H0: The sample comes from the hypothesized distribution H1: The sample doesn’t come from the hypothesized distribution If testing for a normal distribution: Jarque-Bera test

6. Jarque-Bera test, Goodness-of-Fit to normal dist

   Does sample data conform to a normal distribution H0: The sample comes from a normal distribution H1: The sample doesn’t come from a normal distribution

7. Skewness vs curtosis

   Skewness is a measure of the lack of symmetry. Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution Good if between -2 and 2. Normal is S = 0 and K = 3

8. Goodness-of-Fit: testing assitionation

   H0: No association between the variables (in the population) H1: There is a relationship between the variables e.g. is there a relationship between two qualitative variables (gender and hand preference) Expected ij: row*column / total

9. Sign test for Matched Pairs

   Can we assume that in a random pair of measurements they are equally likely to be larger than the other? Magnitude does not matter Steps: Calculate the differences of the paired observations. Discard the differences equal to o, leaving n observations. Record the sign of the difference as „+" or „-" Distribution: binomial H0: P = 0.5 H1: P ≠ 0.5 The test statistic is S = the lowest number of pairs (+ or –)

10. Wilcoxon Signed Rank Test for Matched Pairs

    Is the distribution of differences centered at zero? magnitude matters Calculate the differences of the paired observations. Discard the differences equal to o, leaving n observations. Rank the remaining n absolute differences in ascending order (ties are assigned the average of their ranks). Find the sums of the positive ranks (T+) and the negative ranks (T-).Signed Rank Statistic: T=min(T- ; T+) two sided H0: the distribution of paired differences is centered at zero H1: the distribution of p…

11. Mann-Whitney U Test Independent Samples

    Is the central location (median) of one distribution identical to the central location (median) of another distribution? assumptions The two samples are independent and random. The value measured is a continuous variable. The two distributions are identical except for a possible difference in the central location. The sample size from each population is at least 10. steps Pool the two samples (combine into a singe list) but keep track of which sample each value cames from. Rank the values in th…

12. Wilcoxon Rank Sum Test

    Similar to Mann-Whitney U test Results will be the same for both tests easier to apply H0: Me1 = Me2 H1: Me1 ≠ Me2

13. Overview of tests

    Parametric testing hypothesis testing (statistical inference) Nonparametric testing Mathched samples Sign test Wilconxon Signed Rank Test independent samples Mann-whitney U Test Wilcoxon Rank Sum Test