# Data Analysis week 4

version from 2017-10-28 22:37

## Section 1

Question Answer Column 3
parametric tests -Involve Population Parameters e.g. Population Mean -Have Rigorous Assumptions e.g. Normal Distribution -Require Interval Scale or Ratio Scale -Examples of statistical testz-test, t-test, ANOVA
when should you use parametric test when assumptions of parametric tests are not met (i.e. breached). In these cases we have to use non-parametric tests. They make fewer assumptions about the type of data on which they can be used. Many of these tests use “ranked” data.
Describe non-parametric tests -Do Not Involve Population Parameters -No Stringent Distribution Assumptions: often called “Distribution-free”. -Data Measured on Any Scale: -Ratio or Interval Scales -Ordinal – e.g. Good-Better-Best -Nominal – e.g. Male-Female
Advantages of non-parametric tests -Used with all scales -Simple and logical -Easier to compute: Developed originally before wide computer use. -Make fewer assumptions -Need not involve population parameters -Results maybe as exact as parametric procedures
Disadvantages of non-parametric tests-May waste information: If data permit using parametric procedures. E.g.: converting data from Ratio to Ordinal Scale. -Non parametric tests are less powerful than parametric tests - require a larger sample size than the corresponding parametric test to achieve the same power. -Difficult to compute by hand for large samples.
What does Mann-Whitney U test do(compare two independent groups): a nonparametric alternative to a two independent sample t-test
What does a one Sample Sign Test do (measures the differences between each variable): nonparametric alternatives to the one sample t-test
What does a Wilcoxon signed Rank test do?(compare two repeated measures): nonparametric alternatives to the paired t-test
What does a chi-squared test do (compares observed and expected frequencies)
What does a spearman's rank correlation do (measure association between two variables): a nonparametric alternative to Pearson’s correlation
What does a Kruskal-Wallis do(compare two or more independent groups): a nonparametric alternative to a one-way analysis of variance
What does a Friedman's test do (compare two or more repeated measures): a nonparametric alternative to a repeated-measures analysis of variance
Procedures for non-parametric tests Basic technique is that non-parametric tests mostly do not use the raw data. -Data are ordered or ranked and these values are used in the analysis i.e., the smallest value receives a rank of 1, the next smallest a rank of 2, and so on. -Data are ranked with respect to the entire data set or the ranking will be done within groups. -Nonparametric procedures are also useful if you don’t have precise data values but you do know how the data are ordered.
What are 2 measures of central tendency and when should you use them ?Means are a good measure of average for continuous data when data are normally distributed. Median is a more appropriate measure of the average if data are positively or negatively skewed because it is not affected by extreme values.
give an example of hypotheses for non-parametric statistics H1: there is a significant difference in the medians of the two groups. H0: there is no significant difference in the medians of the two groups.

## Section 2

Question Answer
Describe the Mann-Whitney (2 independent groups test)The Mann-Whitney test (also known as the Mann-Whitney U) is similar to the two independent samples t-test. Data must meet the requirement that the two samples are independent. The Mann-Whitney procedure uses ranks instead of the raw data values. Data values are assigned ranks relative to both samples combined. Mann-Whitney’s test is designed to test whether observations in one population tend to have higher values than those from the other population. Example page 14. SPSS output pgs 22-24
When is it appropriate to use the mann-whitney U test -Data are not normally distributed. -The data contain outliers or extreme values that, because of their magnitude, distort the mean values and affect the outcome of the comparison. -The data are ordinal -Assumes distributions of two groups being compared are the same shape -Assumes not too many ties in ranks of data
2 types of hypothesis for Mann-Whitney U tests -Null Ho: there is no difference between the medians of the populations the samples came from (The two groups have the same distribution). -Alternative Ha: there is a difference between the medians of the populations the samples came from (The two groups do not have the same distribution).
What is the Mann-Whitney U formula U1=n1n2+(n2(n2+1)/2)-R2. U2=n1n2+(n1(n1+1)/2)-R1. Where R=the sum of the ranks of each group, n1 = sample size group 1 and n2 = sample size group 2.
What does 'U' meanreflects the difference between the two rank totals. The SMALLER it is (taking into account n’s) the less likely it is to have occurred by chance. The smaller of the two U values is the one we use:
When using Mann-Whitney when do you reject the null hypothesis if the Calculated U is less than or equal to the Tabulated U value – NB Different to other tests

## Section 3

Question Answer
What does the sign test measure The Sign test can be used to measure the differences between each variable as nonparametric alternatives to the one sample t-test (not covered in this module) can also be used to compare paired data as non parametric alternative to the paired t-test. Page 29
What does the wilcoxon signed-rank test do can be used to compare paired data as nonparametric alternatives to the paired t-test
When do you use the sign test or the wilcoxon signed-rank test when you cannot justify a normality assumption for the differences. They can also be used when the data are ordinal
What does the sign test do it counts the number of differences that are positive (+) and those that are negative (-) and makes a decision based on these counts.
What does the wilcoxon signed-rank test do the same as the sign test but also uses info about the magnitude of the differences. Absolute values of the differences are ranked from smallest to largest, and then the sum of the ranks associated with positive differences is compared with the sum of the ranks for the negative differences.
Example hypotheses for the sign test/Wilcoxon signed-rank test Ho: There is no difference in the medians for the first and second assessment   Ha: There is a difference in the medians between the first and second assessment
How do you calculate z score for proportions PAGE 30p-po / (square root of) po(1-po)/n
What is pproportion positive signs
what is poproportion of expected positive signs
What is n number of differences tested
Sign test SPSS outputpage 33/34
Which is more powerful and why? sign test or wilcoxon signed ranks test Wilcoxon rank test is a more powerful test than the paired sign testsigned. It not only compares whether difference signs are positive or negative, but also takes into account the size of difference. It also ultimately produces a Z- statistic to test for significance.