class: title-slide, center, middle # Methods of Empirical Finance ## Seminar (UE) ### Christoph Huber ### University of Innsbruck #### Master in Banking and Finance ### Winter term 2019/20 (this version: 2019-12-03) --- class: center, middle, inverse # (Non)Parametric Statistical Tests ### Methods of Empirical Finance --- <footer></footer> # (Non)Parametric Statistical Tests ### Parametric vs. Non-parametric tests Parametric: - based on _parametric_ families of _probability distributions_ - rely on assumptions that the data are drawn from a given prob. distribution (e.g. the underlying population is normally distributed) Non-parametric: - _distribution-free_ test statistics - do _not_ rely on assumptions about the data's prob. distribution --- <footer></footer> # (Non)Parametric Statistical Tests ### Parametric vs. Non-parametric tests When should I use a parametric test? When should I use a _non_-parametric test? -- - __scale/level of measurement__ ? non-metric (nominal, ordinal) vs. metric (interval, ratio) data - __the distribution of the data__ ? normally distributed vs. non-normally distributed --- <footer></footer> # (Non)Parametric Statistical Tests ### Parametric vs. Non-parametric tests .smaller[ We mostly use ... ] .pull-left[ ... __parametric__ test statistics if ... - the level of measurement is _metric_ (interval or ratio), - the population is _normally distributed_, - the sample size is _large_ ] .pull-right[ ... __non-parametric__ test statistics if ... - the level of measurement is _non-metric_ (nominal or ordinal), - the population is _non-normally distributed_, - the sample size is _small_ ] --- <footer></footer> # (Non)Parametric Statistical Tests As the appropriate test statistic depends on the data's level of measure, its (assumed) distribution, as well as its sample size, ... ... it makes sense to always get an overview about the data first, ... and — if you want to use parametric test statistics, in particular —, to test for normality of your data --- class: middle <footer></footer> # Testing for Normality --- <footer></footer> # Testing for Normality ### Some useful functions for distributions in _R_ .smaller[ For normal distributions: .pull-left[ ```r dnorm(x=0, mean=0, sd=1) # prob. density function (pdf) ``` ``` ## [1] 0.3989423 ``` ] .pull-right[ ```r x <- seq(-4, 4, length=100) y <- dnorm(x) plot(x, y) ``` <img 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" width="432" /> ] ] --- <footer></footer> # Testing for Normality ### Some useful functions for distributions in _R_ .smaller[ .pull-left[ ```r pnorm(74, mean=70, sd=2) # cumulative density function (cdf) ``` ``` ## [1] 0.9772499 ``` ] .pull-right[ ```r y <- pnorm(x) plot(x, y) ``` <img src="data:image/png;base64,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" width="432" /> ] ] --- <footer></footer> # Testing for Normality ### Some useful functions for distributions in _R_ .smaller[ ```r # e.g. find the Z-score of the 99th quantile of the standard normal distribution qnorm(.99, mean=0, sd=1) # (inverse cumulative density function (cdf)) ``` ``` ## [1] 2.326348 ``` ```r rnorm(5, mean = 10, sd = 2) # generates normally distributed random variables ``` ``` ## [1] 10.858815 7.864668 6.219411 10.179098 7.397888 ``` See [here](https://www.statology.org/a-guide-to-dnorm-pnorm-rnorm-and-qnorm-in-r/), for example. Similarly, these functions are available for most other popular probability distributions. ] --- <footer></footer> # Testing for Normality ### 'Descriptive': Histograms and normal density .smaller[ ```r hist(data$PCT_WOMEN_ON_BOARD, prob = TRUE, breaks = 20) curve(dnorm(x, mean = mean(data$PCT_WOMEN_ON_BOARD, na.rm = TRUE), sd = sd(data$PCT_WOMEN_ON_BOARD, na.rm = TRUE)), col = ubluelight, lwd = 2, add = TRUE, yaxt="n") ``` <img src="data:image/png;base64,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" width="576" /> ] --- <footer></footer> # Testing for Normality ### 'Descriptive': QQ plots .smaller[ ```r qqnorm(data$PCT_WOMEN_ON_BOARD, frame = FALSE) qqline(data$PCT_WOMEN_ON_BOARD, col = ubluelight, lwd = 2) ``` <img src="data:image/png;base64,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" width="576" /> ] --- <footer></footer> # Testing for Normality ### Kolmogorov-Smirnov Goodness-of-Fit Test .smaller[ > tests whether the empirical distribution function of the sample and the > cumulative distribution function of some reference distribution are equal in > location and shape <br> - __nature of independent variable(s):__ no independent variables, 1 population - __scale of dependent variable:__ ordinal or interval <br> - __hypothesis:__ - `\(H_0\)`: `\(F(x) = F_0(x)\)` for all values of `\(x\)` - `\(H_1\)`: `\(F(x) \neq F_0(x)\)` or `\(F(x) > F_0(x)\)` or `\(F(x) < F_0(x)\)` ] --- <footer></footer> # Testing for Normality ### Kolmogorov-Smirnov Goodness-of-Fit Test — Example .smaller[ - Test _whether the variable `CHG_PCT_YTD` is normally distributed_ ```r ks.test(data$PCT_WOMEN_ON_BOARD, "pnorm", mean = mean(data$PCT_WOMEN_ON_BOARD, na.rm=TRUE), sd = sd(data$PCT_WOMEN_ON_BOARD, na.rm=TRUE)) ``` ``` ## ## One-sample Kolmogorov-Smirnov test ## ## data: data$PCT_WOMEN_ON_BOARD ## D = 0.075887, p-value = 0.006166 ## alternative hypothesis: two-sided ``` ] --- <footer></footer> # Testing for Normality ### Shapiro-Wilk Test .smaller[ > tests whether a sample `\(x_1, ..., x_n\)` is drawn from a > normally distributed population <br> - __nature of independent variable(s):__ no independent variables, 1 population - __scale of dependent variable:__ ordinal or interval <br> - __hypothesis:__ - `\(H_0\)`: `\(F(x) = F_0(x)\)` for all values of `\(x\)` - `\(H_1\)`: `\(F(x) \neq F_0(x)\)` or `\(F(x) > F_0(x)\)` or `\(F(x) < F_0(x)\)` ] --- <footer></footer> # Testing for Normality ### Shapiro-Wilk Test — Example .smaller[ - Test _whether the variable `CHG_PCT_YTD` is normally distributed_ ```r shapiro.test(data$CHG_NET_YTD) ``` ``` ## ## Shapiro-Wilk normality test ## ## data: data$CHG_NET_YTD ## W = 0.37452, p-value < 2.2e-16 ``` ] --- class: middle <footer></footer> # One-Sample Test Statistics --- <footer></footer> # One-Sample Test Statistics ### `\(\chi^2\)` Goodness of Fit Test .smaller[ > tests whether the observed proportions for a categorical variable of a single population > differ significantly from hypothesized (expected) proportions <br> - __nature of independent variable(s):__ no independent variables, 1 population - __scale of dependent variable:__ categorical/nominal <br> - __hypothesis:__ - `\(H_0\)`: `\(p_i = p_{i,0} \forall i \in [1, . . . , k]\)` - `\(H_1\)`: `\(p_i \neq p_{i,0} \forall i \in [1, . . . , k]\)` ('The observed proportions ( `\(p_{i,0}\)` ) differ from hypothesized (expected) proportions ( `\(p_{i}\)` ).') ] --- <footer></footer> # One-Sample Test Statistics ### `\(\chi^2\)` Goodness of Fit Test — Example .smaller[ - We use the data from `sp500_data.csv`. - Test _whether the proportion of companies in the S&P 500 with a female CEO is different from 20%_. ```r females <- sum(data$FEMALE_CEO_OR_EQUIVALENT, na.rm=TRUE) total <- sum(!is.na(data$FEMALE_CEO_OR_EQUIVALENT)) x <- c(total - females, females) x ``` ``` ## [1] 479 23 ``` ```r *chisq.test(x, p = c(0.8, 0.2)) ``` ``` ## ## Chi-squared test for given probabilities ## ## data: x ## X-squared = 74.586, df = 1, p-value < 2.2e-16 ``` ] --- <footer></footer> # One-Sample Test Statistics ### One-Sample Wilcoxon Signed Rank Test .smaller[ > tests whether the population from which the data were sampled is symmetric > or not about the default value <br> - __nature of independent variable(s):__ no independent variables, 1 population - __scale of dependent variable:__ ordinal or interval ] --- <footer></footer> # One-Sample Test Statistics ### One-Sample Wilcoxon Signed Rank Test — Example .smaller[ - Test _whether the median yearly net change in prices is different from 0_. I.e., whether the population from which the data were sampled is centered around 0. ```r *wilcox.test(data$CHG_NET_YTD, mu = 0) ``` ``` ## ## Wilcoxon signed rank test with continuity correction ## ## data: data$CHG_NET_YTD ## V = 115647, p-value < 2.2e-16 ## alternative hypothesis: true location is not equal to 0 ``` ] --- <footer></footer> # One-Sample Test Statistics ### One-Sample `\(t\)`-Test .smaller[ > evaluates whether the sample mean ( `\(\mu\)` ) of a test variable significantly differs from > a constant test value `\(μ_0\)` <br> - __nature of independent variable(s):__ no independent variables, 1 population - __scale of dependent variable:__ interval or ratio <br> - __hypothesis:__ - `\(H_0\)`: `\(\mu = \mu_0\)` - `\(H_1\)`: `\(\mu \neq \mu_0\)` or `\(\mu > \mu_0\)` or `\(\mu < \mu_0\)` ('The sample mean `\(\mu\)` significantly differs from the constant test value `\(\mu_0\)`.') <br> - __assumptions:__ - the observations in the sample are independent of each other - the observations follow a normal distribution with mean `\(\mu\)` and variance `\(\sigma^2\)` ] --- <footer></footer> # One-Sample Test Statistics ### One-Sample `\(t\)`-Test — Example .smaller[ - Test _whether the mean yearly net change in prices is different from 0_. ```r summary(data$CHG_NET_YTD) ``` ``` ## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's ## -146.950 5.395 15.170 28.076 33.490 1215.650 6 ``` ```r *t.test(data$CHG_NET_YTD, mu = 0) ``` ``` ## ## One Sample t-test ## ## data: data$CHG_NET_YTD ## t = 9.1499, df = 498, p-value < 2.2e-16 ## alternative hypothesis: true mean is not equal to 0 ## 95 percent confidence interval: ## 22.04771 34.10538 ## sample estimates: ## mean of x ## 28.07655 ``` ] <br> -- .smaller[ __But__: Do our assumptions hold? Is the data _normally distributed_? ] --- class: middle <footer></footer> # Unpaired Two-Sample Test Statistics --- <footer></footer> # Unpaired Two-Sample Test Statistics ### Pearson’s `\(\chi^2\)` Test for `\(r \times\)` c tables .smaller[ > tests whether there is a relationship between two categorical variables (or tests whether or not the `\(r\)` samples are homogeneous regarding the proportion of observations in each of the `\(c\)` categories; `\(\chi^2\)` test for homogeneity) <br> - __nature of independent variable(s):__ 1 independent variables with 2 levels (independent groups) - __scale of dependent variable:__ categorical/nominal <br> - __hypothesis:__ - `\(H_0\)`: `\(O_{ij} = E_{ij}\)` for all cells - `\(H_1\)`: `\(O_{ij} \neq E_{ij}\)` for at least one cell ] --- <footer></footer> # Unpaired Two-Sample Test Statistics ### Pearson’s `\(\chi^2\)` Test for `\(r \times\)` c tables — Example .smaller[ - Test whether there is a relationship between the company's industry group and the percentage of women on its board. ```r chisq.test(data$INDUSTRY_GROUP, data$PCT_WOMEN_ON_BOARD) ``` ``` ## ## Pearson's Chi-squared test ## ## data: data$INDUSTRY_GROUP and data$PCT_WOMEN_ON_BOARD ## X-squared = 2532.7, df = 2419, p-value = 0.05262 ``` ] --- <footer></footer> # Unpaired Two-Sample Test Statistics ### Wilcoxon Rank Sum Test (Mann-Whitney `\(U\)`-test) .smaller[ > tests whether two independent samples are drawn from the same population <br> - __nature of independent variable(s):__ 1 independent variables with 2 levels (independent groups) - __scale of dependent variable:__ ordinal or interval ] --- <footer></footer> # Unpaired Two-Sample Test Statistics ### Wilcoxon Rank Sum Test — Example .smaller[ - Test whether the percentage of women on the board of financial companies are drawn from the same distribution as the pct. of women on board of industrial companies. ```r wilcox.test(PCT_WOMEN_ON_BOARD ~ INDUSTRY_SECTOR, data = data %>% filter(INDUSTRY_SECTOR == "Financial" | INDUSTRY_SECTOR == "Industrial")) ``` ``` ## ## Wilcoxon rank sum test with continuity correction ## ## data: PCT_WOMEN_ON_BOARD by INDUSTRY_SECTOR ## W = 3877, p-value = 0.04192 ## alternative hypothesis: true location shift is not equal to 0 ``` ] --- <footer></footer> # Unpaired Two-Sample Test Statistics ### Kolmogorov-Smirnov Test .smaller[ > tests whether two samples are drawn from the same distribution, or, > more precisely, whether two independent empirical distributions are equal in > location and shape <br> - __nature of independent variable(s):__ 1 independent variables with 2 levels (independent groups) - __scale of dependent variable:__ ordinal or interval ] --- <footer></footer> # Unpaired Two-Sample Test Statistics ### Kolmogorov-Smirnov Test .smaller[ - Test whether the percentage of women on the board of financial companies are drawn from the same distribution as the pct. of women on board of industrial companies or — more precisely — whether the the empirical distributions are equal in location and shape. ```r financial <- data %>% filter(INDUSTRY_SECTOR == "Financial") %>% .$PCT_WOMEN_ON_BOARD industrial <- data %>% filter(INDUSTRY_SECTOR == "Industrial") %>% .$PCT_WOMEN_ON_BOARD *ks.test(financial, industrial) ``` ``` ## ## Two-sample Kolmogorov-Smirnov test ## ## data: financial and industrial ## D = 0.23232, p-value = 0.02783 ## alternative hypothesis: two-sided ``` ] --- <footer></footer> # Unpaired Two-Sample Test Statistics ### Independent Sample `\(t\)`-Test .smaller[ > evaluates whether the sample means ( `\(\mu_1\)` and `\(\mu_2\)` ) of two independent > variables significantly differ <br> - __nature of independent variable(s):__ 1 independent variables with 2 levels (independent groups) - __scale of dependent variable:__ interval or ratio <br> - __hypothesis:__ - `\(H_0\)`: `\(\mu_1 = \mu_2\)` - `\(H_1\)`: `\(\mu_1 \neq \mu_2\)` or `\(\mu_1 > \mu_2\)` or `\(\mu_1 < \mu_2\)` <br> - __assumptions:__ - all observations from both groups are independent of each other - the observations follow a normal distribution with mean `\(\mu\)` and variance `\(\sigma^2\)` - the two independent samples have the same standard deviation, otherwise Welch’s approximation should be applied ] --- <footer></footer> # Unpaired Two-Sample Test Statistics ### Independent Sample `\(t\)`-Test — Example .smaller[ - Test whether the mean percentage of woman is different in financial companies compared to industrial companies. ```r financial <- data %>% filter(INDUSTRY_SECTOR == "Financial") %>% .$PCT_WOMEN_ON_BOARD industrial <- data %>% filter(INDUSTRY_SECTOR == "Industrial") %>% .$PCT_WOMEN_ON_BOARD *t.test(financial, industrial, var.equal=TRUE) ``` ``` ## ## Two Sample t-test ## ## data: financial and industrial ## t = 2.0421, df = 163, p-value = 0.04275 ## alternative hypothesis: true difference in means is not equal to 0 ## 95 percent confidence interval: ## 0.07825703 4.65716398 ## sample estimates: ## mean of x mean of y ## 25.40932 23.04161 ``` ] --- <footer></footer> # Unpaired Two-Sample Test Statistics ### Independent Sample `\(t\)`-Test — Example .smaller[ - What if the two samples have different `\(\sigma\)`s? ```r *t.test(financial, industrial, var.equal=FALSE) ``` ``` ## ## Welch Two Sample t-test ## ## data: financial and industrial ## t = 2.0669, df = 145.08, p-value = 0.04052 ## alternative hypothesis: true difference in means is not equal to 0 ## 95 percent confidence interval: ## 0.1036396 4.6317814 ## sample estimates: ## mean of x mean of y ## 25.40932 23.04161 ``` ] --- class: middle <footer></footer> # Paired Two-Sample Test Statistics --- <footer></footer> # Paired Two-Sample Test Statistics ### Wilcoxon Signed Rank Test .smaller[ > tests whether two _dependent_ samples represent two different populations or > whether the two _dependent_ samples are drawn from the same population <br> - __nature of independent variable(s):__ 1 independent variables with 2 levels (_dependent_ groups) - __scale of dependent variable:__ ordinal or interval <br> - __assumptions:__ - the data are paired and come from the same population - each pair is chosen randomly and independently ] --- <footer></footer> # Paired Two-Sample Test Statistics ### Wilcoxon Signed Rank Test — Example .smaller[ - Test whether the percentage of women on the board of financial companies in 2019 are drawn from the same distribution as the pct. of women on board of financial companies in 2014. <br> `wilcox.test()` ] --- <footer></footer> # Paired Two-Sample Test Statistics ### Dependent `\(t\)`-Test for Paired Samples .smaller[ > evaluates whether the sample means ( `\(\mu_1\)` and `\(\mu_2\)` ) of two _independent_ > samples differ significantly <br> - __nature of independent variable(s):__ 1 independent variables with 2 levels (_dependent_ groups) - __scale of dependent variable:__ interval or ratio <br> - __hypothesis:__ - `\(H_0\)`: `\(\mu = \mu_0\)` - `\(H_1\)`: `\(\mu \neq \mu_0\)` or `\(\mu > \mu_0\)` or `\(\mu < \mu_0\)` <br> - __assumptions:__ - the observations follow a normal distribution with mean `\(\mu\)` and variance `\(\sigma^2\)` - the two samples have the same standard deviation (homogeneity of variance) ] --- <footer></footer> # Paired Two-Sample Test Statistics ### Dependent `\(t\)`-Test for Paired Samples .smaller[ - Test whether the mean percentage of women on the board of financial companies in 2019 is different to the mean pct. of women on board of financial companies in 2014. <br> `t.test()` ] --- class: middle <footer></footer> # `\(n\)`-Sample Generalizations: more than 2 groups --- <footer></footer> # `\(n\)`-Sample Generalizations ### Kruskal-Wallis Test .smaller[ > tests whether two or more independent samples originate from the same > distribution, i.e., extends the Mann-Whitney `\(U\)`-test when there are > _more than_ > _two groups_ (for two groups, both statistics are identical) <br> - __nature of independent variable(s):__ 1 independent variables with two or more levels (independent groups) - __scale of dependent variable:__ ordinal or interval ] --- <footer></footer> # `\(n\)`-Sample Generalizations ### Kruskal-Wallis Test — Example .smaller[ - Test whether the percentage of women on the board of companies from different industry sectors are drawn from the same distribution. ```r kruskal.test(PCT_WOMEN_ON_BOARD ~ INDUSTRY_SECTOR, data = data) ``` ``` ## ## Kruskal-Wallis rank sum test ## ## data: PCT_WOMEN_ON_BOARD by INDUSTRY_SECTOR ## Kruskal-Wallis chi-squared = 9.3157, df = 8, p-value = 0.3164 ``` ] --- <footer></footer> # `\(n\)`-Sample Generalizations ### Jonkheere-Terpstra Test (Jonkheere’s trend test) .smaller[ > tests whether three or more independent samples originate from the same > distribution, (just as the Kruskal-Wallis test) > but with an _ordered_ alternative hypothesis <br> - __nature of independent variable(s):__ 1 independent variables with three or more levels (independent groups) - __scale of dependent variable:__ ordinal or interval <br> - __hypothesis:__ - `\(H_0\)`: `\(\theta_1 = \theta_2 = ... = \theta_k\)` - `\(H_1\)`: `\(\theta_1 \leq \theta_2 \leq ... \leq \theta_k\)` <br> - __assumptions and limitations:__ - all observations from all `\(k\)` groups are independent of each other - hypothesized ordering of groups’ rank-sums required ] --- <footer></footer> # `\(n\)`-Sample Generalizations ### Jonkheere-Terpstra Test — Example .smaller[ - Test whether the percentage of women on the board of companies from financial companies is larger than the percentage in industrial companies, which is then larger than the respective percentage in basic materials companies. ```r library(clinfun) groups <- data %>% filter(INDUSTRY_SECTOR == "Financial" | INDUSTRY_SECTOR == "Industrial" | INDUSTRY_SECTOR == "Basic Materials") groups$INDUSTRY_SECTOR <- factor(groups$INDUSTRY_SECTOR, levels = c("Financial", "Industrial", "Basic Materials"), ordered=TRUE) jonckheere.test(groups$PCT_WOMEN_ON_BOARD, groups$INDUSTRY_SECTOR) ``` ``` ## ## Jonckheere-Terpstra test ## ## data: ## JT = 4237, p-value = 0.1625 ## alternative hypothesis: two.sided ``` ] --- class: middle <footer></footer> # Permutation Tests --- <footer></footer> # Permutation Tests .smaller[ Consider the following hypothetical problem: .pull-left[ - Ten subjects have been randomly assigned to one of two treatment conditions (A or B) and an outcome variable (score) has been recorded. | Treatment A | Treatment B | |:-------------: |:-------------: | | 40 | 57 | | 57 | 64 | | 45 | 55 | | 55 | 62 | | 58 | 65 | ] .pull-right[ - First, let's use a parametric approach to compare Treatment A and Treatment B. `\(\rightarrow\)` `\(t\)`-test: - assume normal distributions, independent groups, and equal variances ```r a <- c(40, 57, 45, 55, 58) b <- c(57, 64, 55, 62, 65) t.test(a, b, var.equal = TRUE) ``` ``` ## ## Two Sample t-test ## ## data: a and b ## t = -2.345, df = 8, p-value = 0.04705 ## alternative hypothesis: true difference in means is not equal to 0 ## 95 percent confidence interval: ## -19.0405455 -0.1594545 ## sample estimates: ## mean of x mean of y ## 51.0 60.6 ``` ] ] --- <footer></footer> # Permutation Tests .smaller[ A permutation test takes a different approach: If the two treatments are truly equivalent, the label (Treatment A or Treatment B) assigned to an observed score is arbitrary. 1. Calculate the observed t-statistic, as in the parametric approach; call this t0. 2. Place all 10 scores in a single group. 3. Randomly assign five scores to Treatment A and five scores to Treatment B. 4. Calculate and record the new observed t-statistic. 5. Repeat steps 3–4 for every possible way of assigning five scores to Treatment A and five scores to Treatment B. There are 252 such possible arrangements. 6. Arrange the 252 t-statistics in ascending order. This is the empirical distribution, based on (or conditioned on) the sample data. 7. If t0 falls outside the middle 95 percent of the empirical distribution, reject the null hypothesis that the population means for the two treatment groups are equal at the 0.05 level of significance. ] --- <footer></footer> # Permutation Tests .smaller[ - In both the permutation and the parametric approach, the exact same `\(t\)`-statistic is calculated. - In the permutation approach, however, the statistic is compared not to a theoretical distribution (e.g. an assumed normal distribution) but to an _empirical distribution_ created from _permutations of the observed data_. <br> - If this empirical distribution contains _all possible permutations_ of the data, the permutation test is called an 'exact' test. - If there are too many possible permutations to compute the test statistic in appropriate time, we ca use (Monte Carlo) _simulations_. ] --- <footer></footer> # Permutation Tests .smaller[ In _R_, we can use the `coin` package to run permutation tests as alternatives for a number of tests. ```r library(coin) ``` ``` ## Loading required package: survival ``` E.g. ```r df <- data.frame(value = c(a, b), treatment = c(rep("A", 5), rep("B", 5))) *oneway_test(value ~ treatment, data = df) ``` ``` ## ## Asymptotic Two-Sample Fisher-Pitman Permutation Test ## ## data: value by treatment (A, B) ## Z = -1.9147, p-value = 0.05553 ## alternative hypothesis: true mu is not equal to 0 ``` <br> See [here](https://cran.r-project.org/web/packages/coin/vignettes/coin.pdf), for example. ] --- <footer></footer> # (Non)parametric Correlation Measures - Parametric: Pearson's `\(\rho\)` - Non-parametric: - Spearman rank correlation `\(\rho\)`: i.e., the Pearson correlation coefficient between the ranked variables - Kendall's `\(\tau\)`: similar to Spearman's `\(\rho\)`; measures _ordinal association_ between two measured quantities .smaller[ <br> The argumentations for using non-parametric _or_ parametric correlation measures are very similar to the ones for using non_parametric or parametric test statistics. Things to consider are: level of measurement, assumptions about the distribution, assumptions about a linear or non-linear relationship, etc. ] --- <footer></footer> # (Non)parametric Correlation Measures ### Pearson's `\(\rho\)` .smaller[ _Linear_ relation between `PCT__WOMEN_ON_BOARD` and `EQY_BETA`? ```r cor(data$PCT_WOMEN_ON_BOARD, data$EQY_BETA, use="complete.obs") ``` ``` ## [1] -0.08745765 ``` For confidence intervals and a significance test, use `cor.test()`. <img 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" width="432" /> ] --- <footer></footer> # (Non)parametric Correlation Measures ### Spearman rank correlation .smaller[ ```r cor(data$PCT_WOMEN_ON_BOARD, data$EQY_BETA, use="complete.obs", method="spearman") ``` ``` ## [1] -0.08065364 ``` ### Kendall's `\(\tau\)` ```r cor(data$PCT_WOMEN_ON_BOARD, data$EQY_BETA, use="complete.obs", method="kendall") ``` ``` ## [1] -0.05475672 ``` See [here](https://en.wikipedia.org/wiki/Spearman's_rank_correlation_coefficient) (Wikipedia) for comparisons between Spearman and Pearson correlations. ] --- class: middle, inverse # Your turn - Load the data in `sp500_data.csv` again - Think about interesting questions and formulate hypotheses you could test with these data - Test your hypothesis(-es) using appropriate tests - Can you reject the `\(H_0\)`? - How do you interpret your results? - Comment on upcoming issues regarding the statistical power, multiple hyptheses, normality assumptions, etc.