# Articles by Todos Logos

### Non-parametric methods for the study of the correlation: Spearman’s rank correlation coefficient and Kendall tau rank correlation coefficient

August 3, 2009 |

We saw in the previous post, how to study the correlation between variables that follow a Gaussian distribution with the Pearson product-moment correlation coefficient. If it is not possible to assume that the values follow gaussian distributions, we have two non-parametric methods: the Spearman's rho test and Kendall's tau test.... [Read more...]

### Parametric method for the study of the correlation: the Pearson r-test

August 3, 2009 |

Suppose you want to study whether there is a correlation between 2 sets of data. To do this we compute the Pearson product-moment correlation coefficient, which is a measure of the correlation (linear dependence) between two variables X and Y; then we ... [Read more...]

### Kruskal-Wallis one-way analysis of variance

July 31, 2009 |

If you have to perform the comparison between multiple groups, but you can not run a ANOVA for multiple comparisons because the groups do not follow a normal distribution, you can use the Kruskal-Wallis test, which can be applied when you can not make ... [Read more...]

### Analysis of variance: ANOVA, for multiple comparisons

July 30, 2009 |

Analysis of variance: ANOVA, for multiple comparisonsThe ANOVA model can be used to compare the mean of several groups with each other, using a parametric method (assuming that the groups follow a Gaussian distribution).Proceed with the following example:The manager of a supermarket chain wants to see if the ... [Read more...]

### Comparison of two proportions: parametric (Z-test) and non-parametric (chi-squared) methods

July 29, 2009 |

Consider for example the following problem.The owner of a betting company wants to verify whether a customer is cheating or not. To do this want to compare the number of successes of one player with the number of successes of one of his employees, of w... [Read more...]

### Wilcoxon signed rank test

July 29, 2009 |

Non-parametric statistical hypothesis test, for the comparison of the means between 2 paired samplesThe mayor of a city wants to see if pollution levels are reduced by closing the streets to the car traffic. This is measured by the rate of pollution every 60 minutes (8am 22pm: total of 15 measurements) in a ... [Read more...]

### Wilcoxon-Mann-Whitney rank sum test (or test U)

July 27, 2009 |

Comparison of the averages of two independent groups of samples, of which we can not assume a distribution of Gaussian type; is also known as Mann-Whitney U-test.You want to see if the mean of goals suffered by two football teams over the years is the same. Are below the ... [Read more...]

### Paired Student’s t-test

July 26, 2009 |

Comparison of the means of two sets of paired samples, taken from two populations with unknown variance.A school athletics has taken a new instructor, and want to test the effectiveness of the new type of training proposed by comparing the average time...

### Two sample Student’s t-test #2

July 25, 2009 |

Comparison of the averages of two independent groups, extracted from two populations at variance unknown; sample variances are not homogeneous.We want to compare the heights in inches of two groups of individuals. Here the measurements:A: 175, 168, 168...

### Two sample Student’s t-test #1

July 24, 2009 |

t-Test to compare the means of two groups under the assumption that both samples are random, independent, and come from normally distributed population with unknow but equal variancesHere I will use the same data just seen in a previous post. The data ...

### One sample Student’s t-test

July 23, 2009 |

Comparison of the sample mean with a known value, when the variance of the population is not known.Consider the exercise we have just seen before.It was made an intelligence test in 10 subjects, and here are the results obtained. The average result of ...

### Two sample Z-test

July 22, 2009 |

Comparison of the means of two independent groups of samples, taken from two populations with known variance.Is asked to compare the average heights of two groups. The first group (A) consists of individuals of Italian nationality (the variance of the ...

### One sample Z-test

July 21, 2009 |

Comparison of the sample mean with know population mean and standard deviation.Suppose that 10 volunteers have done an intelligence test; here are the results obtained. The mean obtained at the same test, from the entire population is 75. You want to c...

### Geometric and harmonic means in R

July 20, 2009 |

Compute the geometric mean and harmonic mean in R of this sequence.10, 2, 19, 24, 6, 23, 47, 24, 54, 77These features are not present in the standard package of R, although they are easily available in some packets. However, it is easy to calculate the...

July 19, 2009 |

### Let us practice with some functions of R

July 18, 2009 |

Given the following data set, compute the arithmetic mean, median, variance, standard deviation; find the greatest and the smaller value, the sum of all values, the square of the sum of all values, the sum of the square of all values; assigne the ranks...