Publications by Todos Logos
Paired Student’s t-test
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 times of 10 runners in the 100 meters. Are below the time in seconds before and after training for e...
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Wilcoxon-Mann-Whitney rank sum test (or test U)
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 number of goals suffered by each team in 6 games for each year.Team A: 6, 8,...
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Wilcoxon signed rank test
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 day when traffic is open, and in a day ...
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Comparison of two proportions: parametric (Z-test) and non-parametric (chi-squared) methods
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 which he is certain that he is not cheating. In a month’s time, the player performs...
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Analysis of variance: ANOVA, for multiple comparisons
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 consumption in kilowatts of 4 stores b...
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Kruskal-Wallis one-way analysis of variance
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 the assumption that the groups follow a gaussian distribution.This test is similar t...
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Parametric method for the study of the correlation: the Pearson r-test
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 compute the value of a t-test to study the significance of the Pearson coefficient R...
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Non-parametric methods for the study of the correlation: Spearman’s rank correlation coefficient and Kendall tau rank correlation coefficient
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....
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Contingency table and the study of the correlation between qualitative variables: Pearson’s Chi-squared test
If you have qualitative variable, it is possible to verify the correlation by studying a contingency table R by C, using the Pearson’s Chi-squared test.A casino wants to study the correlation between the modes of play and the number of winners by age group, to see if the number of winners depends on the type of game that you chose t...
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Two-way analysis of variance: two-way ANOVA in R
The one-way analysis of variance is a useful technique to verify if the means of more groups are equals. But this analysis may not be very useful for more complex problems. For example, it may be necessary to take into account two factors of variability to determine if the averages between the groups depend on the group classification...
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