Hypothesis tests - Revision history

Gauche at 21:28, 1 April 2012

2012-04-01T21:28:45Z

Gauche at 20:27, 1 April 2012

2012-04-01T20:27:41Z

Gauche at 20:21, 1 April 2012

2012-04-01T20:21:22Z

Gauche at 20:19, 1 April 2012

2012-04-01T20:19:14Z

Gauche at 19:54, 1 April 2012

2012-04-01T19:54:06Z

Gauche at 19:53, 1 April 2012

2012-04-01T19:53:34Z

Gauche at 19:52, 1 April 2012

2012-04-01T19:52:54Z

Gauche: /* t-test */

2012-04-01T19:45:44Z

t-test

Gauche: /* t-test */

2012-04-01T19:44:45Z

t-test

Gauche at 11:37, 31 March 2012

2012-03-31T11:37:01Z

@@ Line 56: / Line 56: @@
 ==Comparing a quantitative variable between more than two groups==
-===ANOVA (analysis of variance)===
+===F-test===
 ===Kruskal-Wallis test===

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 ===Mann-Whitney U test===
-The Mann-Whitney U test (also known as the Wilcoxon Rank Sum test) is commonly used for the comparison of two groups where the variable of interest is continuous but not normally distributed for at least one group.
+The Mann-Whitney U test (also known as the Wilcoxon Rank Sum test) is commonly used for the comparison of two groups where the variable of interest is continuous but not normally distributed for at least one group. The basic concept behind the test is that all observations within each group are combined and then ranked in order of magnitude. These are then reassigned to their original groups, and the sums of the ranks in each groups are calculated and compared (by counting, for each observation in either of the groups, the number of observations in the alternate group which have a lower rank, and summing these together). Alternative methods are available for those cases where this approach would not be feasible.
 ==Comparing a quantitative variable between more than two groups==

← Older revision		Revision as of 20:21, 1 April 2012
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	===Mann-Whitney U test===		===Mann-Whitney U test===
		+	The Mann-Whitney U test (also known as the Wilcoxon Rank Sum test) is commonly used for the comparison of two groups where the variable of interest is continuous but not normally distributed for at least one group.
		+

	==Comparing a quantitative variable between more than two groups==		==Comparing a quantitative variable between more than two groups==

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 ==Comparing a quantitative variable between two groups==
 ===t-test===
-The t-test (also known as the 'Student's t-test') is the most commonly used test for the comparison of two normally distributed variables, and can also be used to assess whether a single normally distributed variable differs from a particular value. As for many hypothesis tests, it involves the calculation of a test statistic which is assumed to follow a particular distribution (in this case, the t distribution). When calculating the test statistic for the comparison of two distributions with approximately equal variances and equal numbers of individuals in each group, the difference in mean values between the two groups is divided by the standard error of the difference between these two means (which is calculated as the product of the pooled standard deviation and the square root of two divided by the number of individuals in each group).
+The t-test (also known as the 'Student's t-test') is the most commonly used test for the comparison of two normally distributed variables, and can also be used to assess whether a single normally distributed variable differs from a particular value. As for many hypothesis tests, it involves the calculation of a test statistic which is assumed to follow a particular distribution (in this case, the t distribution). The general approach to the calculation of the test statistic is to divide the difference of interest (whether that is the difference between the mean of interest and a particular value, or the difference between two different means of interest) with the standard error of this difference. The methods of calculation of the standard error therefore differ depending upon the characteristics of the data in question:
 ===Mann-Whitney U test===

@@ Line 45: / Line 45: @@
 ==Comparing a quantitative variable between two groups==
 ===t-test===
-The t-test (also known as the 'Student's t-test') is the most commonly used test for the comparison of two normally distributed variables, and can also be used to assess whether a single normally distributed variable differs from a particular value. As for many hypothesis tests, it involves the calculation of a test statistic which is assumed to follow a particular distribution (in this case, the t distribution). When calculating the test statistic for the comparison of two distributions with approximately equal variances and equal numbers of individuals in each group, the difference in mean values between the two groups is divided by the standard error of the difference between these two means (which is calculated as the product of the pooled standard deviation and the square root of two divided by the number of individuals in each group.
+The t-test (also known as the 'Student's t-test') is the most commonly used test for the comparison of two normally distributed variables, and can also be used to assess whether a single normally distributed variable differs from a particular value. As for many hypothesis tests, it involves the calculation of a test statistic which is assumed to follow a particular distribution (in this case, the t distribution). When calculating the test statistic for the comparison of two distributions with approximately equal variances and equal numbers of individuals in each group, the difference in mean values between the two groups is divided by the standard error of the difference between these two means (which is calculated as the product of the pooled standard deviation and the square root of two divided by the number of individuals in each group).
 ===Mann-Whitney U test===

← Older revision		Revision as of 11:37, 31 March 2012
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	===Fisher's exact test===		===Fisher's exact test===
		+	Fisher's exact test is most commonly used instead of the chi-square test when the sample size is small and/or when expected cell counts are less than 5. This test generally requires the variables of interest to be dichotomous (i.e. a 2x2 contingency table), although methods are available of applying the test to contingency tables of greater size. Instead of assuming the data approximates a distribution (as is the case with the chi-square test), the '''exact''' probability of the particular arrangement of data (and that of 'more extreme' patterns, given the row and column totals in the contingency table are fixed) is calculated (based upon the hypergeometric distribution).

	==Comparing a quantitative variable between two groups==		==Comparing a quantitative variable between two groups==