## Saturday, 30 November 2013

### McNemar's Test Calculator

This blog post implements an online McNemar's Test on a 2 by 2 contingency table.

Referring to the contingency table below, the Null Hypothesis for the McNemar test is that the marginal probability of Test 1 being positive is equal to the marginal probability of Test 2 being positive as well. The Null Hypothesis is also that the marginal probability of Test 1 being negative is equal to the marginal probability of Test 2 being negative. If we denote the following:

1. $p_a$=Probability of Test 1 being positive and Test 2 being positive
2. $p_b$=Probability of Test 1 being positive and Test 2 being negative
3. $p_c$=Probability of Test 1 being negative and Test 2 being positive
4. $p_d$=Probability of Test 1 being negative and Test 2 being negative

The Null Hypothesis is $p_a+p_b=p_a+p_c$ or $p_b+p_d=p_c+p_d$, which leads to $p_b=p_c$. In other words, the Null Hypothesis depends on only the off-diagonal terms of the contingency table.

A low value of the calculated p-value (< 0.05) could be considered a significant result, rejecting the Null Hypothesis.

Please fill in the four text areas with integers greater than or equal to zero.

 Test 2 positive: Test 2 negative: Test 1 positive: Row Sum 1 Test 1 negative: Row Sum 2 Column Sum 1 Column Sum 2 Total

Results pending...

## Friday, 29 November 2013

### Online Critical t value Calculator

An implementation of the Critical t value Calculator occurs below. This calculator is useful for statistical tests where a t statistic is calculated, examples of which include the unpaired and paired Student's t-tests. The t statistic is so called as it possesses a Student's t-distribution. Once the t statistic is calculated, we want to see if it exceeds a critical value based on some significance level, and if so, the result will be significant.

The significance level (which is the area under either the tail (for the one-tailed test) or the tails (for the two-tailed test) of the distribution) needs to be a positive number between 0 and 1 - a commonly used value is 0.05, for the 5% significance level.

 Degrees of freedom: Significance level:

Results pending...

 Plot of distribution ($f(x)$) values against $x$ values $f(x)$ $x$