How to implement tinv manually? Without Statistics and Machine Learning Toolbox

As an exercise, I am trying to implement ttests manually, without using the Statistics and Machine Learning Toolbox.

To obtain the p-value from the t-value, I have used Star Striders excellent method. http://www.mathworks.com/matlabcentral/answers/20373-how-to-obtain-the-t-value-of-the-students-t-distribution-with-given-alpha-df-and-tail-s

Now, I wish to determine the confidence interval. For this, the critical t-value is needed.

With the toolbox, you just use tinv according to http://www.mathworks.com/matlabcentral/answers/20373-how-to-obtain-the-t-value-of-the-students-t-distribution-with-given-alpha-df-and-tail-s

My question is, is there any way to do this without the Statistics and Machine Learning Toolbox? More exactly, how to implement tinv?

Answer 1

[Star Strider]

Thank you for the endorsement!

You have to have all these functions in your workspace simultaneously, and with them, you can use fzero to get the critical t-statistic from the probability (alpha) and degrees-of-freedom (v):

% % Variables: 
% % t: t-statistic
% % v: degrees of freedom
tdist2T = @(t,v) (1-betainc(v/(v+t^2),v/2,0.5));                                % 2-tailed t-distribution
tdist1T = @(t,v) 1-(1-tdist2T(t,v))/2;                                          % 1-tailed t-distribution
t_inv = @(alpha,v) fzero(@(tval) (max(alpha,(1-alpha)) - tdist1T(tval,v)), 5);  % T-Statistic Given Probability ‘alpha’ & Degrees-Of-Freedom ‘v’

Example:

alpha = 0.025;
v     = 10;
T = t_inv(alpha, v) * [-1 1]

T_STB = tinv(alpha, v)                                                          % Statistics Toolbox Function

The Statistics Toolbox uses the one-tailed t-test to calculate the t-statistic, so I used it here as well.

T =
    -2.2281     2.2281

T_STB =
    -2.2281

If you’re doing parameter confidence intervals using polyfit, also give polyparci a look.