Spreadsheet to calculate critical values for standard normal, normal, chi-squared, t- and F distributions.

Considering n Bernoulli independent variables X1,X2,…,Xn with a probability of success p1=p2=…=pn, the X random variable is defined as equal to the number of successes in the n trials and follows a binomial distribution.

Considering n Bernoulli independent variables X1,X2,…,Xn with a probability of success p1=p2=…=pn, the probability that the success on the mth trials follows a geometric distribution.

Considering n Bernoulli independent variables X1,X2,…,Xn with a probability of success p1=p2=…=pn, the X random variable is defined as equal to the number of successes until the mth unsuccessful is observed and follows a negative geometric distribution.

A binomial distribution, with n large and p small, can be approximated by a Poission distribution with parameter (the approach can be made when n>50 and p<0.1).

Normal distribution with a mean and standard deviation s.

Exponential distribution with parameter that can be used to approach a geometric distribution.

Conformity of the mean (normal distribution) with known.

Conformity of the mean (normal distribution) with unknown and n large.

Conformity of the sample proportion with the population proportion.

Conformity of the sample variance with the population variance.

Confidence intervals for the mean (normal distribution) with known.

Confidence intervals for the mean (normal distribution) with unknown and n large.

Confidence interval for proportion.

Confidence intervals for variance.

Confidence intervals for variance ratios. ????

Hypothesis test of two means that follow a normal distribution and with the two known.

Hypothesis test of two means that follow a normal distribution and with the two unknown and n>=30.

Hypothesis test of two means from dependent samples that follow a normal distribution and with known d.

Hypothesis test of two means from dependent samples that follow a normal distribution, with d unknown and n>30.

Hypothesis test for proportions with p1 and p2 known.

Hypothesis test for proportions with p1 and p2 unknown.

Test for variance.

 

Global Binomial test: the test is based on to count the number of correct alignments between the two sequences. This variable follows a binomial distribution that can be approached with a normal distribution if the sequences are very large.

Likelihood ratio: in many cases the null and alternative hypothesis can be compared using a logarithm of the likelihood ratio. This variable follows a binomial distribution that can be approached with a normal distribution if the sequences are very large.

A local success run test: this test is applied to compare two sequences and is based on the length of the local success. The statistic is defined as the maximum length of the well aligned base fragments and follows a distribution of the maximum of n geometric distributions.

BLAST Basic Local Alignment Search Tool (Altschul, S.F., Gish W., Miller W., Myers E.W., and Lipman D.J. J. Mol. Biol. 1990: 215:403-10) is an algorithm used to study nucleic acid sequence alignments and the predicted maximum length of the well-aligned segment is used.

BLAST Basic Local Alignment Search Tool (Altschul, S.F., Gish W., Miller W., Myers E.W., and Lipman D.J. J. Mol. Biol. 1990: 215:403-10) is an algorithm used to study protein sequence and the predicted maximum length of the well-aligned segment is used.