There are other tests that have been developed that do not make the assumptions regarding the distribution of the variables, i.e. they do not assume a normally distributed pattern (as is assumed with t tests).
These involve ranking the data, and uses the median instead of the mean.
N.B. - there are still some assumptions being made when using these tests but not as many as for the t-tests and they are influenced to a lesser degree by outliers. So they are considered to be more robust.
The Chi-squared test (pronounced ‘kye’ as in sky) is used with category (nominal) data, such as frequency counts.
You need a minimum of two categories for your data.
Chi square is often written as 
It is based on a comparison of Expected and Obtained values. The bigger the difference, the less likely it is to have risen from just one population.
The higher the Chi-squared value then the bigger the differences between observed and expected values would be.
You check up on a table to check if the chi-square value you have found is significant or not.
This can be used as an alternative to the between-subjects t test, i.e. it can be used whenever you have two groups of scores which are independent of each other (such as different samples of people).
It involves ranking all the data and ignoring which group the person was in and then comparing the ranks for the two groups.
The Wilcoxon signed ranks test is considered an alternative to the paired t test.
The test involves ranking the data and makes no assumption about the distribution of the variables.
This is an alternative to the between subject ANOVA when you do not want outliers to have a big effect.
It I sometimes referred to as the one-way ANOVA on ranks.
The test determines whether the medians of two or more groups are different.
The test statistic used is called the H statistic.
The Friedman test is an alternative to repeated measures (within subjects) ANOVA.
It is based on the ranking of the data.