For your hypothesis that ' There is no relationship between Age of the BOD and SACCOs performance in Kenya"-

I think test of significance of 'r' is needed.

When you conduct an ANOVA, you are attempting to determine if there is a statistically significant difference among the groups.  If you find that there is a difference, you will then need to examine where the group differences lay.

At this point you could run post-hoc tests which are t tests examining mean differences between the groups.  There are several multiple comparison tests that can be conducted that will control for Type I error rate, including the Bonferroni, Scheffe, Dunnet, and Tukey tests.

For This linear regression will work

chi square is used to check the independence of distribution

anova is used to check the level of significance between the groups

t test is used to find the signi differenc between the two groups

selection of these tests depends upon your variables like nominal, ordinal, categorical or scale

Sir, I suggest that you should use Anova and pearson correlation to check the significance and correlation.

Depends of type of Variable. Numérical varia bles t and ANOVA test, for nominal or categorical variales chi-square test.

Chi-square test is used on contingency tables and more appropriate when the variable you want to test across different groups is categorical. It compares observed with expected counts.

Both t test and ANOVA are used to compare continuous variables across groups. t test is used for only two groups and it compares the means of the two groups. Whereas ANOVA can be used for more than two groups and it compares the variance between group with the average variance within all groups, i.e. it only identifies if there is any group that is different from the average of all other groups. Afterwards you should use post-hoc tests to identify pair-wise differences among all groups.

When the variables you want to compare are not divided by groups but instead are both numerical you should the use correlation tests.