What type of statistical test to use?
Below is an extract from the Handbook of Biological Statistics by Prof John H. McDonald.
This can be used as a further guide to decide what statistical test to use in your research.
Test  Nominal Variables  Measurement Variables  Ranked Variables  Purpose  Notes  Example 

Exact test for goodnessoffit  1  –  –  test fit of observed frequencies to expected frequencies  use for small sample sizes (less than 1000)  count the number of red, pink and white flowers in a genetic cross, test fit to expected 1:2:1 ratio, total sample <1000 
Chisquare test of goodnessoffit  1  –  –  test fit of observed frequencies to expected frequencies  use for large sample sizes (greater than 1000)  count the number of red, pink and white flowers in a genetic cross, test fit to expected 1:2:1 ratio, total sample >1000 
G–test of goodnessoffit  1  –  –  test fit of observed frequencies to expected frequencies  used for large sample sizes (greater than 1000)  count the number of red, pink and white flowers in a genetic cross, test fit to expected 1:2:1 ratio, total sample >1000 
Repeated G–tests of goodnessoffit  2  –  –  test fit of observed frequencies to expected frequencies in multiple experiments    count the number of red, pink and white flowers in a genetic cross, test fit to expected 1:2:1 ratio, do multiple crosses 
Test  Nominal Variables  Measurement Variables  Ranked Variables  Purpose  Notes  Example 

Fisher's exact test  2  –  –  test hypothesis that proportions are the same in different groups  use for small sample sizes (less than 1000)  count the number of live and dead patients after treatment with drug or placebo, test the hypothesis that the proportion of live and dead is the same in the two treatments, total sample <1000 
Chisquare test of independence  2  –  –  test hypothesis that proportions are the same in different groups  use for large sample sizes (greater than 1000)  count the number of live and dead patients after treatment with drug or placebo, test the hypothesis that the proportion of live and dead is the same in the two treatments, total sample >1000 
G–test of independence  2  –  –  test hypothesis that proportions are the same in different groups  large sample sizes (greater than 1000)  count the number of live and dead patients after treatment with drug or placebo, test the hypothesis that the proportion of live and dead is the same in the two treatments, total sample >1000 
CochranMantelHaenszel test  3  –  –  test hypothesis that proportions are the same in repeated pairings of two groups  alternate hypothesis is a consistent direction of difference  count the number of live and dead patients after treatment with drug or placebo, test the hypothesis that the proportion of live and dead is the same in the two treatments, repeat this experiment at different hospitals 
Test  Nominal Variables  Measurement Variables  Ranked Variables  Purpose  Notes  Example 

Arithmetic mean  –  1  –  description of central tendency of data     
Median  –  1  –  description of central tendency of data  more useful than mean for very skewed data  median height of trees in forest, if most trees are short seedlings and the mean would be skewed by a few very tall trees 
Range  –  1  –  description of dispersion of data  used more in everyday life than in scientific statistics   
Variance  –  1  –  description of dispersion of data  forms the basis of many statistical tests; in squared units, so not very understandable   
Standard deviation  –  1  –  description of dispersion of data  in same units as original data, so more understandable than variance   
Standard error of the mean  –  1  –  description of accuracy of an estimate of a mean     
Confidence interval  –  1  –  description of accuracy of an estimate of a mean     
Test  Nominal Variables  Measurement Variables  Ranked Variables  Purpose  Notes  Example 

Onesample t–test  –  1  –  test the hypothesis that the mean value of the measurement variable equals a theoretical expectation    blindfold people, ask them to hold arm at 45° angle, see if mean angle is equal to 45° 
Twosample t–test  1  1  –  test the hypothesis that the mean values of the measurement variable are the same in two groups  just another name for oneway anova when there are only two groups  compare mean heavy metal content in mussels from Nova Scotia and New Jersey 
Oneway anova  1  1  –  test the hypothesis that the mean values of the measurement variable are the same in different groups    compare mean heavy metal content in mussels from Nova Scotia, Maine, Massachusetts, Connecticut, New York and New Jersey 
TukeyKramer test  1  1  –  after a significant oneway anova, test for significant differences between all pairs of groups    compare mean heavy metal content in mussels from Nova Scotia vs. Maine, Nova Scotia vs. Massachusetts, Maine vs. Massachusetts, etc. 
Bartlett's test  1  1  –  test the hypothesis that the standard deviation of a measurement variable is the same in different groups  usually used to see whether data fit one of the assumptions of an anova 
compare standard deviation of heavy metal content in mussels from Nova Scotia, Maine, Massachusetts, Connecticut, New York and New Jersey

Test  Nominal Variables  Measurement Variables  Ranked Variables  Purpose  Notes  Example 

Nested anova  2+  1  –  test hypothesis that the mean values of the measurement variable are the same in different groups, when each group is divided into subgroups  subgroups must be arbitrary (model II)  compare mean heavy metal content in mussels from Nova Scotia, Maine, Massachusetts, Connecticut, New York and New Jersey; several mussels from each location, with several metal measurements from each mussel 
Twoway anova  2  1  –  test the hypothesis that different groups, classified two ways, have the same means of the measurement variable    compare cholesterol levels in blood of male vegetarians, female vegetarians, male carnivores, and female carnivores 
Paired t–test  2  1  –  test the hypothesis that the means of the continuous variable are the same in paired data  just another name for twoway anova when one nominal variable represents pairs of observations  compare the cholesterol level in blood of people before vs. after switching to a vegetarian diet 
Wilcoxon signedrank test  2  1  –  test the hypothesis that the means of the measurement variable are the same in paired data  used when the differences of pairs are severely nonnormal  compare the cholesterol level in blood of people before vs. after switching to a vegetarian diet, when differences are nonnormal 
Test  Nominal Variables  Measurement Variables  Ranked Variables  Purpose  Notes  Example 

Linear regression  –  2  –  see whether variation in an independent variable causes some of the variation in a dependent variable; estimate the value of one unmeasured variable corresponding to a measured variable    measure chirping speed in crickets at different temperatures, test whether variation in temperature causes variation in chirping speed; or use the estimated relationship to estimate temperature from chirping speed when no thermometer is available 
Correlation  –  2  –  see whether two variables covary    measure salt intake and fat intake in different people's diets, to see if people who eat a lot of fat also eat a lot of salt 
Polynomial regression  –  2  –  test the hypothesis that an equation with X^{2}, X^{3}, etc. fits the Y variable significantly better than a linear regression     
Analysis of covariance (ancova)  1  2  –  test the hypothesis that different groups have the same regression lines  first test the homogeneity of slopes; if they are not significantly different, test the homogeneity of the Yintercepts  measure chirping speed vs. temperature in four species of crickets, see if there is significant variation among the species in the slope or Yintercept of the relationships 
Test  Nominal Variables  Measurement Variables  Ranked Variables  Purpose  Notes  Example 

Multiple regression  –  3+  –  fit an equation relating several X variables to a single Y variable    measure air temperature, humidity, body mass, leg length, see how they relate to chirping speed in crickets 
Simple logistic regression  1  1  –  fit an equation relating an independent measurement variable to the probability of a value of a dependent nominal variable    give different doses of a drug (the measurement variable), record who lives or dies in the next year (the nominal variable) 
Multiple logistic regression  1  2+  –  fit an equation relating more than one independent measurement variable to the probability of a value of a dependent nominal variable    record height, weight, blood pressure, age of multiple people, see who lives or dies in the next year 
Test  Nominal Variables  Measurement Variables  Ranked Variables  Purpose  Notes  Example 

Sign test  2  –  1  test randomness of direction of difference in paired data    compare the cholesterol level in blood of people before vs. after switching to a vegetarian diet, only record whether it is higher or lower after the switch 
Kruskal–Wallis test  1  –  1  test the hypothesis that rankings are the same in different groups  often used as a nonparametric alternative to oneway anova  40 ears of corn (8 from each of 5 varieties) are ranked for tastiness, and the mean rank is compared among varieties 
Spearman rank correlation  –  –  2  see whether the ranks of two variables covary  often used as a nonparametric alternative to regression or correlation  40 ears of corn are ranked for tastiness and prettiness, see whether prettier corn is also tastier 
References
Chapter 37+45 of the second edition of Intuitive Biostatistics Harvey Motulsky.
McDonald, J.H. 2014. Handbook of Biological Statistics (3rd ed.). Sparky House Publishing, Baltimore, Maryland.
Campbell MJ, Machin D. In: Medical Statistics: A Commonsense Approach , 2nd edn. Chichester: Wiley, 1993:2.
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