## Why use the ANOVA over a t-test?

### March 25, 2012

The point of conducting an experiment is to find a significant effect between the stimuli being tested. To do this various statistical tests are used, the 2 being discussed in this blog will be the ANOVA and the t-test. In a psychology experiment an independent variable and dependant variable are the stimuli being manipulated and the behaviour being measured. Statistical tests are carried out to confirm if the behaviour occurring is more than chance.

The t-test compares the means between 2 samples and is simple to conduct, but if there is more than 2 conditions in an experiment a ANOVA is required. The fact the ANOVA can test more than one treatment is a major advantage over other statistical analysis such as the t-test, it opens up many testing capabilities but it certainly doesn’t help with mathematical headaches. It is important to know that when looking at the analysis of variance an IV is called a *factor*, the treatment conditions or groups in an experiment are called the *levels* of the factor. ANOVA’s use an *F-ratio* as its significance statistic which is variance because it is impossible to calculate the sample means difference with more than two samples.

T-tests are easier to conduct, so why not conduct a t-test for the possible interactions in the experiment? A Type I error is the answer because the more hypothesis tests you use the more you risk making a type I error and the less power a test has. There is no disputing the t-test changed statistics with its ability to find significance with a small sample, but as previously mentioned the ANOVA allowed for testing more than 2 means. ANOVA’s are used a lot professionally when testing pharmaceuticals and therapies.

The ANOVA is an important test because it enables us to see for example how effective two different types of treatment are and how durable they are. Effectively a ANOVA can tell us how well a treatment work, how long it lasts and how budget friendly it will be an example being intensive early behavioural intervention (EIBI) for autistic children which lasts a long time with a lot hour, has amazing results but costs a lot of money. The ANOVA is able to tell us if another therapy can do the same task in shorter amount of time and therefor costing less and making the treatment more accessible. Conducting this test would also help establish concurrent validity for the therapy against EIBI. The F-ratio tells the researcher how big of a difference there is between the conditions and the effect is more than just chance. ANOVA test assumes three things:

- The population sample must be normal
- The observations must be independent in each sample
- The population the samples are selected from have equal variance a.k.a. homogeneity of variance.

These requirements are the same for a paired and a repeated measures t-test and these measured are solved in the same way for the t-test and the ANOVA. The population sample is assumed to be normal anyway, the independent samples is achieved with the design of the experiment, if the variance is not correct then normally more data (participants) is needed in the experiment.

In conclusion it is necessary to use the ANOVA when the design of a study has more than 2 condition to compare. The t-test is simple and less daunting especially when you see a 2x4x5 factorial ANOVA is needed, but the risk of committing a type I error is not worth it. The time you spent conducting the experiment only to have it declared obsolete because the right statistical test wasn’t conducted would be a waste of time and resources, statistical tests should be used correctly for this reason.

References

http://afni.nimh.nih.gov/pub/dist/HOWTO/howto/ht05_group/html/background_ANOVA.shtml

http://www.statsguides.bham.ac.uk/htg/SPSS9/mixedanova.pdf

http://www.statisticallysignificantconsulting.com/Anova.htm

http://www.physics.csbsju.edu/stats/t-test.html

http://faculty.vassar.edu/lowry/ch11pt1.html

http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm

April 16, 2012 at 9:30 pm

ANOVA are certainly very important for multiple level/ factor analysis but T-tests are still important to ANOVA’s. After an ANOVA has been run in factors with more than two levels we cannot fully understand where the differences lie without post hoc tests. Many common post hoc tests essentially run T-tests between each level of a factor to find out if there is a significant difference between levels.

April 17, 2012 at 12:42 pm

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April 17, 2012 at 8:40 pm

The phrase ‘nothing worth having is easily gained’ is relevant to this discussion. For example, even though conducting ANOVA is a very difficult process and indeed a headache in carrying out, the procedure enables us to test more than one treatment which is a great advantage because it allows us to observe how effective the two treatments are, therefore portraying how even though it is a difficult process, the outcome is worth it. On the contrary, the t-test requires less effort and is not as time consuming as conducting ANOVA, so therefore it is important to criically analysis your results and ask yourself whether the results would benefit from being analysed via ANOVA or t-test.

April 18, 2012 at 9:31 pm

The real advantage of using ANOVA over a t-test is the fact that it allows you analyse two or more samples or treatments (Creighton, 2007). A t-test is appropriate if you have just one or two samples, but not more than two. The use of ANOVA allows researchers to compare many variables with much more flexibility. By using ANOVA over a t-test it will also significantly reduce the possibility of make a Type-1 error which is a very important advantage within research.

April 18, 2012 at 9:33 pm

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April 18, 2012 at 10:03 pm

ANOVA and t test are used when dependent variables are interval/normal. The main reason of using ANOVA over t test is when there are more than 2 samples. Advantage of t test is simple, fast processing. But when there are only 2 samples, both ANOVA and t test are good, they will get the same result(p.s.although t test and ANOVA can give the same results, the t-test gives you the ability to do one-tailed and two-tailed tests.) so at this point ANOVA maybe a better test because it is more useful when samples goes over 2. However, it(ANOVA) is indeed more complicated to carry out,it examines the differences within the groups, then examines how that variation translates into variation between the groups , taking into account how many subjects there are in the groups(df). Whereas t test could be done is a few equations. So it is important for researcher to identify when test should they use before the analysis.

April 18, 2012 at 10:19 pm

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