# Thread: difference between ANOVA and T-test

1. ## difference between ANOVA and T-test

Hello,

my teacher asked me last week if you can use ANOVA to investigate the relation between two variables instead of the unpaired T-test which you normally use ... I said you can choose between these two because they lead to the same result. Is this true?

2. Originally Posted by Leslie
Hello,

my teacher asked me last week if you can use ANOVA to investigate the relation between two variables instead of the unpaired T-test which you normally use ... I said you can choose between these two because they lead to the same result. Is this true?
Yes.

"One factor analysis of variance (Snedecor and Cochran, 1989) is a special case of analysis of variance (ANOVA), for one factor of interest, and a generalization of the two-sample t-test. The two-sample t-test is used to decide whether two groups (levels) of a factor have the same mean. One-way analysis of variance generalizes this to levels where k, the number of levels, is greater than or equal to 2."

http://www.itl.nist.gov/div898/handb...on3/eda354.htm

3. Thanks!

But why does 'Statistica' use these two options instead of only ANOVA?
If the T-test gives us the same results as ANOVA, isn't it crazy? If you always use ANOVA, the T-test becomes unnecessary or am I seeing this the wrong way?

Greets

4. Originally Posted by Leslie
Thanks!

But why does 'Statistica' use these two options instead of only ANOVA?
If the T-test gives us the same results as ANOVA, isn't it crazy? If you always use ANOVA, the T-test becomes unnecessary or am I seeing this the wrong way?

Greets
As far as I know, all the information you would get from a t-test can be gotten from ANOVA, _assuming_ that the two samples have equal variances. I don't know if ANOVA can be tweaked to give the same info a unequal-variances t-test would give.

It could also just be that the Statistica t-test gives both 2-sided, and both 1-sided results, and ANOVA just gives the 2-sided without doing the calculations to provide the 1-sided results as well. Have not used Statistica, I don't know.

5. Although t and ANOVA can give the same results, the t-test gives you the ability to do one- or two-tailed tests.

6. ## Re: difference between ANOVA and T-test

I'm sorry to bump this old topic, but I assumed it would be prefered to making a new topic about this subject.

Is the result of an independent t-test and a ANOVA on 2 treatments ALWAYS the same? Even when you have a small sample size?

Reason I'm asking this because I'm not sure if I fully understand this piece I found:

''First, a little history about this curious name. William Gosset (1876-1937) was a Guinness Brewery employee who needed a distribution that could be used with small samples. Since the Irish brewery did not allow publication of research results, he published under the pseudonym of Student. We know that large samples approach a normal distribution. What Gosset showed was that small samples taken from an essentially normal population have a distribution characterized by the sample size. The population does not have to be exactly normal, only unimodal and basically symmetric. This is often characterized as heap-shaped or mound shaped.''

From:
'For n > 30, the differences are negligible'
http://askville.amazon.com/sample-si...estId=52854836

Does this mean when you have n<30 the difference between a normal distribution and a t-distribution are not neglible? I'm pretty sure I'm missing something because don't the independent t-test and ANOVA both assume a normal distribution?

But the main thing I need to know if a independent t-test and ANOVA always give the same result. Googling around says it is the case (t squared = F).

Thanks in advance

7. ## Re: difference between ANOVA and T-test

Originally Posted by BBD
Does this mean when you have n<30 the difference between a normal distribution and a t-distribution are not neglible? I'm pretty sure I'm missing something because don't the independent t-test and ANOVA both assume a normal distribution?
Yes they both assume normality. But that doesn't mean that the sampling distribution of your statistics will be perfectly normal because we don't have a perfect estimate of the variance. That's why we use the t distribution. Also if you have a large enough sample size then you don't really need to worry about the assumption of normality (depending on what your goals are).

But the main thing I need to know if a independent t-test and ANOVA always give the same result. Googling around says it is the case (t squared = F).
Yes they will give the same results (assuming you use the same assumptions for both). Also note that . In other words a squared t with n degrees of freedom is equal to an F with 1 numerator degrees of freedom and n denominator degrees of freedom. If you think about the standard one way anova situation the numerator degrees of freedom represent the number of groups you're comparing minus one. So if we're doing a t-test we're comparing 2 groups and this seems to work out nicely.

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