As a way to knock out a blog post AND do some studying before the final exam, I thought I'd type out - from memory in most cases - some of the concepts and formulas needed for today's test.

Let's start with t-tests, shall we? There are three types of t-tests: simple, independent and dependent. A t-test determines whether the means of two groups are statistically different. For instance, if I find the average number of drinks students have weekly at the beginning of the semester and the average amount of drinks they have weekly at the end of the semester, I could run a t-test to measure whether there is a statistically significant difference.

t = ybar 2 - ybar 1 / (s/square root of n)

Degrees of freedom for a simple t-test. df = n-1

t = M1 - M2 / Sm

Where Sm = square root of [n1(s1)sq + n2(s2)sq / (n1 +n2) -2 x (1/n1 + 1/n2)]

Degrees of freedom for an independent t-test. df = N-k

t = ED/square root of [n(EDsq) - (ED)sq / n - 1]

Where D = x1 - x2

Degrees of freedom for a dependent t-test. d = N - 1

Once you have a t, you'll look up the "critical value" on a t-table using the degrees of freedom and determine from those numbers (both a positive and negative value) whether your number is significant. Does it fall within the critical value or outside the value? If your number falls outside the

If you find a statistic that is significant, you'll want to test the effect size. There are two ways of doing that: Cohen's d (1988) and rsq.

d = t[square root of (n1 + n2) / (n1 x n2)]

rsq = tsq / tsq + df

Let's start with a One-way ANOVA. We are going to begin with building an ANOVA table from imaginary data

First, compute the Grand Mean.

GM = n1(m1) + n2(m2) / n1+n2

Next, find the Sum of Squares between, within and total.

SSb = n1(m1-GM)sq + n2(m2 - GM)sq

SSw = (n1 - 1)(s1sq) + (n2 - 1)(s2sq)

SSt = SSb + SSw

Then, find Degrees of Freedom

dfb = k-1

dfw = N-k

Next, compute the standard means

MSb = SSb/dfb

MSw = SSw/dfw

And now you are ready to find your omnibus F statistic!

F = MSb/MSw

The F stat is what you can now use to measure whether there is a difference. Figure out the Fcrit using the degrees of freedom.

Fcrit = df = k-1/n-k

Then, go to the F table, find the value and if your number is greater than the Fcrit, you have evidence to show there IS a statistically significant difference.

Don't forget to calculate Eta squared (N2). That measures the effect size just as Cohen's d and rsq measures it for a t-test (see above).

N2 = SSb / SSt

Unfortunately the F stat can't tell you WHERE the difference is so you can utilize a post-hoc test to show where the difference lies.

Those include: Tukey's HSD, Scheffe's test, Dunnett's test and Bonferroni's test.

HSD = q[square root (MSw / n)]

Two-way ANOVA has some crazy degrees of freedom that I need to get back to studying now...

Let's start with t-tests, shall we? There are three types of t-tests: simple, independent and dependent. A t-test determines whether the means of two groups are statistically different. For instance, if I find the average number of drinks students have weekly at the beginning of the semester and the average amount of drinks they have weekly at the end of the semester, I could run a t-test to measure whether there is a statistically significant difference.

**Simple t-test.**t = ybar 2 - ybar 1 / (s/square root of n)

Degrees of freedom for a simple t-test. df = n-1

**Independent t-test.**t = M1 - M2 / Sm

Where Sm = square root of [n1(s1)sq + n2(s2)sq / (n1 +n2) -2 x (1/n1 + 1/n2)]

Degrees of freedom for an independent t-test. df = N-k

**Dependent t-test.**t = ED/square root of [n(EDsq) - (ED)sq / n - 1]

Where D = x1 - x2

Degrees of freedom for a dependent t-test. d = N - 1

Once you have a t, you'll look up the "critical value" on a t-table using the degrees of freedom and determine from those numbers (both a positive and negative value) whether your number is significant. Does it fall within the critical value or outside the value? If your number falls outside the

*tcrit*, you'll reject the null hypothesis, basically saying that there IS evidence to show a difference between the means that you were testing.If you find a statistic that is significant, you'll want to test the effect size. There are two ways of doing that: Cohen's d (1988) and rsq.

d = t[square root of (n1 + n2) / (n1 x n2)]

rsq = tsq / tsq + df

*E = sum**sq = squared***ANOVA**- this is a process similar to regression. Through ANOVA, you can analyze the variance between and within results. We need to be able to HAND COMPUTE One-way, Two-way and Three-way ANOVA for the exam.Let's start with a One-way ANOVA. We are going to begin with building an ANOVA table from imaginary data

First, compute the Grand Mean.

GM = n1(m1) + n2(m2) / n1+n2

Next, find the Sum of Squares between, within and total.

SSb = n1(m1-GM)sq + n2(m2 - GM)sq

SSw = (n1 - 1)(s1sq) + (n2 - 1)(s2sq)

SSt = SSb + SSw

Then, find Degrees of Freedom

dfb = k-1

dfw = N-k

Next, compute the standard means

MSb = SSb/dfb

MSw = SSw/dfw

And now you are ready to find your omnibus F statistic!

F = MSb/MSw

The F stat is what you can now use to measure whether there is a difference. Figure out the Fcrit using the degrees of freedom.

Fcrit = df = k-1/n-k

Then, go to the F table, find the value and if your number is greater than the Fcrit, you have evidence to show there IS a statistically significant difference.

Don't forget to calculate Eta squared (N2). That measures the effect size just as Cohen's d and rsq measures it for a t-test (see above).

N2 = SSb / SSt

Unfortunately the F stat can't tell you WHERE the difference is so you can utilize a post-hoc test to show where the difference lies.

Those include: Tukey's HSD, Scheffe's test, Dunnett's test and Bonferroni's test.

HSD = q[square root (MSw / n)]

Two-way ANOVA has some crazy degrees of freedom that I need to get back to studying now...

## 4 comments

Worst blog post ever, Denae. But I hope it helped you! Good luck.

That is too funny! But I was just going over all of those stats to check if I did mine right for my last survey.

C - Hahaa! Sorry to disappoint. Teri - I should get your email for advice on surveys. I'm diving in head first.

My university has a template for the surveys, so I just copy and paste my questions in. Or are you talking about analyzing the data you get from the surveys?

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