# ANT333Y1 Lecture Notes - Lecture 12: Statistical Hypothesis Testing, Protozoa, Dwarf Lemur

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ANT333 Lecture #12 Comparative Statistics & Meta-Analysis

We’ll Cover 2 Topics

1) Basics comparative statistics & 2). Introduction to meta-analysis

Comparative Statistics

Say you want to compare between samples, but NOT along a cline.

Basically, is something greater than (>) or less (<) than something else?

We’ll cover three (3) kinds today.

1) Student’s t-test (parametric)

2) Mann-Whitney U test (non-parametric)

3) Chi-square test (non-parametric)

The Student’s t-test

W. S. Gossett [1876-1937]

Assesses whether the means of two groups are statistically different from each other.

Three Main t-test Requirements

1) Variables normally distributed (bell-shaped) within each group (parametric).

2) Variation of scores in two groups not reliably different (SDs are ca. equal).

3) Dependent variable is interval or ratio level data.

So Let’s Try Some!

First, let’s state our question: Do different types of music affect marks?

Experimental Design

Randomly sort subjects into 2 groups, A & B (homogeneous for age, sex, GPA, etc.).

Each group takes same test under identical conditions except group A has music of type-I (Celine

Dion) playing in background, while group B has music of type-II (Ozzy Osbourne).

Visually inspect data! Make figures and look for outliers

Results

Students did significantly better with Ozzy than with Celine.

Conclusion: Ozzy rules!

But, What if Not Normally Distributed & Unequal Variance?

Visually inspect data.

Actually, often case in primate datasets.

Can’t use t-test.

Must use of non-parametric test, like Mann-Whitney U, that ranks dependent variables.

Mann-Whitney U Test

Definition: A non-parametric test (distribution-free) used to compare two independent groups

of sampled data.

Since this test does not make a distribution assumption, it’s not as powerful as t-test.

Dependent variable can be ordinal, interval or ratio level data.

## Document Summary

We"ll cover 2 topics: basics comparative statistics & 2). Say you want to compare between samples, but not along a cline. We"ll cover three (3) kinds today: student"s t-test (parametric, mann-whitney u test (non-parametric, chi-square test (non-parametric) Assesses whether the means of two groups are statistically different from each other. Three main t-test requirements: variables normally distributed (bell-shaped) within each group (parametric), variation of scores in two groups not reliably different (sds are ca. equal), dependent variable is interval or ratio level data. Randomly sort subjects into 2 groups, a & b (homogeneous for age, sex, gpa, etc. Each group takes same test under identical conditions except group a has music of type-i (celine. Dion) playing in background, while group b has music of type-ii (ozzy osbourne). Students did significantly better with ozzy than with celine. Must use of non-parametric test, like mann-whitney u, that ranks dependent variables.