BEES2041 Lecture Notes - Lecture 3: Test Statistic

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Two sample T test:
Are two samples different
Do your samples come from population with same mean
Two sample test
Frog biologist collected frogs from ponds with predators & frogs from ponds without
predators
Does frog size differ between ponds with & without predators
Two tailed hypothesis
-Ha: mean 1 Not equals to mean2
-tests for any difference between two means
One tailed hypothesis
-Ha: mean1> mean2
-test a directional hypothesis (is one mean larger than the other)
-must specify this before collecting data
Frog example
Unlikely to have obtained our two samples from populations with same mean
More likely that our samples come from populations with different means
Minor complication
-there are slightly different versions of t-test
- are sample sizes equal?
-are variances equal?
T= mean1-mean2/ measure of variation
2 types:
-unequal sample sizes & unequal variance
-pooled variances
Presenting results of t-tests
Ponds of Frogs without predators Significantly Longer than Ponds of Frogs with predators
-the two sample t-test just ran assumed samples were independent
-independent= no relationship between any individual data points
-there are times when data are linked in some way
Assumptions of parametric tests
1 independence
2 normality
3 homogeneity of variance
Violations of the assumptions mean:
- test statistic may not distribute (as described by known probability distributions
- p values are unreliable
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Document Summary

Do your samples come from population with same mean. Frog biologist collected frogs from ponds with predators & frogs from ponds without predators. Does frog size differ between ponds with & without predators. Test a directional hypothesis (is one mean larger than the other) Unlikely to have obtained our two samples from populations with same mean. More likely that our samples come from populations with different means. Ponds of frogs without predators significantly longer than ponds of frogs with predators. The two sample t-test just ran assumed samples were independent. Independent= no relationship between any individual data points. There are times when data are linked in some way. Test statistic may not distribute (as described by known probability distributions. Observations are sampled randomly from defined populations (independence) A random sample is an unbiased estimate of population. If individual measurements are linked in any particular way, they are not independent.

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