The normal distribution m a r g Histo

The “normal distribution” m a r g Histo

If “normal” … It rep resen It’ c i d e s pr e l b ta ts the Can popu lation use b e …. 95% …. tter t ests

But is it OK? ” d le e w ke S ft “Skew” Ske wed right “just right” y T eak p o o Too “Kurtosis” flat

How to tell if a sample is “normally distributed” …. mean and median should be similar Descriptive stats A Mean 75. 90 Median 76. 54 B 1. 93 1. 00

How to tell if a sample is “normally distributed” …. skew and kurtosis should be -1. 0 to +1. 0 Descriptive stats Kurtosis Skewness A B -0. 34 10. 27 -0. 13 2. 70

How to tell if a sample is “normally distributed” Histogram should be bell shaped

How to tell if a sample is “normally distributed” Probability plot … points should stay in tramlines

… summary : How did we decide ? ……. 1. Mean and median … similar 2. Skew and kurtosis … -1 to +1 3. Histogram … bell shaped 4. Probability plot … straight line Probability plot is the best test

Why all the fuss ? If “normal” … • Sample represents the population • Sample is predictable • Can do better quality analysis

Is the sample “normally” distributed?

Gender Growt h 346 369 349 280 427 358 342 353 Example: we have three samples of growth rate. Four animals in each. Female We need to know whether Female the samples are normally Male distributed Male Castrate 349 s Castrate 280 s There’s a quick way to check Castrate 427 and a proper way s Castrate …

Do a probability plot

w o r G “ e er h t g d n n i t s of ge e t e ple r a We h sam c a e r o f th”

Do the dots stay in the tramlines? That was a simple way of deciding … but … …samples that means all not easy to see with. Yes lots of are “normally” distributed. You really need a proper test with a P value, so move to the next slide

Look at the P values are over 0. 05 Accept the H 0 for all samples Null Hypothesis: There is no difference between each sample and a hypothetical “normal” sample. (that’s saying …. they’re “normal”)

Conclusion The distribution is “normal” This data is OK for a parametric test

T - test

Today working towards …… • Identify what a t-test is. • Outline when a t-test would be used. • Demonstrate ability to complete a t – test on mini tab and write out the results.

What is a t-test and when would it be used? • When you are trying to find a difference between samples. • If the same animal is had been used for both measurements then you would use paired t test • T test when you have lots of replications in your data. For example …. .

An example data set Participant TB foal weight (Kg) Pony foal weight (Kg) 1 70 49 2 65 51 3 62 47 4 70 45 5 62 42 6 65 45 7 68 43 8 70 49 9 62 52 10 65 46

Example data set Participants With enrichment Without enrichment 1 15 31 2 19 33 3 20 38 4 21 32 5 22 36 6 16 29 7 15 31 8 18 33 9 17 36 10 21 29

How to complete a t-test? • Place your data in mini tab • Stat menu • Basic stats • Click 2 sample t • Click each sample in its own column!!! • Get the P value - <0. 05 (significant difference).

How to write up the results from a t - test • Write out the P value as normal • Then outlined the mean and SD on a bar chart with error bars.

For a paired t test… • Exactly the same process and write up • But instead of clicking 2 sample click paired.

For the two data set examples on the previous slides. • Complete the appropriate t –test • Write up the results appropriately. • Present the results in a bar chart with error bars

Now lets make another example • Outline an IV • Outline a DV • Make up a suitable hypothesis • Now make up an appropriate data set with two columns • Complete the correct t – test and write up the results appropriately.

Conclusions?

A good source

Questions? Luzon hornbill (Penelopides manillae)