Hypothesis Testing

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  • Created by: rosieevie
  • Created on: 07-01-18 15:29

Hypotheses

Format - is there a difference/relationship between A/X and B/Y?

Alternative (test) hypothesis (H1) - something to explain, interesting phenomeon, difference/relationship

Null hypothesis (H0) - nothing to explain, no interesting phenomenon no difference/relationship

If theory predicts something like ratio, null hypothesis is not 'there is no difference', it is the ratio (e.g. 2:1, 1:1)

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Type I and II Errors

Type I error (false positive) - accept alternative when null is true

Type II error (false negative) - accept null when alternative is true

Probabilities of making a Type I or Type II error are in balance.

  • Conservative test - increases Type II error, decreases Type I error
  • Liberal test - increases Type I error, decreases Type II error

Conservative tests usually preferred

Compromise in biology - 5% = a (critical value)

  • Accept 5% probability of making a Type I error
  • If probability that difference is not real (random noise) <5% = significant difference

Never truly prove H0 or H1, only accept or reject H0

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P-Values

Statistical tests quantifies differences/strength of association by calculating test statistic

Test statistic + degrees of freedom = p-value

p-value - proabbility that effect seen in data is due to random noise

  • If p>a = accept H0, no sig. effect
  • If p<a = reject H0, significant effect

Very small p-value = small probability that difference is due to random noise

p-value contains information - always give actual value if poss e.g. 0.0000053

Asterisks - used to indicate degrees of significance:

  • * - 0.05-0.01
  • ** = <0.01
  • *** = <0.005 or <0.01

If more 2+ test used in experiment, critical p-value should be reduced to retain critical level of 0.05 across experiment

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Degrees of Freedom

Degrees of freedom - no. of independent values/quantities which can be assigned to statistical distribution

Number related to sample size - accounts for no. observations, no. factor levels and any manipulations

Difficult concept - related to how much info have in terms of replication

Stats need 1+ d.f. - more data points than parameters

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Stats Reporting

Report stats in this format:

(Test used, test statistic, degrees of freedom, p-value)

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Two-Tailed Testing

When testing for a difference between A and B, don't know whether A>B or B>A

  • Don't know which way difference would go

With a=5%, 2.5% data as A>B and 2.5% B>A

  • Half of p is on one end, half on other

= Two-tailed testing

Two-tailed test - statistical test where critical area of distribution is two-sided and tests whether a sample is greater or less than a certain range of values

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One-Tailed Testing

One-tailed test - region of rejection of null hypothesis can only come from a deviation in one direction rather than either

Only use this is absolutely certain that difference can do one way

Used by dividing p-value by 2

If the data actually goes the other way, but there is still a difference, you cannot conclude anything, no matter what the p-value is

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