Statistical Tests Flashcards
Purpose of t-test.
- To compare 2 sets of mean
- If they are significantly different or not
When is t-test used?
Data are:
- continuous
- normally distributed
Formula of t-test.
- t = |Ā - B| / Square root of (SA^2/nA + SB^2/nB)
- degrees of freedom = (nA - 1) + (nB - 1) = nA + nB - 2
Steps for t-test.
- let Ho: Ā = B
- Calculate s. d. of each sample.
- Calculate t-value.
- Find degrees of freedom.
- Find probability of Ā = B
- When P <= 0.05, Ā does not = B
When P > 0.05, Ā = B
How to conclude for t-test?
- critical value (at degrees of freedom = n & p = 0.05) = x
- calculated t-value is, greater / lesser, than critical (t-) value
- null hypothesis, accepted / rejected (at p = 0.05)
Purpose of chi-squared test.
- To test the goodness of fit between
- O & E (observed & expected values)
- When analysing results from:
- genetics / breeding experiments
- ecological sampling
When is chi-squared test used?
Data are:
- discrete
- categoric
Formula of chi-squared test.
χ^2= ∑(O-E)^2/E
Steps for chi-squared test.
- Set up null hypothesis, Ho: there is no significant difference between O & E.
- Calculate chi-squared value.
- Calculate degrees of freedom = n-1 (n = no. of classes)
- Use a chi-squared table to find P(χ2)
- If P(χ2) > 0.05:
- chances of goodness of fit > 5%
- accept Ho
- O = E - If P(χ2) <= 0.05:
- chances of goodness of fit <= 5%
- reject Ho
- O P(χ2) > 0.05:
- chances of goodness of fit > 5%
- accept Ho
- O ≠ E
How to conclude for chi-squared test?
- Conclusion is made with 95% confidence.
- (Because) the rejected value could be rejected wrongly
- Allow 5% in conclusion
Purpose of Pearson’s linear correlation.
Determines whether there is linear correlation between 2 variables
When is Pearson’s linear correlation used?
Data must be:
- quantitative
- show normal distribution
Formula of Pearson’s linear correlation.
r = [ ∑ xy - nx̄ȳ ] / (n-1) SxSy
- r = correlation coefficient
- x = no. of species A
- y = no. of species B
- n = no. of readings
- Sx = standard deviation of species A
- Sy = standard deviation of species B
- x̄ = mean no. of species A
- ȳ = mean no. of species B
Steps for Pearson’s linear correlation.
- Create a scatter graph of data & identify if a linear correlation exists.
- State a null hypothesis, Ho = there is no correlation between the abundance of species A & species B.
- Use the following equation to work out Pearson’s correlation coefficient, r
How to conclude for Pearson’s linear correlation?
If the correlation coefficient, r is close to 1 or -1, then it can be stated that there is a strong linear correlation between the 2 variables & the null hypothesis can be rejected.
