Statistical Tests and Maths

When is the student’s T-test used?

when you have two sets of data that you want to compare.

It tests whether there is a significant difference in the means of the two data sets.

value obtained is compared to a critical value which helps to decide whether differences observed are due to chance

When is a chi-squared test used?

To test whether observed results are statistically different from expected results.

Compare the result to a statistical value- if it is larger than the critical value at P= 0.05, you can be 95% certain that the difference is significant.

When is a correlation coefficient used?

to work out the degree to which two sets of data are correlated.

Result compared to critical value.

What conditions are needed to use a student’s t-test?

data is continuous and normally distributed

variances of the populations should be equal

samples must be independent

What are the steps to conduct a t-test?

state the null hypothesis

calculate the t-statistic using formula provided

calculate degrees of freedom- n₁ + n₂ - 2

compare against critical value

accept or reject- if t-statistic is greater, reject the null hypothesis; if t-statistic is less, accept the null hypothesis

Given the following data, use the student's t-test to determine if there is a significant difference between the mean number of turtle eggs hatched in high and low temperature conditions.

Dataset	Mean (number of eggs)	SD (number of eggs)	Sample size (n)
High temperature	80	5	15
Low temperature	70	5	15

(critical value will be 2.05)

(t-test comes out at t = 5.48)

null hypothesis: there is no significant difference between the number of turtle eggs hatched in high and low temperatures

1) t-test: t= 5.48 (use formula in exam)

2) df = 15+15 -2 = 28

3) with df = 28 and significance of 0.05, the critical value is 2.05

4) 5.48 is greater than 2.05; reject the null hypothesis and conclude that there is a significant difference between hatch rates of turtles in high and low temperatures

A t-test is carried out. The value obtained was greater than the critical value at p = 0.05. What is the outcome?

Reject the null hypothesis. We can be 95% certain that the difference between the two data sets is significant and not due to chance.

A chi-squared test is carried out. The value obtained is is greater than the critical value at p = 0.05. What is the outcome?

Reject the null hypothesis. We can be 95% sure that the difference between the observed and expected values are significant.A

A Spearman’s rank correlation coefficient is found. A value of -0.57 is found. This is greater than the critical value at p = 0.05. What is the outcome.

The critical value must be between -1 and -0.57. Do not reject the null hypothesis. There is not a significant correlation between two variables.

A Spearman’s rank correlation coefficient is found. A value of 0.57 is found. This is greater than the critical value at p = 0.05. What is the outcome.

The critical value must be between 0.57 and 1. Reject the null hypothesis. There is evidence to suggest a significant positive correlation between two variables.

What is a causal relationship?

Where a change in one variable directly causes a change in another. This is difficult to prove; most things are just said to be correlated.

What is the formula for percentage error?

uncertainty/reading x100

What is the uncertainty of a ruler?

±0.5 mm