The document discusses three key statistical tests: the chi-square test, Student t-test, and correlation coefficient calculations. It provides information on what each test is used for and the relevant quantities calculated for each using mathematical formulas. The chi-square test compares observed and expected patterns in data. The Student t-test judges the significance of differences between means of two groups. The correlation coefficient determines the existence of correlation between two data sets.

1. Statistical tests
The statistical tests are used to assess the level of confidence on data sets. The three
key tests :
• Chi-square test (x2)
• Student t-test (t)
• Correlation coefficient calculations ( r )

2. Chi-squared (x2) test Student t test Correlation coefficient (r ) test
Compares the observed pattern with the
chance pattern in data.
Judges the significance of any difference
between the means of data sets of two
different groups.
Determines the existence of correlation
between any two data sets.
df = n – 1
n = number of categories
df = (n1 + n2 ) – 2
n1 = mean of the first data set
n2 = mean of the second data set
df = n – 2
n = number of the data point in both
variables
Enough data for a reliable mean
The data normally distributed
The sample size need not to be equal
Statistical test: For each of the three tests the relevant quantities are calculated using Mathematical formulas given in the table.
The calculated values compared against the standard probabilities tables allow interpretation of the data in a statistically informed way.

3. Q: 1. Scientists used a statistical test to determine whether there was a significant difference in the amino acid
concentration in two types of white wine. They obtained a p value of 0.04. Name the statistical test the scientists
used and give a reason for your answer. Was the difference significant? Give a reason for your answer.
• Name of the statistical test: Student t-test
• Reason for choice: Since the investigation requires comparison of means of two data sets.
• Explanation of test result: Since the p value is below 5% (0.04), the Null hypothesis is rejected and therefore, the
difference is significant.
Past paper example: 1

4. Q:2. Doctors carried out a statistical test to determine whether the antibody concentrations were significantly
different in girls given two doses of vaccine, compared with those given three doses. They determined the mean
concentrations of antibody 9 months after the first dose of vaccine.
• What statistical test the should the doctors have used? Student-t test as the investigation involves comparison of
means of two data sets.
• Give the reason for your choice: as the investigation involves comparison of means of two data sets.
Past paper example: 2