Topic 1: Statistical Analysis

 

1.1.1 State that error bars are a graphical representation of the variability of data.

·         Error bars can be used to show either the range of the data or the standard deviation.

1.1.2 Calculate the mean and standard deviation of a set of values. (Use graphics calculator). 

·         Students should specify the standard deviation (s), not the population standard deviation.

·         Students will not be expected to know the formulas for calculating these statistics. They will be expected to use the standard deviation function of a graphics display or scientific calculator.

1.1.3 State that the term standard deviation is used to summarize the spread of values around the mean, and that 68% of the values fall within one standard deviation of the mean.

·         For normally distributed data, about 68% of all values lie within +-1 standard deviation (s or σ) of the mean.

·         This rises to about 95% for +-2 standard deviations.

1.1.4 Explain how the standard deviation is useful for comparing the means and the spread of data between two or more samples.

·         A small standard deviation indicates that the data is clustered closely around the mean value.

·         Conversely, a large standard deviation indicates a wider spread around the mean.

1.1.5 Deduce the significance of the difference between two sets of data using calculated values for t and the appropriate tables (using a graphics calculator).

·         For the t-test to be applied, the data needs to have a normal distribution and a sample size of at least 10.

·         T-test is used to compare two sets of data and measure the amount of overlap.

·         Students will not be expected to calculate values of t.

·         A two-tailed, unpaired t-test is expected.

·         You need to show how to calculate such values using a graphics calculator.

1.1.6 Explain that the existence of a correlation does not establish that there is a casual relationship between two variables.

• A correlation between two variables may mean one causes the other.
• However, the correlation does not confirm causality.
• Experimental investigations are needed to study cause and effect
• For example, there could be a high positive correlation between teenagers that watch the news each night and teenagers that own a pet dog.
• It cannot be confirmed that one causes the other.
• Calculations of such values is not expected.