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.
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