This document discusses key concepts in statistical analysis: 1) Error bars represent the variability in data and can show the range or standard deviation. The standard deviation summarizes how data values are spread around the mean, with 68% of values within one standard deviation. 2) The standard deviation is useful for comparing means and spreads between samples. Larger differences in means and standard deviations between samples indicate they are less likely from the same population. 3) A t-test measures the overlap between two data sets and determines if their differences are statistically significant or likely due to chance. A significance level of 5% is commonly used, below which the null hypothesis that sets are the same is rejected.

1. 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.
• Students are not expected to know the formulas for calculating these statistics. They will be
expected to use the standard deviation function of a graphic display or scientific calculator.
1.1.3 State that the term standard deviation is used to summarise the spread of values around the
mean, and that 68% of the values fall within one standard deviation of the mean.
• If data is normally distributed, 68% of all values lie within the range of the mean, ± one
standard deviation (s or σ). This rises to 96% for ± two standard deviations.
• 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.
1.1.4 Explain how the standard deviation is useful for comparing the means and the spread of
data between two or more samples.
• The size of a standard deviation might be the result of genetic or environmental factors.
• When comparing two samples from two different populations, the closer the means and the
standard deviations, the more likely the samples are drawn from a similar population. The
bigger the difference the less likely this is so.
• This is dependent on sample size; larger samples make more reliable results.
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1.1.5 Deduce the significance of the difference between two sets of data using calculated values for
t and the appropriate tables.
• For the t-test to be applied, the data must have a normal distribution and a sample size of at least
10.
• The t-test can be used to compare two sets of data and measure the amount of overlap.
• .For example are plants treated with fertiliser taller than those without? If the means of the two
sets are very different, then it is easy to decide, but often the means are quite close and it is
difficult to judge whether the two sets are the same or are significantly different.
• To compare two sets of data use the t-test, which tells you the probability (P) that there is no
difference between the two sets. This is called the null hypothesis (H0
).
• P varies from 0 (impossible) to 1 (certain).
• The higher the probability, the more likely it is that the two sets are the same, and that any
differences are just due to random chance. The lower the probability, the more likely it is that that
the two sets are significantly different, and that any differences are real.
• Where do you draw the line between these two conclusions? In biology the critical probability is
usually taken as 0.05 (or 5%). This may seem very low, but it reflects the facts that biology
experiments are expected to produce quite varied results. So if P > 5% then the two sets are the
same (i.e. accept the null hypothesis), and if P < 5% then the two sets are different (i.e. reject the
null hypothesis).
• Students will not be expected to calculate values of t
1.1.6 Explain that the existence of a correlation dos not establish that there is a causal relationship
between two variables.
• Correlation statistics are used to investigate an association between two factors such as age and
height; weight and blood pressure; or smoking and lung cancer.
• After collecting as many pairs of measurements as possible of the two factors, plot a scatter graph
of one against the other.
• If both factors increase together then there is a positive correlation, or if one factor decreases when
the other increases then there is a negative correlation. If the scatter graph has apparently random
points then there is no correlation.
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