Standard deviation and T test

Standard deviation

• a measure of how spread out the data is

• the more spread out the data the more variation that exists

• represented by sigma symbol

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Statistical tests

• can be used to give a likelihood of any variation in the data being statistically significant

  • not just due to normally occurring variation in the data

• we use a p value of 0.05

  • means there is only a 5% chance that our conclusion is wrong

  • 95% sure we are correct

Carrying out a statistical test

• state null hypothesis

• calculate test statistic

• compare this to a table of probability values

• accept/reject null hypothesis

• state clear conclusion

Null hypothesis

• prediction that there is no significant difference between the groups/populations being studied

• any observed difference is thus chance

  • part of normal variation seen in any population

p values

• used to determine how likely it is that the observed outcome is due to natural variation

• if the calculated statistical value is less than the critical value for p=0.05 then we accept the null hypothesis

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Degrees of freedom

• greater number of data points = greater the potential spread of results

• it is necessary to take into account the potential spread of results by calculating the degrees of freedom

• unpaired t test:

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Unpaired t test

• data collected should be:

  • normally distributed

  • enough to calculate a reliable mean

    • approx n = 15

• the two groups can have different sample sizes

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