Review Feb 2015

Adapted from: Taylor, S. (2009). Statistical Analysis. Taken from:

Some useful rules (Taken from 'Error Bars in experimental Biology'). Rule 1: Always state on the graph which type of error bar is being used. Mean + Range Mean +/- SD (standard deviation) Rule 2: Always state the number (n) of the sample size in the legend of the graph. Rule 3: Error bars and statistics should only be shown for indendently repeated experiments, and never for replicates. If we wanted to find the mean height of sycamore trees then you would measure the height of different trees (independently repeated experiments) not the same tree many times (replicates).

To decide if there is a significant difference between two samples we must compare the mean height for each sample… … and the spread of heights in each sample. In statistical analysis, the standard deviation of a sample is useful for comparing the means and the spread of data between two or more samples. S x = Σx 2 - (Σx) 2 n n - 1 Where: Sx is the standard deviation of sample Σ stands for ‘sum of’ x stands for the individual measurements in the sample n is the number of individuals in the sample You can calculate standard deviation using the formula:

What does the following scatter graph show? A.No correlation between these variables B.Strong positive correlation between these variables C.Strong negative correlation between these variables D.Weak negative correlation between these variables (Total 1 mark)

What does the size of the standard deviation indicate about data? A.How accurately the data were measured B.How widely the data are spread above and below the mean C.Whether the mean is larger or smaller than it should be D.Whether the reliability of the data is greater or less than 68% (Total 1 mark)

Are our results reliable enough to support a conclusion? Browne, G. (2005). T-test. Taken from:

Imagine we chose two children at random from two class rooms… D8C1 … and compare their height …

D8C1 … we find that one pupil is taller than the other WHY?

REASON 1: There is a significant difference between the two groups, so pupils in C1 are taller than pupils in D8 D8 YEAR 7 C1 YEAR 11

REASON 2: By chance, we picked a short pupil from D8 and a tall one from C1 D8C1 TITCH (Year 9) HAGRID (Year 9)

How do we decide which reason is most likely? MEASURE MORE STUDENTS!!!

If there is a significant difference between the two groups… D8C1 … the average or mean height of the two groups should be very… … DIFFERENT

If there is no significant difference between the two groups… D8C1 … the average or mean height of the two groups should be very… … SIMILAR

Remember: Living things normally show a lot of variation, so…

It is VERY unlikely that the mean height of our two samples will be exactly the same C1 Sample Average height = 162 cm D8 Sample Average height = 168 cm Is the difference in average height of the samples large enough to be significant?

Which hypothesis can be tested using the t-test? A.The difference in variation between two samples is not significant. B.The difference between observed values and expected values is not significant. C.The change in one variable is not correlated with a change in another variable. D.The difference between the means in two samples is not significant. (Total 1 mark)

What conditions must be met for the t-test to be applied? I.Population sampled must have a normal distribution II.Variable measured is continuous III.Sample size must be >30 A.I only B.II and III only C.I and II only D.I, II and III

Taken from: