Stats

Question 1

Statistics key terms:
Define probability?

Answer 1

The chance of something happening, e.g. there is a 50% or 1/2 chance of tossing a coin and getting a head. If we toss a coin twice the chance of 2 heads is 1/2 x 1/2 = 1/4 (or 25%).

Question 2

Statistics key terms:
Define standard deviation?

Answer 2

A measure of the spread from the mean. It is a better measure than the range of the results. We can draw error bars of S.D on a bar chart.

Question 3

Statistics key terms:
Define Hypothesis?

Answer 3

A statement about what we expect our results will show, e.g. there will be a significant difference between 2 sets of measurements.

Question 4

Statistics key terms:
Define Null hypothesis?

Answer 4

A statement that there is no significant difference between 2 sets of measurements. (Any difference is down to chance alone.)
- we reject or accept a null hypothesis based on probability. We reject if its probability is less than 5%/ 0.05 (or a 1/20 chance).
- If we reject a null hypothesis then we state that there is a significant difference between the 2 sets of data.
- for error bars
overlap = no significant difference
no overlap = significant difference
- we want low standard deviation (small difference between values)

Question 5

standard deviation-
- what sort of data is used?
- use?
- how to calculate degrees of freedom?
- how to accept/ reject null hypothesis?

Answer 5

use: measure range of values around a mean

degrees of freedom:
N/A

Accept/ reject Null Hypothesis:
There is an/ no overlap in the +/- SD bars. This indicated the difference in the means of… are likely/ unlikely to be due to chance.

Overlapping SD bars means the difference between two values is not significant.

(The smaller the standard deviation, the narrower is the range, which translate to a higher reproducibility. the smaller standard deviation means the experimental values are clustered together tightly (higher precision)).

Question 6

Statistical tests - General point?

Answer 6

• We calculate a value using a formula and then see if this is higher than the critical value at the 5% level of probability. If it is, we say the results shows a significant difference. This gives a probability that any differences in our data are just down to chance.
• We need to consider the sample size to find the ‘degrees of freedom’ for our data. The value of the degrees of freedom will affect the critical value that has to be exceeded, for the results to be significant.
• We can compare our critical value at the 1% or 0.1% level of probability, to see if it is even more unlikely that any differences in our data are just down to chance.

Question 7

What are the 3 statistical tests we need to know?

Answer 7

1. chi squared test
2. spearman’s rank correlation coefficient
3. student t-test

Question 8

Chi-squared test-
- what sort of data is used?
- use?
- how to calculate degrees of freedom?
- how to accept/ reject null hypothesis?

Answer 8

To find the difference between 2 groups. the two groups need to be categoric, e.g. blue or brown eyes. Often used in genetics.

use:
used to compare observed results with theoretical expected frequencies. The higher the X² value the greater the difference.

Degrees of freedom: (n-1)

Accept/ reject null hypothesis:
If the calculated value is greater/ less than critical value at 0.05 level then you can accept/ reject the null hypothesis.

Greater value than critical value/ reject null hypothesis

(Often used for genetics and fieldwork sampling.)

Question 9

Spearman’s rank correlation coefficient-
- what sort of data is used?
- use?
- how to calculate degrees of freedom?
- how to accept/ reject null hypothesis?

Answer 9

This is a measure of correlation.
It tells us if a correlation is significant; a value of 1 is a perfect positive correlation and a value of -1 is a perfect negative correlation. This is to look for association (e.g. is the number of plantains in a field associated with light levels.)

REMEMBER: a correlation does not always mean that there is a cause/ effect relationship.

use:
Used to see the strength of the correlation (association) between 2 sets of numerical data.

Degrees of freedom:
n

Accept/ reject null hypothesis:
If your calculated number is the same of higher than critical value then your correlation is significant and you would reject the null hypothesis.

(remember to rank the data. The results will always be between 1 and minus 1)

Question 10

Students t-test-
- what sort of data is used?
- use?
- how to calculate degrees of freedom?
- how to accept/ reject null hypothesis?

Answer 10

This tells us if the difference between 2 means is significantly different. For example we could compare the mean of the height of grass in two different fields. To calculate these we need to find the S.D. of each population and then put them into a formulae to find a value of ‘t’.

use:
to find the difference between two means and whether it is significant

degrees of freedom:
(n1 + n2) - 2

accept/ reject null hypothesis:
If the t value is less/ greater than the critical value, then there is a 5% probability that the means… are/ not due to chance. We accept/ reject null hypothesis.

(less/ due to chance/ accept null hypothesis.
Greater than critical value/ not due to chance/ reject null hypothesis.)

Question 11

What does the standard deviation tell you?

Answer 11

• the standard deviation tells you how much the values in a single sample vary. It’s a measure of the spread of values about the mean
• sometimes you’ll see the mean as, e.g. 9+ or - 3. This mean that the mean is 9 and the standard deviation is 3, so most of the values are spread between 6 to 12
• a large standard deviation means the values in the sample vary a lot. A small standard deviation tells you that most of the sample data is around the mean value, so varies little
• a steeper graph shows the values are similar and the standard deviation is small
• a fatter graph shows the values vary a lot and the standard deviation is large

Question 12

What can you use the standard deviation to do?

Answer 12

• standard deviations can be plotted on a graph or chart of mean values using error bars
• error bars extend one standard deviation above and one standard deviation below the mean (so the total length of an error bar is twice the standard deviation)
• the longer the bar, the larger the standard deviation and the more spread out the sample data is from the mean