Statistics

Question 1

Variability of results.
How do you increase the validity of results?
What is the problem with this method?

Answer 1

To increase the validity of values that are used, it is normal to take replicate readings and calculate a mean value. However, this value gives no indication of how variable the original results were. Two means may have different values but the range of original values in both data sets may overlap so much that it is not possible to be confident that they really are significantly different. Alternatively, two means may have been produced from data sets that hardly overlap and there is a significant difference between them.

Question 2

Variability of results.
How can the degree of variability be calculated?

Answer 2

The degree of variability can be calculated as the standard deviation.

For normally distributed results, it is possible to estimate the percentage of all values that are within a particular range around the mean.
Where a graph is drawn using means, error bars may be added to show the standard deviation. This can help to assess whether the differences in mean values are statistically significant.

Question 3

Significance.
What do most scientific investigations produce?

Answer 3

Most scientific investigations produce quantitative results that are compared to establish the significance of any differences.

Question 4

Significance.
What do good scientific analysis never ‘proves’?

Answer 4

Good scientific analysis never ‘proves’ anything as there is always some remaining uncertainty. The key issue is the level of confidence that can be held over the significance of a conclusion.

Question 5

Significance.
What makes a result statistically significant?

Answer 5

A result is statistically significant if a result is unlikely to have occurred by random chance. The probability that the result was produced by random chance can be calculated. The lower it is, the greater the reliability if the results.

Question 6

Significance.
What value refers to the probability if an event being caused by random chance?

Answer 6

The P-value refers to the probability of an event being caused by random chance and is usually expressed as the probability that a single event was significant: 0.9, 0.95, 0.99, 0.995, or as a degree of confidence that the difference investigated is significant.

Question 7

Interpreting significance.
Comparing P-values and significance levels .
what is the significance level of P-values of:
0.1
0.05
0.01
0.005

Answer 7

Showing that a result is significant does not mean it is important or that a casual relationship has been found. Two correlated factors may both be caused by another variable that has not been investigated.
P- value Significance level: % confidence
that the results were NOT
produced by random chance.
0.1 90%
0.05 95%
0.01 99%
0.005 99.5%

Question 8

Statistical tests.
What is it important you ensure when choosing a statistical test?

Answer 8

It is important that the test selected is appropriate.

Question 9

Statistical tests.
What are you trying to do-
if you are comparing the relationship between two variables what test should you use?

Answer 9

Spearman’s rank correlation coefficient

Question 10

Statistical tests.
What are you trying to do-
If you are comparing the means of two data sets and the data was produced through calculated or counted what test should you use?

Answer 10

Mann-Whitney u test

Question 11

Statistical tests.
What are you trying to do-
if you are comparing means of two data sets and the data was produced by being measured and the data is normally distributed what test should you use?

Answer 11

T-test

Question 12

Statistical tests.
What are you trying to do-
if you are comparing means of two data sets and the data was produced by being measured and the data is not normally distributed what test should you use?

Answer 12

Mann-Whitney U test

Question 13

Statistical tests.
What are you trying to do-
if you are comparing the frequencies of items or events what test should you use?

Answer 13

Chi-squared

Question 14

Statistical tests.
when is the spearman rank correlation coefficient used?
what does it assess?

Answer 14

This is used to see whether there is a consistent change in the value of one variable as another variable increases or decreases. It assesses how closely two variables are correlated by comparing the rank orders of the two variables in a variety of sampling situations.

Question 15

Statistical tests.
Examples of hypotheses that can be tested using the Spearman’s rank correlation coefficient?

Answer 15

• crop yield increases as fertiliser application increases
• noise levels decrease as distance from a road increases
• per capita energy use increases as per capita income increases
  the number of moths increases as temperature rises
• the number of earthworms declines as soils become more acidic

Question 16

Statistical tests.
What is the Chi-squared test used to compare?
What data can it not be used for?

Answer 16

The chi-squared test is used to compare the frequencies or numbers of things in different groups are statistically significant. It cannot be used for data that can be continuously variable, such as measured or calculated data.

( compares our observed data to our expected data, used when data is counted in various categories. Used to see if there is a significant relationship between variables, often used in ecology, especially in genetics (expected number of phenotypes vs observed number of phenotypes). The number (we get) is then used to see if there is significance between the variables by comparing it to a critical value chart)

Question 17

Statistical tests.
Examples of hypotheses that can be tested using the chi-squared test?

Answer 17

• the different management practices in a range of woodlands affects the number of dormice
• a range of new GM varieties of wheat produce more seeds per seed head than a traditional variety

Question 18

Statistical tests.
When is the t-test used?

Answer 18

This is used to see if there is a significant difference between two means, where the data were measured, for example, mass, length, wind speed, and dissolved oxygen concentration. It can only be used if the data are normally distributed, which may be difficult to determine with small samples . If there is uncertainty the the Mann-Whitney U test should be used instead.

Question 19

Statistical tests.
Examples of hypotheses that can be tested using the t-test?

Answer 19

• The mean mass of lobsters is higher in areas where collection is banned
• the dissolved oxygen level is lower in a sewage-polluted river
• wind speed is lower in a woodland than in a clearing
• soil water content is lower on the south side of a hedge than on the north side

Question 20

Statistical tests.
What is the Mann-Whitney test used to measure?

Answer 20

This is used to see if there is a significant difference between two median values, where the data were counted, such as numbers of organisms or vehicles, or were counted such as diversity indices.

Question 21

Statistical tests.
Examples of hypotheses that can be tested using the Mann-Whitney U test?

Answer 21

• fewer cars use a road when road charging is introduced
• biodiversity is higher in a hedge that is trimmed less frequently
• more wading birds visit a nature reserve after the water level is raised
• more bats feed over an uncut grassland than over a close-mown one
• fewer seeds germinate at pH 5 than at pH 7

Question 22

How are degrees of freedom calculated?
What are they used for?

Answer 22

degrees of freedom = Number of categories (k) - 1

This number is then used to pick the correct column to see the level of significance (if any)

This is used to disprove a null hypothesis

Question 23

why do we run a chi-squared test?

Answer 23

We run a chi-squared test to see if there is in fact a significant relationship seen in the data.

Question 24

what is the general null hypothesis.

Answer 24

there is no significant difference in_______________.