Variation - stats

Question 1

Discontinuous variation

Answer 1

• discrete - a characteristic that can only result in certain values
• determined by genetic factors only
• represented as a bar chart or pie chart
• e.g. sex, blood group, shape of bacteria

Question 2

Continuous variation

Answer 2

• characteristic that can take any value within a range
• continuum = graduation in values
• controlled by a number of genes (polygenes) + environmental factors
• represented in a frequency table + histogram with curve drawn
• e.g. height, mass

Question 3

Normal distribution

Answer 3

• continuous distribution usually produces a bell-shaped curve - normal distribution curve
• mean, mode, median = same
• Bell-shape = symmetrical distribution about the mean
• 50% of values are < mean, 50% of values > mean
• most values lie close to the mean - individuals at extremes are low
• 68% of the data are 1SD away from the mean, 95% of the data are 2SD away from the mean

Question 4

What is Spearman’s rank correlation coefficient?

Answer 4

• a statistical test for the correlation between 2 sets of data - to consider the relationship
• measures strength in correlation - positive or negative or none
• need at least 8 pairs of data
• Rs values are always between -1 and +1
• 1 indicates a perfect relationship; -1 = perfect inverse relationship; 0 = no relationship

Question 5

Null hypothesis for Spearman’s rank

Answer 5

H₀: no statistically significant correlation

Question 6

When to reject or accept H₀ - Rs

Answer 6

• if Rs is less than the critical value, we accept the null hypothesis = >5% probability that any association is due to chance and <95% certain of a statistically significant correlation
• if Rs is greater than the critical value, we reject the null hypothesis = <5% probability that any association is due to chance and >95% certain of a statistically significant correlation

Question 7

How to calculate Rs

Answer 7

1. Each of the data needs to be put into order of rank
2. 2 or more tied data share the no. of ranks (average them)
3. Find the difference between the ranks and square them
4. Apply the formula
5. Compare Rs to critical value

Question 8

Conclusion for Spearman’s rank test

Answer 8

The calculated Rs of ___ is greater/less than the critical value of ___ for ___ pairs of data. Therefore accept/reject H₀ at the 5% significance level. There is/is not a statistically significant correlation at the 5% significance level.

Question 9

What is the students T-test?

Answer 9

• test for comparing the means of data values of 2 populations
• can only be used on normally distributed data
• t-score/value is a ratio between the difference between 2 groups and the difference within the groups. The larger the t-score, the more difference between groups; small t-score = more similarity between groups

Question 10

Difference between paired and unpaired t-tests

Answer 10

• paired - both sets of data from the same individual: df = number of pairs - 1
• unpaired - sets of data come from different samples: df = number of samples - 2

Question 11

Differences between the tails

Answer 11

• 1 tailed - H₁ considers only 1 alternative: < or>

- 2 tailed - H₁ considers either alternative: /=

Question 12

When to accept and reject H₀ - t-test

Answer 12

• if the t-value exceeds the critical value at p=0.05, then we reject the null hypothesis

Question 13

Null hypothesis for t-test

Answer 13

H₀: there is no statistically significant difference between the means of the data