T - Tests and Spearman's Rank

Question 1

What does a t - test do

Answer 1

Compares two samples of the same type of data and works out whether any difference between the two groups can be explained by chance variations, or whether the variables in the two samples are really different from each other.​ (E.g. June temperatures in two cities)

Question 2

What is the formula for t - test

Answer 2

t = (x1 - x2) ÷ √(σ1)²/n1 + (σ2)²/n1

Question 3

What does each symbol stand for in the formula for t - test

Answer 3

σ = Standard Deviation (Shows up twice because there’s 1 for each data set)

x1 and x2 = The means of the 2 sets of data

n1 and n2 = Refer to the number of individual values in each set of data

Question 4

What is the result you get in a t - test compared to

Answer 4

Critical Values in a table

Question 5

What does it mean if your t value is high

Answer 5

the results are unlikely to be different due to chance alone

Question 6

How do you work out the number of degrees of freedom

Answer 6

Total the number of values in each data set and take away 1 from each e.g. (10 - 1) + (10 - 1) = 18

Question 7

What is the critical value which tests for statistical significance in the table

Answer 7

0.05, if t - value is more than the value in the 0.5 section of the table we would have a less than 0.05 (or 5 %) chance of getting results, meaning its likely not down to chance

Question 8

What is spearman’s rank used for

Answer 8

to look for a correlation between two sets of data.

Question 9

What happen with each data point when calculating spearman’s rank

Answer 9

Each data point must be paired with another (height and hand length for each person in this example).​

Data points are ranked (e.g. the tallest of 9 people might be ranked 9, the second tallest ranked 8, and so on.).

Question 10

What do you do if two data points are equal in spearmans rank

Answer 10

split the difference – instead of calling them 7 and 6, for example, both data points are ranked 6.5. ​

Question 11

What is the formula for spearmans rank

Answer 11

rs = 1 - 6∑d² ÷ n(n² - 1)

Question 12

What is does each symbol stand for in the spearman’s rank formula

Answer 12

rs = correlation coefficient

n = number of pairs of data

d = difference between ranks of data

Question 13

What is a coefficient of 1 equivalent to

Answer 13

A perfect positive relationship

Question 14

What is a coefficient of -1 equivalent to

Answer 14

A perfect negative relationship

Question 15

What is a coefficient of 0 equivalent to

Answer 15

No relationship at all