6.2 Handling Data

Question 1

What is a null hypothesis?

Answer 1

A hypothesis that states that there will be no significant difference or relationship between the two variables being investigated. The results of an experiment determine if this is accepted or rejected.

Question 2

What is probability?

Answer 2

The likelihood of an event occurring, but is different from chance as it can be expressed mathematically.

Question 3

What is chance?

Answer 3

Chance is essentially luck. Statistical tests can be carried out to assess the probability that the results of an investigation were due to chance.

Question 4

What is critical value?

Answer 4

A number that causes rejection of the null hypothesis if a given test statistic is this number or more, and acceptance of the null hypothesis if the test statistic is smaller than this number.

Question 5

What is the equation to calculate the mean?

Answer 5

Mean = sum of all measurements / number of measurements

Question 6

What is standard deviation?

Answer 6

Standard deviation measures the spread of the results around the mean value.

Question 7

What are error bars and what do they show?

Answer 7

Error bars are calculated by plotting the highest value and the lowest value, and they show the extremes of the data.

-how spread the data is around the mean
-how accurately the mean value represents the data
-no overlap of error bars show there is a significant difference between sets of data
-an overlap shows there is no significant difference between the sets of data

Question 8

What are the rules to determine if the results are due to chance?

Answer 8

If the probability is more than 5% due to chance, then there is no significant difference between the variables, so the results are due to chance. Accept the null hypothesis.
If the probability is less than 5% due to chance, then there is a significant difference between the variables, so the results are not due to chance. Reject the null hypothesis.

Question 9

What is a chi-squared test?

Answer 9

It is concerned with frequencies, finding the number of individuals in different categories (categorical data). It determines if there is a significant difference between the observed and expected frequencies in an experiment, to determine if the difference is significant or not.

Question 10

How is the degrees of freedom calculated?

Answer 10

Number of categories - 1

Question 11

What is concluded if the chi-squared value is greater than the critical value?

Answer 11

There is a less than 5% probability that the results are due to chance. There is a significant difference between the results so we reject the null hypothesis.

Question 12

What is concluded if the chi-squared value is less than the critical value?

Answer 12

There is a more than 5% probability that the results are due to chance. There is no significant difference between the results so we accept the null hypothesis.

Question 13

What is the critical value?

Answer 13

A number given in a table, depending on the probability and degrees of freedom. It is compared to the chi-squared value to determine if the results are due to chance or not.

Question 14

What is the spearman’s rank test?

Answer 14

Used to assess the degree of association between different measurements from the same sample. It is looking for a positive or negative correlation between two variables, to determine whether the correlation between two variables is statistically significant.

Question 15

Describe the process of conducting the spearman’s rank test?

Answer 15

Assign ranks to the values from lowest (1) to highest. If they are tied, add the ranks together and give them both the mean rank. Eg. 8 and 9 are both given 8.5
Calculate the difference between the two ranks
Use the spearman’s rank equation to calculate spearman’s rank.
If the spearman’s rank value is positive, then there is positive correlation between the variables, but if the spearman’s rank value is negative, then there is negative correlation between the variables.
If the value lies between 1 and -1, we must carry out a test for significance, by comparing it to the critical value.

Question 16

What can we conclude if the spearman’s rank correlation is bigger than the critical value?

Answer 16

If the calculated value for spearman’s rank is bigger than the critical value, there is a less than 5% probability that the correlation is due to chance. We reject the null hypothesis.

Question 17

What can we conclude if the spearman’s rank correlation is bigger than the critical value?

Answer 17

If the calculated value for spearman’s rank is smaller than the critical value, there is a more than 5% probability that the correlation is due to chance. We accept the null hypothesis.

Question 18

When is the students T-test used?

Answer 18

the students t statistical test is used when looking for the difference between two means, and you want to know if it is significant.
it is used to find out if there is a significant difference between mean values.

Question 19

Describe how the students t-test is conducted?

Answer 19

1) write the null hypothesis
2) use the formula to calculate the value of t
3) calculate the critical value
4) interpret the results (decide whether to accept or reject the null hypothesis)

Question 20

What can we conclude if the students t-test value is more than the critical value?

Answer 20

The calculated value for t is greater than the critical value. There is a less than 5% probability that the difference between the two means is due to chance. We reject the null hypothesis.

Question 21

What can we conclude if the students t-test value is less than the critical value?

Answer 21

The calculated value for t is less than the critical value. There is a more than 5% probability that the difference between the two means is due to chance. We accept the null hypothesis.