10. Quantitative Data Analysis

Question 1

Define mean.

Answer 1

Arithmetical average (adding up all the values and divided the number of values).

Question 2

What is a strength of using the mean?

Answer 2

A sensitive measure because it reflects the values of all the data in the final calculation.

Question 3

What is a weakness of using the mean?

Answer 3

Can be unrepresentative if data set if there are extreme values.

Question 4

Define median.

Answer 4

The middle score of a set of numbers. Place all the values in order and select the middle value. If there are two middle values, calculate the mean of these 2 values.

Question 5

What is a strength of using the median?

Answer 5

Not affected by extreme scores.

Question 6

What is a weakness of using the median?

Answer 6

Not as sensitive as the mean because not all values are reflected in the final calculation of the median.

Question 7

Define mode.

Answer 7

The most common number in a set of numbers. Identify the group or groups which is most frequent/common.

Question 8

What is a strength of using the mode?

Answer 8

Useful when data is in categories.

Question 9

What is a weakness of using the mode?

Answer 9

Not a useful way of describing data when there are several modes.

Question 10

Define range.

Answer 10

The range is a measure of dispersion, found by finding the highest number and taking away the lowest number giving the difference between the two.

Question 11

What is a strength of finding the range?

Answer 11

-A convenient way to express how spread out a data set is as highest and lowest value are used.
-Quick and easy to calculate.

Question 12

What is a weakness of finding the range?

Answer 12

-Affected by extreme values.
-Fails to take account of the distribution of the data set, for example it doesn’t indicate whether most numbers are closely grouped around the mean or spread out evenly,

Question 13

Define standard deviation.

Answer 13

-Measure of how far scores vary (deviate) from the mean average.
-The higher the standard deviation, the greater the spread of scores around the mean value (the data is more varied).
-A low SD indicates that.the scores tend to be close to the mean of the set (data is less varied).
-The lower the SD, the more accurate and representative the mean of the data set is.

Question 14

What is a strength of finding the standard deviation?

Answer 14

-A precise measure of dispersion because all the exact values are taken into account.
-It is not difficult to work out if you are using a calculator.

Question 15

What is a weakness of finding the standard deviation?

Answer 15

-May hide some of the characteristics of the data set (eg extreme values).
-Cannot be immediately sensed from the data, whereas the range is fairly quick to identify.

Question 16

In the standard deviation formula, what does x stand for?

Answer 16

Each score.

Question 17

In the standard deviation formula, what does x̄ stand for?

Answer 17

The mean of average.

Question 18

In the standard deviation formula, what does n stand for?

Answer 18

The number of values.

Question 19

In the standard deviation formula, what does the symbol Σ (sigma) stand for?

Answer 19

The sum of the values.

Question 20

What are the steps for finding the standard deviation?

Answer 20

1. Work out the mean of the results first.
2. Find (x-x̄)^2 for each value.
3. Add these numbers together.
4. Divide total amount by n-1
5. Take the square roof of your answer.

Question 21

Define ordinal data.

Answer 21

-Elements of the data describe properties of objects or events that are ordered by some characteristic (eg rating on a scale of 0-10 for attractiveness, where 0 is the least attractive).
-The order of the object does not, however, provide any information about the distance along the continuum between any two adjacent items.
-Can also be a number that is not ordered but subjective, eg a score on an obedience questionnaire, which does not meet the criteria for interval data.

Question 22

Define interval data.

Answer 22

-Actual scores that are mathematical in having equal intervals between them so that calculations can be conducted.
-Eg reaction times, number of words recalled, age, height (internationally recognised measures such as weight in kg, heart rate in bps).

Question 23

Define nominal data.

Answer 23

-Categories.
-This is simply putting items together by category, eg obedient or not obedient, tallies can be made when observing behaviour.

Question 24

When should a Wilcoxon tested be used?

Answer 24

-When we are looking for a difference between the two conditions.
-The same ppts perform both conditions in the study, ie it’s appropriate for analysing the data from a repeated measures design with 2 conditions or matched pairs.
-Data can be ordinal or interval.

Question 25

What is the Wilcoxon Signed Ranks test process?

Answer 25

1. Calculate the difference between two scores by taking one from another.
2. Rank the differences, use midpoints.
3. Add up the ranks for positive differences.
4. Add up the ranks for negative differences.
5. Observed value T is the smaller of the total ranks.
6. Decide if hypothesis is directional or non-directional.
7. Find N, the number of scores left, ignore those with 0 difference.
8. Find critical value using table in front of exam paper.
9. Compare observed value to critical value. Observed value must be equal to or less than the critical value to be significant.

Question 26

When should the Mann Whitney U statistical test be used?

Answer 26

-When two different groups of participants perform separate conditions in the study (independent groups design).
-Data can be ordinal or interval.
-We are looking for a difference between the two groups.

Question 27

What determines if the observed value is significant in the Mann Whitney U test?

Answer 27

The observed value needs to be equal to or less than the critical value (in the table) to be significant.

Question 28

At p<0.05, is the result significant? Explain why/why not.

(Example structure if results are significant)

Answer 28

The results are significant. The observed value of U (?) is smaller than the critical value (?) (at p<0.05, one/two tailed, Na=? and Nb=?)

Question 29

If results are significant what happens to the null and alternate hypothesis?

Answer 29

If results are significant, we can reject the null hypothesis and accept the alternative hypothesis (CONTEXTUALISE by saying what the alternative hypothesis is).