Evaluation: Descriptive Statistics

Question 1

Two important aspects to summarising a sample?

Answer 1

Central tench of the distribution of scores in the sample and the spread, dispersion or variation among the scores in the sample.

Question 2

Measures of Central Tendency?

Answer 2

Mean, mode and Median: Summary of the sample of scores

Question 3

Measures of Spread

Answer 3

Range, variance, SD and COV

Question 4

What is the Coefficient of Variation?

Answer 4

How large the SD is, relative to the size of the mean

Question 5

What is the CV useful for?

Answer 5

Comparing different people or clients in terms of the degree of relative variability of a measure- takes into consideration that people can differ in their overall level of scores

Question 6

Measurements of CV?

Answer 6

less than 10% low variation

CV 20% or greater is highly variable

Question 7

Why to consider variability?

Answer 7

When developing new measurement protocols it is useful to consider the amount of variability to see whether the measure is subject to a lot of measurement error. How many times does the sample have to be undertaken to capture a representative mean?

Question 8

Frequency Distributions?

Answer 8

Single sample that can be viewed by plotting the number of cases with measure on horizontal axis

Question 9

Histograms?

Answer 9

Categories and bars represent, the dependent variable: Common way of visually evaluating distributions

Question 10

Box Plots?

Answer 10

Provide visual information about the shape of the distribution as well as being useful to see the spread and central tendency- evidence of outliers

Question 11

What are the different types of shape?

Answer 11

Normal, uni modal, bi modal, multi modal and rectangular

Question 12

Skewness

Answer 12

Degree of symmetry, 0=symmetrical >0 is positive skew and <0 is negative skew

Question 13

Kurtosis

Answer 13

Peakedness or flatness of distribution

Question 14

Checking for outliers

Answer 14

Representation of scores that are aberrant or extreme, have strong effects on means, variance, SD and correlation.

Question 15

What is the point of data transformation?

Answer 15

Sometimes a skewed distribution can be made more or less normal by transforming the score: May be a viable option in order to perform statistical analyses such as a multivariate statistical procedure

Question 16

Ways to transform data?

Answer 16

• Take square root of the scores
• Logarithm of each score
• Take the inverse of each score

Question 17

Why is it important to consider the implications of data transformation?

Answer 17

May not be appropriate if the meaning of the variable changes and becomes less comprehensible.

Question 18

What are Z score transformations?

Answer 18

Transformation that does not change the shape of the distribution, they can not be used to make a distribution normal, although have properties of a normal distribution.

Question 19

Ways of evaluating how well sample means represent the sample distribution.

Answer 19

• Check distribution with histogram, make sure unimodal
• Check size of standard deviation (smaller the better the mean represents the raw data in the sample)
• Convert SD to coefficient of variation, compare with conventions of evaluating variability

Question 20

What is sampling error?

Answer 20

Difference between the sample mean and then population mean

Question 21

What is the standard error

Answer 21

Size of average sampling error, used to evaluate how well the sample mean estimates the population mean. Smaller the standard error the better the mean estimates the population.

Question 22

What happens when the sample is larger

Answer 22

Smaller sampling error, and the closer to the mean of the sample is to the population mean
The more time and effort is needed to collect the sample, trade off between effort and accuracy

Question 23

What happens when reducing measurement error?

Answer 23

Smaller the standard deviation and smaller the standard error.