Lecture Week 3

Question 1

6 reasons for conducting exploratory data analysis

Answer 1

1. Check for data entry errors
2. Obtain a descriptive analysis of the data
3. Find patterns that are not obvious
4. Analyse and deal with missing data
5. Checking for outliers
6. Checking assumptions

Question 2

What is Central Tendency

Answer 2

Tendency for the values of a random variable to cluster round its mean, mode, or median.

Question 3

Multiple Measures of Central Tendency

Answer 3

• Summary statistic that represents the center point value of a dataset
• Three most common measures of central tendency are the mean, median, and mode.

Question 4

Multiple Measures of Variability

Answer 4

• Define how far away the data points tend to fall from the center.
• Range, Interquartile Range, Variance and Standard Deviation

Question 5

Quantitative measures of Shape

Answer 5

• The distribution shape of quantitative data can be described as there is a logical order to the values, and the ‘low’ and ‘high’ end values on the x-axis of the histogram are able to be identified.
• Histograms
• Kurtosis
• Skewedness

Question 6

Confidence Intervals

Answer 6

• For 95% confidence intervals, an average of 19 out of 20 contain the population parameter.
• Suppose you have a 95% confidence interval of [5 10] for the mean.
• You can be 95% confident that the population mean falls between 5 and 10

Question 7

Normality & Sample Size

Answer 7

• Normality and Skewness divided SE Skewness are impacted by sample size
• If there is a really large sample, tests become hypersensitive
• Even trivial deviations from normality will violate the assumption of normality
• Can create a false positive
• Skewness doesn’t really change though

Question 8

Monte Carlo Tests

Answer 8

• Simultated Studies that change the characteristics of the data show that even gross deviations from Normality don’t impact the statsistical significance of the tests.
• Most tests can withstand even gross deviations from Normality - they are called robust
  *

Question 9

Central Limit Theorem

Answer 9

• If you have a population with mean μ and standard deviation σ and large random samples
• The distribution of the sample means will be approximately normally distributed.

Question 10

What to do if you decide that data is not Normal?

Answer 10

• No simple answer
• You could do a transformation
• Sometimes transforming the data can fix a problem of Normality
• If transforming the data successfully converts the data to normality you can be confident the data is in fact Normally Distributed

Question 11

Transformation

Answer 11

Applying a simple mathematical operation to data to deal with violations of assumptions

Question 12

Common Transformations

Answer 12

• Log 10
• Square Root
• Reciprocal

Question 13

Log10 Transformation

Answer 13

• Base 10 Logarithm
• Formula in SPSS: Transform/Compute Variable/rename Target Variable/Numeric Expression: lg10(Variable)

Question 14

Square Root Transformation

Answer 14

Formula in SPSS: Transform/Compute Variable/rename Target Variable/Numeric Expression: sqrt(variable)

Question 15

Reciprocal Transformation

Answer 15

Formula in SPSS: Transform/Compute Variable/rename Target Variable/Numeric Expression: 1/Variable

Question 16

Homogeneity of Variance

Answer 16

• This is problematic when we have an unbalanced sample
• Tested Using Levene’s Test
• Assumption underlying both t tests and F tests
• Population variances of two or more samples are considered equal.
• Corrected using one Transformation called a Power Transformation

Question 17

Levene’s Test

Answer 17

• Tests Homogeneity of Variance
• Must include a grouping variable - that is a variable which can be placed into groups (such as gender)
• Formula in SPSS: Analyse/Descrfiptive Statistics/Explore/Dependent List: variable/Factor List: grouping variable/Plots/Spread vs Level with Levene Test/Power Estimation
• In output look at Test of Homogeneity of Variance and then look at Based on Mean
• And Standard Deviation

Question 18

Power Transformation

Answer 18

• Used to transform data when the assumption of Homogeneity of Variance has been violated
• This is raising figures to a Power Value sauch as squared or cubed
• In SPSS Transform/Compute Variable/Rename: Target Variable/Numeric Expression: state ** variable

Question 19

Spread vs Level Plot

Answer 19

• Plot itself is kinda pointless
• In the fine print it says: Power for Transformation
• This is the number to use when doing a Power Transformation to fix a problem with Levene’s Tests

Question 20

General comments about transformations

Answer 20

• They are not a magic bullet
• They don’t cope with zeros (there needs to be a constant such as adding 10 to every score)
• They are unpredictable and can affect Normality and Homogeneity of Variance even if you weren’t planning to.
• Some data is “untransformable”
• Only use transformed figures to fix statistical tests
• Only report from the true data

Question 21

Acceptable Skewness level to acheive Normality Assumption

Answer 21

Skewness statistic divided by std error equals either >+2 or <-2