Week1_Topic 1: Screening and cleaning data

Question 1

1) Why is Data Screening Important?

Answer 1

• An important (often time consuming!) precursor to any serious data analysis.
• Crucial to check relevant statistical assumptions for any subsequent analyses.
• Data screening can often provide an important first insight into the key variables of your study.

Question 2

2) Data Screening:

What should be your first step?

Answer 2

• The first step in data screening should involve checking for the accuracy of the data entry:

– Out of range values

– Plausible values

– Check accuracy of coding in SPSS

• The Frequencies window in SPSS –

Descriptive Statistics is often useful for the above checks.

Question 3

3) Missing Data:

It is problematic because it may reduce the

represeativeness of your data

It is a problem in many areas of psychological

research - give 4 examples:

Answer 3

1. Participant attrition (sustained pressure)
2. Items/tasks not completed
3. Completed data misplaced
4. Equipment malfunctions

Question 4

4)

Why is meticulous data collection is important?

Answer 4

– Ensure participants complete all tasks/ questionnaires

– Remind them to check that they’ve completed everything

– Program your task to minimize missing data

Question 5

5)

Describe - missing completely at random (MCAR):

Answer 5

• Cause of missing data is independent of other variables in the study
• Non-missing data is representative of total data
• Best possible situation, but rare
• Should not cause any problems if relatively small loss (<5%) in moderate and large datasets.

Question 6

6) Describe - missing at random (MAR):

Answer 6

• The pattern of missingness is predictable from other variables in the dataset.
• For instance, patients might be less likely to complete a certain questionnaire.
• If <5% most missing value procedures yield similar results.

Question 7

7)

Describe - missing not at random (MNAR):

Answer 7

• Non-random missingness.
• Value of variable is related to reason why it’s missing.
• Patients are less likely to complete a questionnaire because of their scores on the questionnaire.
• Can seriously bias results if left as is.

Question 8

8) SPSS Missing Value Analysis:

What is a logical appraoch?

Answer 8

• Separate missing and non-missing into two groups and compare on other variables e.g. ttest with IV (miss vs. non-miss) on all other variables.
• Little’s MCAR test: if non-significant then assume MCAR; if significant, but missingness is predictable from other variables (other than DV), then assume MAR. If t-test is significant for missingness across DVs, then assume MNAR.

Question 9

9)

Dealing With Missing Data:

Omission (but still report it)

Answer 9

– Usually ok if low frequency and MCAR/MAR (<5%), and dataset is moderate to large (default option in SPSS).

– Can be problematic in small datasets and in experimental designs e.g. unequal group sample sizes, loss of power etc

– If MNAR, can distort results.

Question 10

10)

Dealing With Missing Data

Estimate (‘impute’) missing data - Knowledge of area/previous research is good..

Another option is mean substitution - what are teh concequences?

Answer 10

– Mean substitution

• Easy to implement
• Conservative option
• Reduces variance in variable

Question 11

11) Dealing With Missing Data

Estimate (‘impute’) missing data using Regression

Answer 11

• Use complete cases to derive a regression equation with a series of IVs predicting relevant DV.
• Use equation to predict scores for missing cases.
• Tends to reduce variance and inflate relationships with other variables.
• Relies on relationships between DV and potential IVs.

Question 12

12) Dealing With Missing Data

Estimate (‘impute’) missing data using Expectation maximisation (EM)

Answer 12

• Calculates missing values for DVs when missing data is random.
• Uses a maximum likelihood approach to iteratively generate values (usually) using a normal distribution.
• Produces biased standard errors for hypothesis testing.

Question 13

13) Dealing With Missing Data

Estimate (‘impute’) missing data using Multiple imputation

Answer 13

• Makes no assumptions about randomness of missing data.
• Complex to undertake in SPSS.

Question 14

14) Contrasting different methods

List 3 recomendations….

Answer 14

1. It is worth repeating your analysis with and without missing data when using any type of imputation strategy.
2. Discrepant results will be a cause for concern.
3. The method you should select should not be based on the analysis outcome.

Question 15

15)

Define Outliers

Answer 15

Outliers are extreme values on one variable (univariate outlier) or a combination of variables (multivariate outlier), that distort or obscure the results of analyses.

Question 16

16) Outliers can be the result of:

(list 4 answers)

Answer 16

• Data entry errors
• Invalid missing data coding
• Case sampled is not from the intended population
• Case sampled is from the intended population, but simply represents an extreme value within that population, ie a genuine outlier.

Question 17

17)

How should you check for univariate outliers?

Answer 17

– Standardise variable and look for absolute values of z > 3.29 (.1% of sample)

– Use graphical methods to inspect for outliers e.g. histograms, boxplots, etc.

– The selection of an outlier detection method should be independent of the results.

– Address univariate outliers as a starting point, as this will often limit the number of multivariate outliers.

Question 18

18)

How can we check for multivariate outliers?

Answer 18

• Best assessed using formal statistical procedures rather than graphical methods of detection.
• Mahalanobis Distance is the distance of a case from the centroid of the remaining cases (centroid is the intersection of the variable means).
• The MD is tested using a χ2 distribution, with a conservative value of alpha (usually p < .001).

Question 19

19)

How can the Mahalanobis Distance be assessed in SPSS?

Answer 19

Using regression:

– Use any DV, with relevant variables as predictor IVs.

– Use the Save dialog to request MD values.

– Evaluate MD values using a χ2 distribution at p < .001, with df equal to the number of IVs in the model.

Question 20

20)

When are Leverage, Discrepancy and Influence used?

Answer 20

– Most often used in the context of multiple regression.

Question 21

21) Detecting Outliers

What is leverage similar to?

Answer 21

– Leverage (identifying influence values) is similar to Mahalanobis Distance (MD), but measured on a different scale.

Question 22

22) Detecting Outliers

What does discrepancy measure?

Answer 22

– Discrepancy measures the extent to which a case deviates from others (usually deviation from a straight line).

Question 23

23) Detecting Outliers

What is influence?

Answer 23

• Influence is the product of both leverage and discrepancy. It is the extent to which regression coefficients change when a case is deleted.
• Influence can be assessed using Cook’s Distance, obtained in the Save dialog of SPSS Regression.

Question 24

24) Detecting Outliers

Describe the plot for leverage, discrepancy and influence in terms of high, moderate and low

Answer 24

Answer:

• High leverage
• Low discrepancy
• moderate influence

Question 25

25) Detecting Outliers Describe the plot for leverage, discrepancy and influence in terms of high, moderate and low

Answer 25

Answer: High leverage High discrepancy High influence

Question 26

26) Detecting Outliers Describe the plot for leverage, discrepancy and influence in terms of high, moderate and low

Answer 26

Answer: Low leverage High discrepancy Moderate influence

Question 27

27) Detecting Outliers ## Footnote When you have detected multivariate outliers, you should seek to determine why the cases are extreme. How do you do this?

Answer 27

Can create a dummy variable with the outliers as one value and the rest of the cases with another value. Use the dummy variable as a DV in **logistic regression**, to determine the IVs that best predict group membership. Means, SDs etc can then be checked for the outliers on the variables identified in this way.

Question 28

28) Dealing with Outliers List some solutions..

Answer 28

1. Check for data entry error, coding mistakes etc. 2. Omit cases if not part of the population (with caution). 3. Otherwise, * Transform variable * Reduce/increase score to next unit above/below the next highest/ lowest score (e.g. Winsorize / nearest-neighbor). * Trim an a priori percentage of cases from the upper and lower tails of the distribution.

Question 29

29) Dealing with Outliers list 4 more points to consider..

Answer 29

1. If you still have multivariate outliers after dealing with univariate outliers and N is large, may be simplest to omit cases. 2. Run analyses with and without outliers to check on effect of omissions. 3. Make sure all outlier remedies are reported in the results section. 4. Non-parametric statistics are less sensitive to the influence of outliers, but not wholly insensitive.

Question 30

30) Normality:

Answer 30

* Assumption of multivariate normality is the assumption that each variable, and all linear combinations of the variables, are normally distributed. * This assumption underlies the use of many statistical tests and tests become less robust as distributions depart from normality.

Question 31

31) Normality Describe normality for grouped data (e.g. ANOVA)

Answer 31

* normality applies to sampling distribution of the variables means. With large enough N (ie \> 20), **Central Limit Theorem** shows sampling distribution will be normally distributed regardless of the distribution of the variables

Question 32

32) Normality ## Footnote Describe normality for ungrouped data (e.g. Regression)

Answer 32

– Testing for **multivariate normality** impractical. The assumption can be largely checked by examining the normality, linearity, and **homoscedasticity** of individual variables and any analysis residuals.

Question 33

33) Define **Homoscedasticity.**

Answer 33

Homoscedasticity. This assumption means that the variance around the regression line is the same for all values of the predictor variable (X). The plot shows a violation of this assumption. For the lower values on the X-axis, the points are all very near the regression line

Question 34

34) Normality ## Footnote Normality can be assessed by statistical and graphical means. What is the test and distribution to look for with a visual inspection?

Answer 34

* Kolmogorov-Smirnoff test * Skewness is the degree of symmetry in the distribution. * Kurtosis is the peakedness or flatness of the distribution.

Question 35

35) Normality ## Footnote A normal distribution has skewness and kurtosis values of \_\_\_\_\_\_

Answer 35

A normal distribution has skewness and kurtosis values of 0. ## Footnote **Skewness** and **kurtosis** values and their standard errors are provided by SPSS Frequencies. Can test a hypothesis using a z score that skewness and kurtosis differ significantly from 0. z = skewness/**standard error** (SE), z = kurtosis/SE Small samples (n\<50): Z\>1.96: data is non- normal

Question 36

36) Normality For small to moderate N, use ________ \_\_\_\_\_\_\_\_ values e.g. p \< \_\_\_\_. For large N, likely to make a __________ as SEs become \_\_\_\_\_. Better to examine the _________________________ or look at absolute values.

Answer 36

For small to moderate N, use **conservative alpha** values e.g. p \< **.001**. For large N, likely to make a **Type 1 error** as SEs become **small**. Better to examine the **shape of the distribution** or look at absolute values.

Question 37

37) Normality ## Footnote \_\_\_\_\_\_\_\_\_\_\_\_ suggest normality can be assumed if skewness values are not greater than _______ and kurtosis values are not greater than \_\_\_\_\_\_\_\_. Note that the consequences of departures from \_\_\_\_\_\_\_\_are generally more serious when variables are _______ in different directions.

Answer 37

**Curran et al. (1996)** suggest normality can be assumed if skewness values are not greater than **abs val 2** and kurtosis values are not greater than **abs val 7.** Note that the consequences of departures from **normality** are generally more serious when variables are **skewed** in different directions.

Question 38

38) Normality ## Footnote Graphical methods - list 3

Answer 38

1. **Frequency histogram** (with normal curve overlay in SPSS) 2. **Normal probability plot** * For normality, points should fall along the diagonal line. * Plots observed values against expected values based on a normal distribution. 3. **Detrended normal probability plot** • Similar to above, but plots the deviations from the diagonal.

Question 39

39) Normalise To address normality.... list 6 ways..

Answer 39

1. Transform variable (eg log transform) 2. Winsorize/Trim 3. Check modified variable to ascertain normality 4. Examine how any changes impact analyses 5. Choose a method based on what is effective in yielding a normal distribution 6. If normality violations can’t be corrected, consider using non-parametric statistics

Question 40

40) Define **Linearity**

Answer 40

* The assumption that variables have linear (straight line) relationships with each other. * Underlies many statistical tests e.g. Pearson correlation, regression, etc * Can be assessed using bivariate scatterplots. * Some variables may inherently have a non-linear * relationship. * See Tabachnick and Fidell for alternate analyses if nonlinearity present.

Question 41

41) Linearity Waht is the reliationship?

Answer 41

Quadratic relationship

Question 42

42) Linearity What is the relationship?

Answer 42

**Cubic relationship**

Question 43

43) Homoscedasticity ## Footnote Homoscedaticity is the __________ that ________ in scores for one ______________ is roughly the same at all levels of \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

Answer 43

Homoscedaticity is the **assumption** that **variance** in scores for one **continuous variable** is roughly the same at all levels of **another continuous variable**.

Question 44

44) Homoscedasticity ## Footnote For grouped data what is the homogeneity of variance assumption:

Answer 44

variability in **DV** is expected to be similar across all levels of the **discrete IV**.

Question 45

45) Homoscedasticity How do you assess it?

Answer 45

Can be assessed with **Levene’s test**.

Question 46

46) Homoscedasticity What should you do for ungrouped data?

Answer 46

For ungrouped data, inspect the **bivariate scatterplots.** **Heteroscedasticity** is caused by **nonnormality** in _one_ or _both_ of the variables. Tests usually robust to some heteroscedasticity.

Question 47

47) **Homoscedasticity** Describe the plot below:

Answer 47

**Homoscedasticity** with both variables normally distributed.

Question 48

48) Homoscedasticity Describe the plot below:

Answer 48

Heteroscedasticity with skewness on one variable

Question 49

49) Data Transforms List 5 key points.

Answer 49

1. Generally recommended if there are significant departures from normality and/or problems with outliers etc. 2. An exception may be if the variable is measured on an inherently meaningful scale, as interpretation becomes more difficult after transformation. 3. It is worth trying several types of transformations to try to produce the best distribution. 4. Always check a transformed variable for normality etc. 5. If no transformation seems to work, try dichotomizing the variable or using NP statistics.

Question 50

50) Data Trasforms If data is skewed what is a good option?

Answer 50

Log transformations are often helpful with skewed data.

Question 51

51) Multicolllinearity **Multicollinearity** is a problem that occurs in a **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_**when variables are too **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** to each other (e.g. \> .90).

Answer 51

**Multicollinearity** is a problem that occurs in a **correlation matrix** when variables are too **highly related** to each other (e.g. \> .90).

Question 52

52) Multicollinearity List 3 Problems with multicollinearity

Answer 52

1. Conceptually, it indicates redundancy in the variables. 2. It can be an important issue in regression. 3. It doesn’t necessarily impact the model as a role (eg in regression), but rather individual predictors

Question 53

53) Multicollinearity How to detect multicollinearity?

Answer 53

* Basic principle is to examine overlap between variables. * Examine correlation matrix for preliminary check. * Specific test depends to some degree on type of analysis e.g. tolerance/VIF in multiple regression (more on this in a few weeks).

Question 54

54) Multicollinearity How do we deal with multicollinearity?

Answer 54

Remove or combine relevant variables

Question 55

55) Data Screeing • Putting it altogether:

Answer 55

– See Tabachnick and Fidell pg. 91 for a checklist of data screening prior to analysis. – Also see end of chapter 4 for fully worked examples of data screening using SPSS, for ungrouped and grouped data.