Lecture 4: Analysis of Continuous and Categorical Variables

Question 1

Descriptive vs Inferential Statistics

Answer 1

descriptive: describing the central tendency and dispersion of data

inferential: use sample data to draw conclusions about the population that the sample is mean to represent (sampling will naturally involve error)
o Estimate parameters and test hypotheses to make inferences about the population
o Compare means and evaluate relationships
o Test statistics, p-values, confidence intervals

Question 2

Which test do I apply if I have 2 related samples and parametric data?

Answer 2

paired t-test

Question 3

Which test do I apply if I have 2 related samples and non- parametric data?

Answer 3

Wilcoxon test

Question 4

Which test do I apply if I have 2 independent samples and parametric data?

Answer 4

Independent t-test

Question 5

Which test do I apply if I have 2 independent samples and non-parametric data?

Answer 5

Mann-Whitney U test

Question 6

Which test do I apply if I have 3 or more groups and parametric data?

Answer 6

ANOVA

Question 7

Which test do I apply if I have 3 or more groups and non-parametric data?

Answer 7

Kruskal-Wallis test

Question 8

What is student t-test?

Answer 8

Used to compare means between two groups
o Related groups: paired t-test (e.g. pre- and post- study measures on the same participants)
o Independent groups: unpaired/independent t-test

Question 9

What is the null hypothesis in student t-test?

Answer 9

the means of the groups are not statistically different

Question 10

What is the degrees of freedom in student t-test?

Answer 10

amount of information provided by the data that can be used to estimate population parameters and
variability of the estimates

o df = n - # of estimated parameters
o As df increase, t-distribution more closely resembles a normal distribution

• E.g. One sample independent t-test to estimate the population mean
o Estimates the standard deviation about the mean o Uses a t-distribution with df = n-1
o Df=n–1 for paired t-test as well
• E.g. Two sample independent t-test to compare two means
o Uses a t-distribution with df = n1 + n2 – 2

Question 11

What are the assumptions of T-test?

Answer 11

• Samples are independent
• Variable is normally distributed
• Variance homogeneity variance within each group is equal
o Levene’s test for equality of variances in SPSS (automatically conducted)
o Informs you whether to use results for pooled or unpooled variance
• T-tests fairly robust even if assumptions are not perfectly met

Question 12

What is t-statistics?

Answer 12

Difference between the means divided by the pooled or unpooled standard error of the mean

Question 13

What is confidence interval?

Answer 13

Degree of uncertainty: area around the sample statistics where the corresponding population parameter is likely to be

Question 14

True/False

The larger the sample, the smaller the CI

Answer 14

True

Greater likelihood that the sample statistics approximates the population parameter

Question 15

True/False

If CI contains 0 (null value) then the means are not statistically different (non-significant finding)

Answer 15

True

Question 16

How to report independent t-test results?

Answer 16

Report the means and standard deviations for both groups, t-value, degrees of freedom, and p-value.

o E.g. Males (mean ± StD): 24.0 ± 4.1, Females (mean ± StD): 22.9 ± 4.0; t = 1.3, df = 116, p = 0.20

P-values from t-test often reported in subject characteristics table when data is compared between two groups (e.g. males vs. females, intervention vs. control group)

Question 17

Analysis of Variance ANOVA

Answer 17

Test to determine if means differ between 3 or more groups o Unlike t-tests, uses variance to assess differences
• Test null hypothesis that variances between the groups are equal
o F-test will result in rejection of null hypothesis when variability between group means is sufficiently larger than variability
within the groups.

Question 18

F-statistics

Answer 18

If ratio is large, indicates not all means are equal –> significant p-value will result

Question 19

In an F-test what does it mean to reject the null hypothesis?

Answer 19

variability between group means is sufficiently larger than variability within the groups

Question 20

Degrees of freedom in ANOVA

Answer 20

• Df1: df associated with the number of the F-statistics o Df=k–1
o K: # of group means
• Df2: df associated with the denominator of the F-
statistic
o Df=n–k

The first one represents between group variability, so this is calculated by k-1 (k is the number of groups). Nominator is the within group variability and that is calculated by n-k (sample size – the group means).

Question 21

What does variability look like in SPSS?

Answer 21

if the group has low group variability within the dots are close together. if there is high variability between the groups then the dots are more dispersed, so you are more likely to find a significant difference with high variability between your groups.

If the dots are more spread apart there will be more variation less dispersion more precision high variability within group, the difference between the groups are larger than the difference within the groups, you will have a significant finding.

Question 22

True/False

Low F value, less variability between your groups will lead to a retainment of the null hypothesis.

Answer 22

True

Question 23

What are the assumptions of ANOVA?

Answer 23

• Variable is normally distributed
• The errors are normally distributed
• The cases are independent from each other
• Variance homogeneity

Question 24

How to report ANOVA results?

Answer 24

• Report means and standard deviations for all groups, as well as the F value, degrees of freedom, and p-value
• Test for this example:

o Analysis of variance indicated that the different physical activity groups report different levels of caloric intake: 
§ Sedentary:1640.1±516.7
§ Light:2030.8±570.9
§ Moderate:1999.4±670.7 
§ High:2005.1±633.5
§ F(3,144)=3.3,p=0.02

Question 25

Post hoc test ANOVA

Answer 25

• ANOVA tells you if there is a difference between means, but not specifically which means differ
o Conduct multiple comparisons post-hoc test to determine which means differ

Question 26

What are the post hoc tests that ANOVA offers

Answer 26

o Tukey’s Test
o Least Squared Difference
o Dunnett’s test for between group comparisons

Question 27

One-way ANOVA

Answer 27

considers only one independent variable (factor) for independent groups

Question 28

Repeated measures one-way ANOVA

Answer 28

one-way ANOVA for related groups

Question 29

Multivariate ANOVA (MANOVA)

Answer 29

ANOVA with several dependent variables

Question 30

Factorial ANOVA

Answer 30

Compares means across two or more independent variables (factors)

Question 31

What are the tests that can be done for Analysis of Categorical Variables

Answer 31

• Chi-square test of independence
o Tests whether there is a significant association between two or more categorical variables

• Fisher’s Exact Test
o Use when 20% or more of the cells have <5 counts of data

• Test for Trend
o More powerful for ordinal data

Question 32

Chi-square test of independence

Answer 32

Tests whether there is a significant association between two or more categorical variables

• Utilizes contingency tables (also referred to as cross-tabulation, crosstab, or two-way table) o 2 x 2 table when each variable has 2 groups
o 2 x k table when each variable has k groups
• Assesses goodness of fit between observed values and theoretically expected values
• Df = k -1 (k=number of groups-columns)

Question 33

Fisher’s Exact Test

Answer 33

Use when 20% or more of the cells have <5 counts of data

Question 34

Test for Trend

Answer 34

More powerful for ordinal data

• Referred to as Linear-by-Linear association in SPSS
o Tests for trends in contingency tables larger than 2x2
• Takes into account ordered nature of data
o Relates to odds rather than variances
o Assumes that a change in ranks makes no difference to the odds of the outcome (i.e. Odds Ratio = 1)
o Therefore, df = 1

Question 35

What are the assumptions of Chi-squared test?

Answer 35

o Variable are ordinal or nominal
o Groups/categories are independent
§Use McNemar test for related groups (if the observation are from the same people)