Parametric Tests I

Question 1

What are the type of data to consider when deciding on an appropriate statistical test for hypothesis testing between groups?

Answer 1

1. The number of groups being compared
2. Whether the groups are independent or paired/related
3. Whether the data are continuous, ordinal or nominal
   » For continuous data: whether the data are normally distributed or not.
4. Assumptions underlying a specific statistical test

Question 2

Characteristics of parametric tests

Answer 2

Type of data:
continuous (normally distributed)

Data summarized as:
Mean +/- SD

Question 3

Parametric tests, two groups, independent

Answer 3

Independent samples t-test

Question 4

Parametric tests, two groups, paired

Answer 4

Paired samples t-test

Question 5

Parametric tests, >two independent groups

Answer 5

One-way ANOVA

Question 6

Assumptions of parametric tests

Answer 6

• Samples are drawn from normally distributed populations (i.e. underlying distributions of samples are normal).
• Variances are the same

Question 7

Assumptions for paired samples t-test

Answer 7

• The samples are random samples of their populations
• The two underlying populations are paired
• The population of differences in values for each pair is normally distributed.

Question 8

Assumptions for independent samples t-test (based on the concept that H0: μ1 = μ2)

Answer 8

• The samples are random samples of their populations
• The two underlying populations are independent, normally distributed and have equal variances.
  » If variances are not significantly different (i.e. p≥0.05 for F test or Leven’s test for equality of variances), use the independent-samples t-test for equal variances.
  » If variances are significantly different (i.e. p < 0.05 for F test or Leven’s test for equality of variances), use the independent-samples t-test for unequal variances.

Question 9

What are the principles of paired-samples t-test?

Answer 9

• To test the null hypothesis that the mean of the underlying population of differences in values for each pair is zero (i.e. H0: μd= 0)
• With paired samples, each observation in the first group has a corresponding observation in the second group.
  » Self-pairing: measurements are taken on a single subject at two distinct points in time (e.g. “before and after” experiment)
  » Matching: subjects in one group are matched with those in a second group, so that the members of a pair are as similar as possible with respect to characteristics such as age, gender, etc.

Question 10

What are the steps to carrying out a paired-sample t-test?

Answer 10

1. Define the problem
2. State H0 and H1
3. Compute test statistic
4. Find p-value and compare with α
5. State conclusion

Question 11

How do you define the problem in a paired-sample t-test?

Answer 11

• Identify how many and which samples are being compared (i.e. the two groups)
• For 2 samples, identify if samples are independent or paired.
• Identify the variable/outcome of interest
• Identify the type of data to be analyzed [continuous (normally distributed or not), ordinal or nominal data].
• Identify whether two-tailed or one-tailed test.
• Perform paired samples t-test to analyze the data.
  » Find the paired differences by taking the first group – second group.
  » Assess normality of differences.

Question 12

Find p-value and compare with α

Answer 12

• Find df = n-1
• Find the α value that the t-value corresponds with.
• If the p-value is less than the significance level, reject H0.