Question

Examples of clinical experiments for which t-test would be preferred over ANOVA

Answer 1

One way ANOVA

• Assumptions
  1. Homogeneity of variance
  2. Dependent variable is measured on ratio/interval scale of measurement
  3. Independent variable is measured on nominal scale of measurement
  4. Independent variable has at least 3 categories

• 5-Step Hypothesis

Hypothesis

Ho: there is no significant difference in the means of categories of independent variable. That is ?1=?2=…=?n

Ha: at least one of the means of categories of independent variable differs significantly. That is ?1??2?…??n

ANOVA Table

Critical value: F(1-a/2,n_1-1,n_2-1), F(a/2,n_1-1,n_2-1)  

P-value: 2*(1-P(F?|f|))  

Decision rule: Reject Ho if F < F(1-a/2,n_1-1,n_2-1) or F > F(a/2,n_1-1,n_2-1)

Post Hoc Analysis: To determine which of the means are significantly different from one another Post Hoc Analysis is used. Simultaneous comparisons between all pairs of groups can be done here. Turkey Crammer, Bonferroni procedure, Scheffe’s method, Dunnett’s correction are methods of Post Hoc analysis.

T test for independent samples with equal variances:

• Assumptions

1. Dependent variable is continuous (measured on interval or ratio scale of measurement).
2. Independent variable is categorical (grouped into 2 independent samples)
3. There is no relationship/dependency between 2 samples
4. Method of simple random sampling is used
5. Data is normally distributed
6. Homogeneity of variance between 2 independent samples. This can be tested using Levene’s Test or F test

• 5-Step Hypothesis

Null and Alternative Hypothesis

• Ho: there is no significant difference in the population means of 2 groups. ?1-?2=0

• Ha1: there is significant difference in the population means of 2 groups. ?1-?2?0 (Two tailed test)

Ha2: population mean of sample 1 is less than that of sample 2. ?1-?2<0 (Left tailed test)

Ha3: population mean of sample 1 is greater than that of sample 2. ?1-?2>0 (Right tailed test)

Test Statistic:

Critical value:

• • -t(a/2,n1+n2-2),t(a/2,n1+n2-2) (Two tailed test)
  • -t(a,n1+n2-2) (Left tailed test)
  • t(a,n1+n2-2) (Right tailed test)

P-value:

• 2*(1-P(T?|t|) (Two tailed test)
• P(T?t) (Left tailed test)
• P(T?t) (Right tailed test)

Decision rule;

• Reject Ho if |t| > t(a/2, df) or p-value < alpha (two tailed test)
• Reject Ho if –t < -t(a, df) or p-value < alpha (left tailed test)
• Reject Ho if t > t(a, df) or p-value < alpha (right tailed test)