Question

Generally, we compare two independent sample means via independent two-sample t test. Is it possible to compare two independent sample means using ANOVA? please give me a different answer/ explanation. I know someone already asked about this question here, please don't copy it and give me the same answer. THANKS.

Answer 1

Yes, it is possible to compare two independent sample means using ANOVA

In fact

t^2 = F

t is Test statistic for t-test Two-Sample Assuming Equal Variances

F is test statistic for Anova: Single Factor

p-value remains same for both test

random data

24	26
62	61
37	38
91	88

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	4	214	53.5	873.6667
Column 2	4	213	53.25	747.5833
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	0.125	1	0.125	0.000154	0.990495	5.987378
Within Groups	4863.75	6	810.625
Total	4863.875	7

t-Test: Two-Sample Assuming Equal Variances
	Variable 1	Variable 2
Mean	53.5	53.25
Variance	873.6666667	747.5833333
Observations	4	4
Pooled Variance	810.625
Hypothesized Mean Difference	0
df	6
t Stat	0.01241781	0.000154202
P(T<=t) one-tail	0.49524744
t Critical one-tail	1.943180281
P(T<=t) two-tail	0.990494879
t Critical two-tail	2.446911851