In: Statistics and Probability
In the paper, "Sex Differences in Static Strength and Fatigability in Three Different Muscle Groups" Research Quarterly for Exercise and Sports, J. Misner et al. published results of a study on leg strength of males and females. Using the data in the data set named Leg Strength, conduct a 2-Sample t-test to determine if there is a significant difference in mean leg strengths for males and females. Assume equal variances and a 95% confidence level.
1) What is the p-value associated with the 2-Sample t-test?
2) What is the p-value reported in the ANOVA table?
MALE | FEMALE | Leg Strength | Sex |
2632 | 1344 | 2632 | MALE |
1796 | 1351 | 1796 | MALE |
2256 | 1369 | 2256 | MALE |
2235 | 2479 | 2235 | MALE |
2298 | 1573 | 2298 | MALE |
1917 | 1665 | 1917 | MALE |
1105 | 1791 | 1105 | MALE |
1926 | 1866 | 1926 | MALE |
2644 | 1544 | 2644 | MALE |
1569 | 2359 | 1569 | MALE |
3129 | 1694 | 3129 | MALE |
2167 | 2799 | 2167 | MALE |
1977 | 1868 | 1977 | MALE |
2098 | 1344 | FEMALE | |
1351 | FEMALE | ||
1369 | FEMALE | ||
2479 | FEMALE | ||
1573 | FEMALE | ||
1665 | FEMALE | ||
1791 | FEMALE | ||
1866 | FEMALE | ||
1544 | FEMALE | ||
2359 | FEMALE | ||
1694 | FEMALE | ||
2799 | FEMALE | ||
1868 | FEMALE | ||
2098 | FEMALE |
Using Excel
1)
for 2- sample t-test
data -> data analysis -> t-Test: Two-Sample Assuming Equal Variances
t-Test: Two-Sample Assuming Equal Variances | ||
MALE | FEMALE | |
Mean | 2127 | 1842.857143 |
Variance | 263156.1667 | 198884.4396 |
Observations | 13 | 14 |
Pooled Variance | 229734.8686 | |
Hypothesized Mean Difference | 0 | |
df | 25 | |
t Stat | 1.539136356 | |
P(T<=t) one-tail | 0.068166802 | |
t Critical one-tail | 1.708140761 | |
P(T<=t) two-tail | 0.136333605 | |
t Critical two-tail | 2.059538553 |
p-value = 0.136333605
2)
for Anova
data -> data analysis -> Anova: Single Factor
Anova: Single Factor | ||||||
SUMMARY | ||||||
Groups | Count | Sum | Average | Variance | ||
MALE | 13 | 27651 | 2127 | 263156.2 | ||
FEMALE | 14 | 25800 | 1842.857 | 198884.4 | ||
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | 544228.3 | 1 | 544228.3 | 2.368941 | 0.136334 | 4.241699 |
Within Groups | 5743372 | 25 | 229734.9 | |||
Total | 6287600 | 26 |
p-value =0.136334
Note that p-value remains same in t-test and ANOVA