T: This is the t-statistic test computed as 99147 df



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interpretimg t test results


Methodology

Paired t-test was used to determine whether there is a significant difference between the ovarian diameter before hormonal injection on day zero and after hormonal injection on day 7 on dairy cattle.



Data: In this case, we used the vectors called ovarian diameter at day 0 and ovarian diameter at day 7. The total number of characters analyzed were 168.

t: This is the t-statistic test computed as -0.99147

df: This is the degrees of freedom associated with the t test-statistic. In this case, it’s 167

p-value: This is the p-value that corresponds to a t test-statistic of -0.99147and df = 167. The p-value turns out to be 0.3229

Null hypothesis: In this case the null hypothesis is that the difference in means between the two diameters is equal to zero.

alternative hypothesis: The alternative hypothesis used for this particular t-test is that the true difference in means between the two diameter is not equal to zero.

95 percent confidence interval: This tells us the 95% confidence interval for the true difference in means between the two groups. It turns out to be [-0.15490421 0.05133279].

H0µ1 = µ2 (the two population means are equal)

HAµ1 ≠µ2 (the two population means are not equal)

Because the p-value of our test 0.3229 is greater than alpha = 0.05, we fail to reject the null hypothesis of the test. This means we have sufficient evidence to say that the mean diameter of the Ovarian between the two populations is not different.

Notes

The t.test() function in R uses the following syntax:

t.test(x, y, alternative = “two.sided”, mu = 0, paired = TRUE, conf.level = 0.95)

where:

  • x, y: The names of the two vectors that contain the data.

  • alternative: The alternative hypothesis. Options include “two.sided”, “less”, or “greater.”

  • mu: The value assumed to be the true difference in means.

  • paired: Whether or not to use a paired t-test.

  • conf.level: The confidence level to use for the test.

Assumptions

used a two-sided alternative hypothesis.



tested whether or not the true difference in means was equal to zero.

used a paired t-test.

used a 95% confidence level.
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