In many biostatistics books, the negative sign is ignored in the calculated t value.
in left tail t test we include a minus sign in the critical value.
eg.
result of paired t test left tailed
calculated t value = -2.57
critical value = - 1.833 ( df =9; level of significance 5%) (minus sign included since
it is a left tailed test)
now, we can accept or reject the null hypothesis.
if we do not ignore the negative sign i.e. -2.571.833 null hypothesis rejected.
No, we do not need to ignore the negative sign in calculated t test value. A negative t-value simply means that the difference between the means of the two groups is negative, or that the mean of the first group is smaller than the mean of the second group. The negative sign does not affect the significance of the difference between groups, which depends on the absolute value of the t-value and the degrees of freedom.
For a left-tailed test, we are testing whether the mean of the first group is significantly smaller than the mean of the second group, or equivalently, whether the difference between the means is significantly negative. Therefore, we compare the calculated t-value with the critical value from the left tail of the t-distribution with a given level of significance and degrees of freedom. If the calculated t-value is smaller (more negative) than the critical value, we reject the null hypothesis and conclude that there is a significant difference between groups. If the calculated t-value is larger (less negative) than the critical value, we fail to reject the null hypothesis and conclude that there is no significant difference between groups.
For example, in your case, you have a calculated t-value of -2.57 and a critical value of -1.833 for a left-tailed test with 9 degrees of freedom and 5% level of significance. Since -2.57 < -1.833, you reject the null hypothesis and conclude that there is a significant difference between groups. If you ignore the negative sign and compare 2.57 with 1.833, you will get a wrong conclusion.
Therefore, it is important to keep the negative sign in calculated t-value and compare it with the appropriate critical value for a left-tailed test.
It is regarding to the observed data. If replicate-2 is negative then do not delete the negative sign. If replicate-2 is positive then you could ignore negative sign.
A negative t-value refers to inverse direction of the effect, which has no bearing on the significance of the difference between groups (pre/ post).
AND the magnitude of the effect or difference bet. groups depend on p-value.
That is in two tailed tests we can ignore the negative sign in t value and it does not affect the test inference
but while performing one tailed test (left or right), we should not ignore the negative sign.
Am I correct?
please provide some references to prove this point.
Your conclusion is right, you should not ignore the negative sign in the calculated t-value for a one-tailed test. The negative sign indicates that the sample mean is less than the hypothesized mean, which is relevant for a left-tailed test but not for a right-tailed test.
Some references that explain this point are:
(1) One-Tailed and Two-Tailed Hypothesis Tests Explained. https://statisticsbyjim.com/hypothesis-testing/one-tailed-two-tailed-hypothesis-tests/.
(2) One-Tailed Hypothesis Tests: 3 Example Problems - Statology. https://www.statology.org/one-tailed-test-example-problems/.
(3) 13.2: Sign Test - Statistics LibreTexts. https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_%28Webb%29/13%3A_Nonparametric_Tests/13.02%3A_Sign_Test.
Negative values mean that the observed difference between the mean is in the opposite direction to what you thought it would be. If you are doing a two tailed test, i.e. you don't have any idea which mean would be greater, you should ignore the sign.
Le signe négatif en mathématique en général et en statistique en particulier a toute son importance notamment au niveau des commentaires des résultats (exemple: la corrélation positive s'oppose à la corrélation linéaire négative). Les signes sont à respecter.
The question of ignoring does not at all arise. The value along with the sign is required for taking decision regarding acceptance or rejection of null hypothesis.
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