What does it mean to say that the averages for two groups are statistically different? Consider the three situations shown in Figure 2. The first thing to notice about the three situations is that the difference between the means is the same in all three. But, you should also notice that the three situations don't look the same -- they tell very different stories. The top example shows a case with moderate variability of scores within each group. The second situation shows the high variability case. the third shows the case with low variability. Clearly, we would conclude that the two groups appear most different or distinct in the bottom or low-variability case. Why? Because there is relatively little overlap between the two bell-shaped curves. In the high variability case, the group difference appears least striking because the two bell-shaped distributions overlap so much.
This leads us to a very important conclusion: when we are looking at the differences between scores for two groups, we have to judge the difference between their means relative to the spread or variability of their scores. The t-test does just this.


Türkçe

t testi ne anlama gelir?
İki grup ortalamalarının istatistiksel olarak anlamlı bir fark göstermeleri ne anlama gelir? İki grubun skor dağılımları ne kadar az örtüşüyorsa birbirinden o kadar farklıdırlar demektir. Buna göre üç durumdan grup içi değişkenliklerin en az olduğu (low variability) durumuna bakacak olursak gruplar arası farkın bu durumda en anlamlı olacağını görebiliriz. Grup içi değişkenliklerin çok yüksek olduğu durumdaysa(high variability) iki grubun skorlarının hemen hemen örtüştüğünü ve grup skorları arasında anlamlı bir fark bulunmadığı görülebilir.

For more info please refer to: http://www.socialresearchmethods.net/kb/stat_t.php