(20分，urgent)t-stat和pearson correlation在t-test for means中有何意思

Pearson Corrleation:

-0.108324354 is the correlation coefficient. If the coefficient is +ve, the two variables have positive relationship i.e. When variable A increase, variable B also increase. If the coefficient is -ve, the two variables have negative relationship. i.e. When variable A increase, variable B decrease. In this case, the coefficient is negative so the two variables are negatively correlated. This number also tell us the percentage change of variable A explained by the percentage change of variable B (or the percentage change of variable B explained by the percentage change of variable A). In this case, 0.108324354 square = 0.011734 change of A is explained by B (And vice versa). Please note that correlation coefficient doesn't tell you the casual relationship, it only tell you the correlation between the two variables. To find out the causual relationship, you have to conduct experiment and analyse the data using t-test or ANOVA

T stat:

T test is the test to compare between two sample means. By comparing them, t-test shows us how likely a particular mean difference is if there is no difference between the two samples. In each sample, there is a mean and a standard error (Actually, you can consider it the standard deviation of the sample). Mean is the average in the sample and standard error is the typical variation in the sample. t-stat is the mean difference in terms of standard error (Mean difference/Standard error of the two sample). To make it easier to understand, I would have to set alternative hypothesis and null hypothesis (I think you know that). our hypothesis is people in sample A do not have the same height with people in sample B (Look, this is a two-tail test because we are looking at the difference) We will use t-test to see whether mean A is different from mean B i.e. The statistic program will use mean B - mean A or mean A -mean B to check the difference (You can set it yourself), in this case, I assume it is mean B - mean A). In this case, t stat is equal to -3.036179688. When t stat is negative, it means that the mean B is smaller than mean A for 3.036179688 standard error. By looking at the t-table or using SPSS/Statpro, you can see that the chance of having t stat = -3.036179688 is very small (less than .1%).

P(T<=t) one tail is the probability of T stat smaller or equal to a particular value when we are looking at whether one variable is larger than/less than the other variable (i.e. mean A > mean B)

P(T<=t) two tail is the probability of T stat smaller or equal to a particular value when we want to find out whether one variable is not equal to the other variable (i.e. mean A not equal to mean B)

t Critical is the value of t stat of a particular p-value (significance level) you set for rejecting the null hypothesis. e.g. When you set p value < .05, T stat is approximately 1.98.

皮爾遜相互關係-0.108324354
t 統計資料-3.036179688(假設的平均的Difference0.05)

P(T<= t)一條尾巴
t 關鍵的那個尾巴
P(T<= t)兩條尾巴
t 關鍵的兩條尾巴