# What’s Difference Between Z Score and T Score

They indicate how many SD an observation in a data is above or below the mean.

Most commonly used in a z-test, z-score is similar to T score for a population.

When you know the population standard deviation and population mean for a population, it is better to use Z test. When you do not have all this information and instead have sample data, it is prudent to go for T test.

In Z test, you compare a sample to a population. On the other hand, T test can be performed for a single sample, two distinct samples that are different and not related or for two or more samples that are matching.

When the sample is large (n greater than 30), Z- score is normally calculated but T-score is preferred when the sample is less than 30. This is because you do not get a good estimate of the standard deviation of the population with a small sample and this is why a T score is better.

Z Score vs T Score

• T scores and Z scores are measures that measure deviation from normal.

• In case of T scores, the average or normal is taken as 50 with a SD of 10. So a person scoring more or less than 50 is above or below average.

• The average for Z score is 0. To be considered above average, a person has to get more than 0 Z score.

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# T检验、F检验和统计学意义（P值或sig值）

1.T检验和F检验的由来

F值和t值就是这些统计检定值，与它们相对应的概率分布，就是F分布和t分布。统计显著性（sig）就是出现目前样本这结果的机率。

2. 统计学意义（P值或sig值）

3. T检验和F检验

4. T检验和F检验的关系

t检验过程，是对两样本均数(mean)差别的显著性进行检验。惟t检验须知道两个总体的方差(Variances)是否相等；t检验值的计算会因方差是否相等而有所不同。也就是说，t检验须视乎方差齐性(Equality of Variances)结果。所以，SPSS在进行t-test for Equality of Means的同时，也要做Levene’s Test for Equality of Variances 。

4.1

4.2.

4.3

4.4

t检验有单样本t检验，配对t检验和两样本t检验。

F检验又叫方差齐性检验。在两样本t检验中要用到F检验。

via http://blog.znsun.com/2008/04/653/t-test-and-f-test-and-p-or-sig-value

One-way Anova(單因子變異數分析)是只有一個類別變數當作independent variable，檢驗此類別變數與其它連續變數(continuous variable)和結果的關係。比方說如果你想看性別、IQ對數學成績的影響，性別就是類別變數，IQ是連續變數，數學成績是結果變數(outcome variable)。

Two-way Anova(雙因子變異數分析)是有兩個以上的類別變數作為independent variables。比如說性別、種族與IQ對數學成績的影響，性別和種族就是類別變數。

2009/4/17 補充：

2011/11/18修正：原本寫的是

「另外，常犯的錯就是把前、後測是否有顯著差異用T-test來檢定。即使有兩組，前、後測也不是用T-test來檢定的，更別說有人「假裝」把前測當一組，後測當一組，拿來做T檢定。」

「另外，常犯的錯就是把前、後測是否有顯著差異用two-sample t-test來檢定，不能「假裝」把前測當一組，後測當一組，拿來做two-sample T檢定，而是應該用paired-sample t-test來檢驗是否有差異。」

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