统计学笔记

统计量

r2=t2t2+df t检验对 H0 的解释度

T-test

T -test Assumptions

1. X and Y should be random samples from two independent populations.
2. Populations are approximately normal.
3. Sample data can estimate population variances.
4. Population varances are roughly equal.

Independent Samples t-test

Pooled−variance(合并方差)=S2p=SSx+SSydfx+dfy(Σ(xi−x¯)2=SSx) {样本量n不一致的时候用}

Standard Error (Sx¯+y¯)=s2pnx+s2pny−−−−−−−√

H0:μx−μy=10

t−Statistic=(X¯−Y¯)Observed−difference−(μx−μy)expected−differenceSx¯−y¯Standard−Error

样本类型

Dependent Samples(repeated measures; Within-subject designs)

• Two conditionals
• Longitudinal
• Pre-test, post-test

Advantages

• Controls for individual differences
• Use fewer subjects
• Cost-effective
• Less time-consuming
• Less expensive

Independent Samples(Between-subject designs)

• Experimental
• Observational

Disadvantages

• Carry-over effects Second measurement can be affected byu first treatment
• Order may influence results

统计计算

t−Statistic="Difference−between−means"Standard−error=(x1¯¯¯−x2¯¯¯)−(μ1−μ2)SE

SD=s21+s22−−−−−−√

SE=sn√=s21+s22√n√=s21n1+s22n2−−−−−−√

df=n1+n2−2