Methodology

Statistic vocabulary

Hypothesis

• H₀(null hypothesis)
  • there is no difference between the data groups
• H1(alternative hypothesis)
  • This is the hypothesis that we are trying to demonstrate.

truth and reality

• truth
  • humans consider to be correct
• reality
  • is what exists in the natural world
  • The work of the scientist is to make TRUTH match REALITY as closely as possible, without ever being certain of actually achieving it.

前半

Remind methodology I

• 观察 → 提出问题 → 建立假设 → 设计实验 → 数据分析 → 得出结论

α 和β

• α
  • H0实际为真，却被错误拒绝 （type I error）
  • 一般被设定为0.05，表示可接受的犯错概率上限
• β
  • H0实际为假，却被错误接受 （type II error）
  • 与统计功效（1−β）相关

P value（如果P>α，无法说明任何事，仅代表现有数据不足以拒绝H0，可能是样本量不足； 如果P<α，有充分证据证明组间有真实差异，结论的错误风险小于α）

• 正态性检验
  • Shapiro-Wilk 检验：判断数据是否服从正态分布
• 方差齐性与均值比较
  • Student's t 检验：两组独立正态数据均值比较
  • Welch's t 检验：方差不齐时的修正 t 检验
  • ANOVA：多组均值比较，需满足正态性和方差齐性

理解 cups of tea

WALKTHROUGH A STATISTIC ANALYSIS

1. Specify the biological question you are asking

2. Put the question in the form of a biological null hypothesis and alternate hypothesis.

3. Put the question in the form of a statistical null hypothesis and alternate hypothesis.

4. Determine which variables are relevant for the question.

5. Determine what kind of variable each one is.

• variable types
  • Measurable variable (temperature,speed,weight)
  • Nominal variable(male/female)
  • Ranked variables(1st,2nd,3rd)
• 还有俩
  • Independent variable(自变量） is fixed
  • Dependent variable（因变量）

6. Design an experiment that controls or randomizes the confounding variables.

• Confounding variables are variables that are not related to the variables of interest but may affect them.

7. Based on the number of variables, the kinds of variables, the expected fit to the parametric assumptions, and the hypothesis to be tested, choose the best statistical test to use.

• Do the variable follow a normal distribution?(是否符合正态）
  • Yes,检测Homogeneous Variance?(方差齐性）就是看几组数据的方差分布是否相近
    • Parametrical test（（Comparison of the mean (sum of data values divided by the number of data) of the groups, considering the variance (distance between the data) of each group.）
    • Parametrical test with variance correction
  • Non parametrical test （Comparison of the medians (point at which 50% of the data is lower and 50% is higher) of the groups, considering the ranks (position in the order of the data) of the values.）
• 两组/三组以上
  • 两组
  • 三组及以上

8. Do a power analysis to determine a good sample size for the experiment.

• Beta : the risk of false negative. Usually we choose 20%. So Power = 1 – β = 80%
• Alpha (α) : the risk of false positive. Usually we choose 0.05

9. Do the experiment

10. Examine the data to see if it meets the assumptions of the statistical test

11. Apply the statistical test you chose, and interpret the results.

12. Communicate your results effectively, usually with a graph or table.