生物統計研讀筆記 - 基礎與如何描述資料分布

學習 An Introduction to Biostatistic 並準備博士班資格考的筆記， 順便測試佈景的 Katex 能不能運作。

• 資料來源：

  • An Introduction to Biostatics
  • 台大生物統計公開課程

• 基礎

  • 統計學的主要意義是什麼？
    • 闡述如何搜集、分析、呈現以及詮釋資料的科學，詮釋中可以產生新的認知及理解
    • Probability, probability distribution, and hypothesis testing
  • 資料的類型有哪些？ What type of the dataset?
    • Quantitative variables:
      • Continuous variables (or interval data)
        • Interval: 資料間的距離相同的，零並不代表真正的「無」，而是自行定義資料區段中的一個點而已，例如：IQ 值
        • Ratio: 零值是有意義的，以及資料間的距離相同，被定義的。例如：血壓值、血糖值、身高
      • Discrete variable: 資料間的距離是相同的，但是只能是包含零的正整數，比如子女的數目、牙齒數量
    • Ranked (Ordinal): 意義不在其值，而是在順序，比如說癌症分期
    • Categorical data (Nominal): 測量值不具數量的意義. ex: species, gender, genotype, phenotype, healthy/diseased, and marital status.
    • 溫度是哪一種？ 如果是攝氏溫度 -> Interval,因為攝氏溫度的零度沒有意義，但是如果是絕對溫度的零度，則是 Ratio,因為零度有定義是完全沒有能量
  • Nonparametric tests vs parametric tests? (無母數統計)
    • Statistical analysis do not require distribution to meet the required assumptions to be analyzed
  • Scientific method Process ?
    • Observation: collect the data (categories, type…etc)
    • Formulation of problem: including why question
    • Hypothesis construction: testable cause and and relationship, ex: high level of hypertension is caused by dict
    • Making a prediction
  • Random variables and parameter
    • Characteristics of populations
    • Parameter: descriptive measure of random variables over the entire population
      • 對整個 population 描述性 variables, 如中位數
  • Why we need statics?
    • The whole population is too large, it’s difficult to calculate.

資料分布

• What is central tendency?
  • Mean
  • Median
  • Mode
• What is measure of dispersion and variability?
  • Range, Variance, Standard Deviation, and Standard Error
• What is the definition of “variance”?
  • Each observation has distance from the mean -> Deviation
  • Sample Variance: $$s^2=\frac{\sum_{i=1}^n\left(X_i-\bar{X}\right)^2}{n-1}$$
• Standard Deviation
  • positive square root of the population or sample variance
  • Used to demostrate differences in scatter between samples or populations
• Standard Error
  • the variability of the sample mean.

$$\mathrm{SE}=\frac{s}{\sqrt{n}}$$ -

• Accuracy vs Precision
  • Accuracy: the closeness of a measured or computed value to its true value,
  • Precision: the closeness of repeated measurements of the same quantity to each other.