University:
York University
Course:
MATH 1131 | Introduction to Statistics I
Academic year:

2022
Views:

243

Pages:

3
Author:

Niklas

Title: LECTURE 2 Types of Representation of Data Two Variable Matrix: A rectangular array of data, where each row represents a statistical unit and each column represents a variable. Two modalities: When a variable has two possible values, it's often represented as a binary variable. Example: Sex-Starp Study Sex Starp Watched Qualitative Subject Dioxin Vietnam 1 H 8 2 1 0 Vietnam 2 F 6 30 Not Watched 2 3 3 H 9 5 Watched 7 4 Binary Variables A binary variable has two possible values, often represented as 0 and 1. Example: Ever contracted Lyme disease, smoking status, presence of congenital anomalies. Example: Birth Weight, Pregnancy Duration, Smoking Birth Weight Pregnancy Duration Smoking 2940 38 1 2420 36 0 3130 38 0 2619 35 0 Example: Measurements of Inorganic Phosphate Level (PHL) in Plasma Data: Hyperglycemic (01), non-hyperglycemic (0N), obese, non-obese, control subjects. Measurement: Inorganic phosphate level one hour after the test. Matrix Form: A table representing the data, with rows for subjects and columns for different groups and measurements. Title: Lecture 2 Variables To encode categorical variables, we introduce 0/1 variables, also known as indicator variables or dummy variables. These are not truly variables because they indicate the presence or absence of a mode. To encode a categorical variable with k categories, we need k-1 indicator variables. Statistical Distribution We consider a set of N statistical units on which we observe the variable Y. The distribution of Y is the set of observations relating to the N units of the data. The distribution is denoted as Y₁, Y₂, ..., YN. Absolute Frequency Distribution The list of observed modalities associated with their respective absolute frequencies. 3 Types of Representation Qualitative: Modality, Absolute Frequency Synthetic: Modality, Relative Frequency Interval: Interval, Absolute Frequency Rules for Interval Representation All values of the modalities should be included in the intervals. A statistical unit can only be placed in one interval. The number of intervals can be chosen by necessity or by making intervals. Intervals should start with a lower value. Note on Interval Representation By making intervals, you lose some information because you don't have the specific height in this case. Key Concepts: Frequency Density: Tells us the expected number of statistical units for each unit of measurement of the variable. Density: Absolute frequency on the interval / length of the interval Frequency Table: A listing of possible values for a variable, together with the number of observations for each value. Proportion: The number of observations falling in a certain category divided by the total number of observations. Percentage: Proportion multiplied by 100. Relative Frequencies: Proportions and percentages. Table: Interval Frequency Interval Width Density (0,500] 169 500 0.338 (500,1000] 150 500 0.3 (1000,1500] 59 500 0.118 (1500,2000] 17 500 0.034 (2000,2500] 10 500 0.02 (2500,3000] 6 500 0.012 (3000,3500] 5 500 0.01