Statistics Notes Chapters 2 & 3

Chapter 3: Key Concepts

Missing Variable

x = given Median * 2 - ((1 of 2) median numbers if even): ascending order

Unreadable Score

(U * N of unreadable) - (U * N of readable)

Degrees of Freedom

1 # of freedom is lost

Chebyshev's Theorem

K = Deviation

Calculate time % within K Dev of mean - (1 - 1/k^2) * 100 = %

Finding Values

Find x K devs from mean - (mean - K * given standard dev) = XLow...(mean + k * given standard dev) = XHigh

Finding % Within Times Xlow-Xhigh

K = (XHigh - Mean) / Given Standard dev....then do Chebyshev's - (1 - 1/k^2) * 100 = %

Z-Score Simplified

(Mean - Given Mean) / Given Standard Dev = ZScore

Finding Minimum Score Accepted

(Min devs) * (Given Devs) + (Mean) = Min Score

Weighted Mean

Chart Xi / Wi /XiWi

Use Empirical Rule if distribution is bell-shaped. Sum of deviations = 0. Range does not use all observations. The more dispersion, the higher the standard deviation.

Chapter 2: Statistical Concepts

Statistics

Statistics is the science of organizing data to draw conclusions.

Descriptive Statistics

Descriptive statistics describe data through numerical summaries or graphs, "for those surveyed".

Variables

Variables are characteristics of individuals in a population.

• Discrete: You can count (1, 2, 3).
• Continuous: You measure (1.2, 1.34, 1.675, etc.).

Levels of Measurement

• Nominal: Name
• Ordinal: Nominal + rank/order
• Interval: 0 has no meaning, equal space between numbers
• Ratio: 0 has meaning, can be any numbers (factory quest)

Types of Variables

• Response: What is being studied
• Explanatory: Variable that affects the response
• Factor: Variable whose effect on the response variable is to be assessed by the experimenter
• Confounding: Not separating variables
• Lurking: Explanatory variable not considered

Studies only show association.

Types of Studies

• Cross-Sectional: Group of people in a short amount of time
• Case-Control: Looking to the past for answers
• Cohort: Group of people over a long time

Sampling

• Frame: List of individuals being studied, not always accurate because the population is always changing
• Simple Random Sampling: Pick names out of a hat or chart, not always preferred, expensive
• Stratified Sampling: Separating the population into different groups then obtaining a simple random sample of individuals from each group
• Systematic Random Sampling: Selecting every nth individual. Does not require a frame; K = Pop/Sample, p, p+k, ...p+(N-1)*k
• Cluster Sampling: Randomly selecting a group then obtaining a sample from all

Bias

• Bias: Sample does not represent the population
• Non-Sampling Bias: Undercoverage (smaller in sample) or favors one part of the population, may result from non-response or improperly worded questions

Experiments

• Experiment: Study conducted to determine the effect 1 or more explanatory variables have on a response
• Treatment: Combination of the values of a factor
• Experimental Unit: Person being studied
• Matched Pairs: Before and after, husband and wife

Frequency

• Relative Frequencies: Add up to 1

Charts

• Stem and leaf plots: Not good for large data but show original data
• Histograms: Organize data of all sizes

Data Analysis

• Difference between values between quarters: (High - Low) / High
• Difference between values of highest and lowest: (High - Low) / Low
• Class Width: (Max entry - Low entry) / Number of entries

Quantitative variables are required for time plots.

>= greater than, <= less than