PM 510 Biostatistics

A variable

a measurable characteristic, attribute, or quality of a person, object, or event that can vary or change over time.

Data

are the measurement(s) or observation(s) made on the sampled subjects

Sample

A subset of individuals or observations selected from a larger population to represent the population in analysis.

Parameter

Whole Set, The totality of subjects under study.

Sample Variables are

Roman Letters

Parameter Variables

Greek Letters

What is the best order of Sampling

Simple Random > Stratified > Cluster > Systematic > Voluntary > Convenience

Standard Four Characteristics

Central Tendency(mean, median, mode)

Kurtosis(Peaked, Tailedness)

Variability (Standard Deviation, Range, Variance)

Skewness (Symmetry/Asymmetry)

Standard Normal Distribution

Mean = 0 Standard Deviation = 1

What types of data are Categorical

Nominal and Ordinal

What types of data are Numeric

Discrete and Continuous

Nominal

1. Rank does not matter, No Order

2. Qualitative Categories with no natural order or ranking.

3. Names, Colors, Jerseys, Labels, Gender

Ordinal

1. Rank does matter, There is an Order

2. Categories that have a meaningful order, but the differences between them are not measurable in exact units.

3. Time Laps, Positions Held, Races

Independent Variables

is the variable that is manipulated, categorized, or used to predict changes in another variable.

Dependent Variables

A variable that represents the outcome or effect being measured in a study.

Which of the following best defines quantitative data in statistics?

numerical data that can be measured or counted.

Qualitative

Data that describe categories, labels, or qualities, such as eye color, jersey number categories, or satisfaction ratings.

Numeric

values that are expressed in numbers. In statistics, this usually means quantitative data (measured or counted).

Discrete Numeric (Mostly Whole Numbers)

Countable, Ordered Numerical Data, Example: Counting Mice or the amount of balls. 

Continuous Data

Ordered Numerical Data, Can take any value. Usually has a decimal with it (Height, Weight, Age)

Which Type of Graph do you want to use for Categorical Data

Bar charts and pie charts

Which Type of Graph do you want to use for Numeric Data

Histograms, box-and-whisker plots, scatter plots, or line graphs

Categorical

are often assigned or stored as numbers (e.g., 1 = female, 2 = male) but the meaning of the numbers is completely arbitrary (e.g., could also use 1 = male, 2 = female, or even 36 = female, 25 = male)

Interval

1. Order Matters

2. Differences can be measured

3. No true “0” Starting Point

4. Quantitative Data

5. Allow Mathematical Manipulation; Pemdas)

Numeric

Actual Measurements

Distributions

The distribution of data is a complete description of all values that occur in the population

A chart used for frequencies and proportions of each category circle into slicers

Pie Chart

A chart used to obtain frequencies and proportions for each category, One Variable for each group on the x axis

Bar Graph

Which statement correctly compares pie charts and bar charts?

Pie charts show proportions of categories relative to the whole, while bar charts compare counts or frequencies of categories directly.

Symmetric distribution

distribution has identical halves when folded in half at the midpoint

A normal distribution

is symmetric and bell-shaped (Gaussian Distribution)

Ranking of Types of Data

Ratio → Interval → Ordinal → Nominal

Negatively skewed or left-skewed

left tail is pulled out; the long tail points toward negative or small values

Positively skewed or right-skewed

right tail is pulled out; the long tail points toward positive or large values

The modality of a distribution describes the number of

modes (peaks) a distribution has

Unimodal

one peak/One mode

Are Histograms Quantitative or Qualitative

Quantitative

Range of Data are broken down into smaller bins of fixed size  intervals.

For what Data should Stem-And-Leaf be used

Continuous Data

What is the purpose of the (Stem) in the stem-leaf plot

Used to group data

What is the purpose of the (leaf) in the stem-leaf plot

Used to show individual values

When should we use Line and Scatter Plot

Continuous Data like Time, Data between two variables. 

Bimodal

two peaks/Two mode

Multimodal

three or more peaks/multimodal

Good Sampling Strategies

Simple Random → Stratified → Cluster → Systematic → Voluntary → Convenience

What 2 Parameters define Normal Distribution (Bell Shaped)

Population mean(mu) and population variance(sd)

Which statement best describes the Student’s t-distribution?

A symmetric, bell-shaped distribution with heavier tails than the normal distribution, used when sample

What central tendency is a normal distribution

Mean = Median = Mode

What central tendency is a right skewed distribution

Mean > Median > Mode

What central tendency is a left skewed distribution

Mean → Median → Mode

According to the Empirical Rule, approximately what percentage of data fall within 2 standard deviations of the mean in a normal distribution?

95% 

What percentage of data falls within 1 standard deviation of the mean in a normal distribution?

68%

What percentage of data falls within 3 standard deviations of the mean in a normal distribution?

99.7%