Basic Concepts

Question 1

What is Statistics?

Answer 1

The art and science of answering questions and exploring ideas through the process of gathering data, describing data and making generalizations about a population on the basis of a smaller sample.

Question 2

Basic concept: Unit

Answer 2

The basic objects on which the data is collected.
When conducting a research study, information is collected concerning units.

Question 3

Basic concept: Variable

Answer 3

Characteristic of units that can take on different values (in other words, something that can vary).

Question 4

Variables can be classified as (2 options)

Answer 4

Categorical (or qualitative) and Quantitative.

Question 5

Basic concept: Categorical variables

Answer 5

Categorical (or qualitative) variables refer to variables with calues that can’t be quantifiable. These can be classified as:
Nominal (describes a name, label, or category without logical order);
Ordinal (whose values are defined by order between the different categories)

Question 6

Basic concept: Quantitative variables

Answer 6

Quantitative (or numeral) variables have numerical values with magnitudes that can be places in a meaningful order with consistent intervals. These can be classified as:
Discrete (can only take on a set number of values - whole numbers)
Continuous (can take on any value or any value beteween values)

Question 7

Categorical or Quantitative?
- Weight
- Favorite ice cream flavor
- Children per household
- Running distance
- Religion
- Satisfaction rating

Answer 7

• Quantitative
• Categorical (nominal)
• Quantitative (discrete)
• Quantitative (continuous)
• Categorical (nominal)
• Categorical (ordinal)

Question 8

Basic concept: Sample

Answer 8

A smaller subset of the population.

Question 9

Basic concept: Statistics vs Parameters

Answer 9

Values concerning a sample are referred to as SAMPLE STATISTICS while values concerning a population are referred to as POPULATION PARAMETERS.

Question 10

Basic concept: Sampling Bias

Answer 10

Systematic favoring of certain outcomes due to the methods employed to obtain the sample.

Question 11

How to avoid sampling bias?

Answer 11

The most common probability-based sampling method is the SIMPLE RANDOM SAMPLING method.

Question 12

Basic concept: Simple random sampling

Answer 12

A method of obtaining a sample from a population in which every member of the population has an equal chance of being selected.

Question 13

Basic concept: Central tendency measures

Answer 13

Describe the “center” arounf which the data is distributed. Mean and Median are two of the most commonly used.

Question 14

Basic concept: Variability measures

Answer 14

Describe “data spread” or how far away the measurements are from the center.
Variance and Standard deviation are the most commonly used.

Question 15

Basic concept: Relative standing measures

Answer 15

Describe the relative position of specific measurements in the data. Ex - percentile and quartiles

Question 16

Basic concept: Mean

Answer 16

The numerical average; calculated as the sum of all of the data values divided by the number of values.
The sample mean is represented as ¯x (”x-bar”) and the population mean is denoted as the Greek letter µ (”mu”).

Question 17

Basic concept: Median

Answer 17

The middle of the distribution that has been ordered from smallest to largest; for distributions with an even number of values, this is the mean of the two middle values.

Question 18

Basic concept: Standard Deviation

Answer 18

Roughly the average difference between individual data values and the mean.
The standard deviation of a sample is denoted as s.
The standard deviation of a population is denoted as σ.
The standard deviation is equal to the square root of the variance.

Question 19

Basic concept: Correlation

Answer 19

A measure of the direction and strength of the relationship between two variables.
The correlation between two quantitative variables of a sample is denoted r.
The correlation between two quantitative variables of a population is denoted ρ (Greek letter ”rho”).

Question 20

6 properties of correlation

Answer 20

1. −1 ≤ ρ ≤ +1.
2. For a positive association, ρ > 0, for a negative association ρ < 0, if there is no relationship ρ = 0.
3. The closer ρ is to 0 the weaker the relationship and the closer to +1 or -1 the stronger the relationship.
4. The sign of the correlation provides direction only.
5. Correlation is unit free; the x and y variables do NOT need to be on the same scale (ex: correlation between height in cm and weight in lbs).
6. It doesn’t matter which variable you label as x or y. The correlation between x and y is equal to the correlation between y and x.