Statistics Competency Exam Study Guide

Be familiar with sampling techniques, such as snowball sampling

○      Snowballing Sampling: Participants recruit additional participants. Used for hard-to-reach populations

○      Example: Studying people with rare disorders.

Nominal scale

■      A measurement scale that places data into categories with no order.

Ordinal scale

■      A measurement scale that places data into categories with a meaningful order, but the differences between categories are not equal.

Ratio

■      A numerical scale with equal intervals and a true zero, allowing all mathematical operations.

Interval

■      A numerical scale where equal differences are meaningful, but there is no true zero. You can add and subtract, but ratios don't make sense.

Correlation coefficient

■      A number between -1 and +1 that measures the strength and direction of a relationship between two variables

P-value

■      The probability that the results occurred by chance if there is actually no real effect (the null hypothesis is true)

Confidence interval

■      A range of values that is likely to contain the true population value, usually with 95% confidence

Sample

■      A subset of a population that is actually studied

Population

■      The entire group researchers want to learn about

Mode:

■      Most frequently occurring value.

■      Example:
 2, 3, 3, 5, 7

■      Mode = 3

Quantitative variables: continuous vs Discrete variable

○      Continuous: Can take any value within a range. Continuous is usually measured. Examples are height, weight, and time

○      Discrete: Can take only specific, separate values. Usually counted. Examples are the number of cars in the parking lot, number of children in a family, etc.

Definition/examples of descriptive statistics

○      Descriptive statistics are methods used to organize, summarize, and describe the main features of a dataset. They do not make predictions or draw conclusions about a larger population; they simply describe the data you have.

○      Examples:

■      Frequency Distributions

■      Graphical Displays

■      Measures of Variability

■      Measures of Central Tendency

Independent vs dependent variables and examples

○      IV: The variable manipulated or grouped.

○      DV: The measured outcome.

Skewing, such as skewing of results (e.g., right skew, left skew) and what it can mean

○      Skewness describes whether a distribution is symmetrical or has a longer tail on one side.

○      There are three types:

■      Normal (No Skew)

●      Mean = Median = Mode

■      Right Skew (Positive Skew)

●      The mean is the largest because high outliers pull it upward.

■      Left Skew (Negative Skew)

●      The mean is the smallest because low outliers pull it downward.

Correlation and its relation to causation

○      Correlation: Two variables are related.

○      Causation: One variable causes another.

○      Correlation does not imply causation.

How to calculate the mean

○      Mean=Number of values Divided by Sum of all values​

How to calculate the median

○      Middle value after ordering numbers.

○      2, 4, 5, 7, 10     Median = 5

○      2, 4, 6, 8           Median = 4+6 divided by 2 = 5       Median = 5

How to calculate the first and third quartiles

○      Order the data from smallest to largest.

○      Find the median (Q2).

○      Find the median of the lower half = Q1.

○      Find the median of the upper half = Q3.

How to calculate variance

○      This measures how spread out a set of data points are from their average (mean)

○      Find the mean

○      Subtract the mean from each data point

○      Square each result

○      Add the squared differences together

○      Divide by the number of data points

Standard deviations on normal distribution

○      68% of data fall within +/- 1 of the mean

○      95% of data falls within +/- 2 of the mean

○      99.7% of data falls within +/- of the mean

Be familiar with general formula of how you calculate the coefficient of variation

○      Find the mean.

○      Find the standard deviation.

○      Divide the standard deviation by the mean.

○      Multiply by 100 to express it as a percentage.

○      CV = (standard deviation / mean) x 100

Be familiar with normal distribution and how the measures of central tendency are positioned on this type of distribution

○      In a perfectly normal distribution (a symmetrical bell-shaped curve), the mean, median, and mode are all exactly equal.

○      They all align at the exact center of the distribution, representing the highest peak of the curve where the data is most densely clustered.