HTHSCI 2S03: Descriptive Statistics, Data Visualization, and Foundations of Probability Vocabulary

Vocabulary flashcards covering basic concepts, measurement scales, graphical displays, measures of central tendency and dispersion, and fundamental probability principles for HTHSCI 2S03.

Descriptive Statistics

The branch of statistics focused on the collection, organization, summarization, and presentation of data.

Inferential Statistics

The branch of statistics concerned with drawing inferences and conclusions about a larger group of data based on a sample.

Data

The raw material of statistics, usually defined as numbers derived from taking a measurement or counting.

Variable

A characteristic that takes on different values in different persons, places, or things.

Dependent Variable

The outcome variable of interest in a study, which is expected to change in response to an intervention.

Independent Variable

The variable being manipulated, representing an intervention or factor that may exert an effect on the dependent variable.

Quantitative Variable

A variable that can be measured numerically, such as height, weight, age, or blood pressure.

Qualitative Variable

A variable that cannot be measured numerically and is categorized into groups, such as gender, hair color, or ethnic group.

Discrete Variable

A variable with values that can assume only distinct whole numbers, such as hospital visits or patient counts.

Continuous Variable

A variable that can take on any numerical value within a defined range, such as weight, height, or blood pressure.

Random Variable

A variable whose observed values are obtained as a result of chance factors and cannot be exactly predicted in advance.

Nominal Scale

The simplest level of measurement consisting of mutually exclusive, collectively exhaustive, unordered categories where numbers act only as labels without mathematical meaning.

Ordinal Scale

A measurement scale where observations fall into ordered categories that can be ranked, but the precise distance between categories is unknown.

Interval Scale

A measurement scale where observations are ordered and differences between values are meaningful, but zero is arbitrary and does not represent a total absence of the trait.

Ratio Scale

The highest level of measurement featuring meaningful distances, meaningful ratios, and a true zero representing total absence of the measured trait.

Contingency Table

A two-way frequency table used to display the joint frequency distribution of two categorical variables simultaneously.

Histogram

A specialized bar graph used to graphically display the frequency or relative frequency distribution of continuous quantitative data.

Scatter Plot

A graph displaying paired data points to show the relationship between two continuous quantitative variables.

Stem-and-Leaf Plot

A graphical display that illustrates the shape of a data distribution while maintaining all individual observations by splitting each value into a stem and a leaf.

Boxplot Structural Components

The key features of a box-and-whisker plot, including the minimum, lower quartile ($Q_1$), median ($Q_2$), upper quartile ($Q_3$), maximum, interquartile range ($IQR$), whisker limits ($Q_1 - 1.5 \times IQR$ and $Q_3 + 1.5 \times IQR$), and potential outliers.

Statistic

A descriptive measure computed from a sample, such as the sample mean ($\bar{X}$) or sample size ($n$).

Parameter

A descriptive measure computed from an entire population, such as the population mean ($\times$) or population size ($N$).

Measures of Central Tendency

Descriptive statistics that convey information regarding the average value of a dataset, including the mean, median, and mode.

Arithmetic Mean

The sum of a set of numbers divided by the total number of observations, represented as $\bar{X} = \frac{\text{sum}_{i=1}^n x_i}{n}$ for a sample or $\times = \frac{\text{sum}_{i=1}^N x_i}{N}$ for a population.

Median

The middle value in an ordered dataset at the $\frac{n+1}{2}\text{th}$ position, dividing the data into two equal halves.

Mode

The value or values that occur most frequently in a set of observations.

Measures of Dispersion

Descriptive statistics that quantify the amount of variability or spread present within a set of data.

Range

The difference between the largest and smallest observations in a dataset, calculated as $R = \text{Maximum} - \text{Minimum}$.

Percentile

The value $P$ in a dataset such that $p$ percent or less of the observations are less than $P$ and $(100 - p)$ percent or less are greater than $P$.

Quartiles

Specific percentiles dividing an ordered dataset into four equal parts: the first quartile ($Q_1$ at 25%), second quartile ($Q_2$ / median at 50%), and third quartile ($Q_3$ at 75%).

Interquartile Range

The difference between the third quartile and first quartile, calculated as $IQR = Q_3 - Q_1$, which comprises the middle 50% of the data.

Symmetric Distribution

A distribution where the left half of the graph is the mirror image of its right half, and the mean, median, and mode are equal.

Skewed Distribution Relationships

The positional relationships among central tendency measures in asymmetric distributions: left-skewed curves feature $\text{Mean} < \text{Median} < \text{Mode}$, whereas right-skewed curves feature $\text{Mode} < \text{Median} < \text{Mean}$.

Sample Variance

A measure of variability representing the sum of squared deviations from the sample mean divided by the sample size minus one, calculated as $s^2 = \frac{\text{sum}_{i=1}^n (x_i - \bar{X})^2}{n - 1}$.

Population Variance

A measure of variability representing the sum of squared deviations from the population mean divided by population size, calculated as $\text{sigma}^2 = \frac{\text{sum}_{i=1}^N (x_i - \times)^2}{N}$.

Standard Deviation

The positive square root of the variance ($s = \text{sqrt}(s^2)$), measuring dispersion in the original units of the variable.

Empirical Probability

Probability based on observing relative frequencies from collected data.

Theoretical Probability

Probability calculated mathematically from a known sample space without collecting experimental data.

Sample Space

The set of all possible results or outcomes of a statistical study or experiment.

Mutually Exclusive Events

Events that cannot occur simultaneously in a single trial, meaning the occurrence of one prevents the occurrence of another.

Marginal Probability

The probability of a single event occurring without conditioning on another event, calculated as $P(A) = \frac{m}{N}$.

Complement of an Event

The occurrence that event $A$ does not happen, calculated as $P(\text{bar}{A}) = 1 - P(A)$.

Conditional Probability

The probability that event $A$ occurs given that event $B$ has already occurred, written as P(A|B)

What is joint probability?

The probability of two events occurring simultaneously P(A∩B)

Therefore P(A∩B) = P(A) x P(B|A) or P(A∩B) = P(B) x P(A|B)

Multiplcation rule applies applies: P(A) x P(B|A)

Simplication exists if events are independent: P(A) x P(B

What is either/or probability?

If events A and B are mutually exclusive, then the either/or probability is simply the sum of the two marginal probabilities P(AUB) = P(A) + P(B)

Addition rule always applies: P(A) + P(B) – P(A∩B)

Simplication exists if the events are mutually exclusive: P(A) + P(B)

What is a discrete probability distribution?

The probability distribution of a discrete random variable is a table, formula, or any other device that specifics all possible values of a discrete random variable along with their corresponding probabilities

Examples: Coin flip, cancer stages

What is a normal probability distribution?

Is a continuous distribtuion tion defined by its mean and standard deviation, representing data that cluster around the mean and follow the symmetric bell-shaped curve.

1. Symetrical to the mean

2. the mean, median and mode are all equal

3. The % of values falling with 1, 2 & 3 standard deviations of the mean is known

What is sampling distribution?

The distribution of all possible values of a statistic that can be computed from all possible samples of the same size randomly drawn from the same population is called the sampling distribution of the statistics

What is point estimate?

a single value used to approximate a population parameter

What is an internal estimate?

concists of two numerical values defining a range, that with a specified degree of confidence, includes a paramete being estimated

What is hypothesis testing?

a claim or statement about one or more populations that can be tested using statistical methods to determine the validity of the claim based on sample data.

What is a null hypothesis?

States that a population parameter is equal to a certain value (often based on existing evidence)

What is a alternative hypothesis?

A statement that contradicts the null hypothesis, indicating that a population parameter is not equal to a certain value.

What is the fisher method in hypothesis testing?

1. state the claim (or claim in question)

2. state the counter claim (everything other then the claim)

3. assign the claim with the equality to H0 and the remaining claim to HA

What is a directional (one tailed test) hypothesis test?

A hypothesis test that evaluates the probability of a parameter falling within a specified direction (greater than or less than) from a hypothesized value, as opposed to testing both directions.

What is a non-directional (two tailed)n test?

A hypothesis test that evaluates the probability of a parameter being different from a hypothesized value, considering both directions (greater than or less than) equally.

What is a P value in hypothesis testing?

A P value is the probability of observing results at least as extreme as the actual results under the assumption that the null hypothesis is true. It helps determine the statistical significance of the test results.

True or False: P-value and critical value approach are equivalent in terms of the decision to reject H0

TRUE