STAT 109 Biostatistics Review (Chapters 1 - 3)

Comprehensive Question and Answer flashcards covering Chapters 1 through 3 of STAT 109 Biostatistics, including definitions, formulas, rules of probability, and screening test evaluation metrics.

What is the main concern of descriptive statistics?

Organizing, summarizing, and describing data.

What is the primary objective of inferential statistics?

Drawing inferences and reaching decisions about a population when only a sample of the data is observed.

What are the four main sources of data mentioned in Biostatistics?

1) Routinely kept records, 2) Surveys, 3) Experiments, and 4) External sources.

How is a discrete quantitative variable defined?

A quantitative variable that has jumps or gaps between its values, such as family size or number of patients.

How is a continuous quantitative variable defined?

A quantitative variable with no gaps between values that can take any value within a certain interval, such as height or blood sugar level.

What distinguishes an ordinal qualitative variable from a nominal qualitative variable?

An ordinal variable classifies observations into ranked or ordered categories, whereas a nominal variable classifies them into non-ranked categories.

What is simple random sampling?

A sampling method where a sample of size $n$ is selected from a population of size $N$ in such a way that each element has the same chance of being selected.

What is stratified random sampling?

A sampling method where population elements are classified into homogeneous groups (strata), and an independent simple random sample is drawn from each group.

What is the formula for calculating the mid-point of a class interval?

$$\text{Mid-point} = \frac{\text{upper limit} + \text{lower limit}}{2}$$

How are the true upper and lower limits of a class interval calculated using gap $d$?

$\text{True upper limit} = \text{upper limit} + \frac{d}{2}$ and $\text{True lower limit} = \text{lower limit} - \frac{d}{2}$

How are relative frequency and percentage frequency computed?

$\text{Relative frequency} = \frac{f}{n}$ and $\text{Percentage frequency} = \text{Relative frequency} \times 100\%$

What is the difference between a parameter and a statistic?

A parameter is a descriptive measure computed from population values (usually unknown), while a statistic is computed from sample values (known and used to estimate parameters).

What is the formula for the sample mean $\bar{x}$?

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

What is a major disadvantage of using the mean as a measure of central tendency?

The mean is sensitive to and can be distorted by extreme values.

How is the rank of the middle value calculated when finding the median of $n$ observations?

$$\text{rank} = \frac{n + 1}{2}$$

How is the median calculated when the sample size $n$ is even?

The median is the average of the two middle values at ranks $m$ and $m + 1$, where $m = \frac{n}{2}$: $\text{Median} = \frac{y_m + y_{m+1}}{2}$

What is the definition of the mode of a data set?

The value that occurs most frequently in the data set.

What is the formula for the sample variance $S^2$?

$$S^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n - 1}$$

Why is standard deviation often preferred over variance as a measure of dispersion?

Standard deviation is expressed in the original units of the data, whereas variance is expressed in squared units.

What is the formula for the sample Coefficient of Variation (C.V.)?

$$\text{C.V.} = \frac{S}{\bar{x}} \times 100\%$$

Why is the Coefficient of Variation used to compare variability between two data sets instead of standard deviation?

Because the Coefficient of Variation is unit-less and allows fair comparison when data sets have different units or different means.

How is the probability of an event $E$ calculated when all outcomes in sample space $\Omega$ are equally likely?

$$P(E) = \frac{n(E)}{n(\Omega)}$$

What defines two mutually exclusive (disjoint) events $A$ and $B$?

Two events are mutually exclusive if $A \cap B = \emptyset$, meaning $P(A \cap B) = 0$.

What defines exhaustive events $A_1, A_2, \dots, A_n$?

Events are exhaustive if their union is the entire sample space: $A_1 \cup A_2 \cup \dots \cup A_n = \Omega$, making $P(A_1 \cup A_2 \cup \dots \cup A_n) = 1$.

What is the general addition rule of probability for any two events $A$ and $B$?

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

What is the formula for conditional probability $P(A|B)$?

$P(A|B) = \frac{P(A \cap B)}{P(B)}$, provided $P(B) \neq 0$.

What are three conditions, any of which proves that two events $A$ and $B$ are independent?

1) $P(A|B) = P(A)$, 2) $P(B|A) = P(B)$, or 3) $P(A \cap B) = P(A) P(B)$

What is the sensitivity of a screening test?

The probability of a positive test result given the presence of the disease: $P(T|D) = \frac{n(T \cap D)}{n(D)}$.

What is the specificity of a screening test?

The probability of a negative test result given the absence of the disease: $P(\bar{T}|\bar{D}) = \frac{n(\bar{T} \cap \bar{D})}{n(\bar{D})}$.

What is a false positive result in a screening test?

A positive test result when the true disease status is negative: $P(T|\bar{D}) = 1 - \text{Specificity}$.

What is a false negative result in a screening test?

A negative test result when the true disease status is positive: $P(\bar{T}|D) = 1 - \text{Sensitivity}$.

How is the predictive value positive $P(D|T)$ calculated using Bayes' theorem?

$$\text{P}(D|T) = \frac{\text{Sensitivity} \times P(D)}{\text{Sensitivity} \times P(D) + (1 - \text{Specificity}) \times P(\bar{D})}$$

How is the predictive value negative $P(\bar{D}|\bar{T})$ calculated using Bayes' theorem?

$$\text{P}(\bar{D}|\bar{T}) = \frac{\text{Specificity} \times P(\bar{D})}{\text{Specificity} \times P(\bar{D}) + (1 - \text{Sensitivity}) \times P(D)}$$