SOCY2339 Exam Revision - Statistics and Data Analysis

Flashcards covering quantitative research methods, variable classifications, measures of central tendency and dispersion, distribution shapes, correlation, and probability basics.

What defines experimental quantitative research?

Research involving two or more groups with random assignment, where the researcher manipulates one group and compares results to a control group to determine causality.

What is the main purpose of associational (observational) quantitative research?

To investigate relationships between observed, pre-existing variables without manipulating or controlling them, using correlation or regression analysis.

What is the difference between validity and reliability in measurement?

Validity evaluates whether a tool measures what it intends to measure, whereas reliability assesses whether the tool consistently measures the same thing.

What is the primary difference between descriptive and inferential statistics?

Descriptive statistics describe or summarize characteristics of a sample, while inferential statistics draw conclusions about an entire population based on sample data.

How do population parameters and sample statistics differ?

A parameter describes a measurable characteristic of an entire population, whereas a statistic is calculated from sample data to estimate a population parameter.

What symbols represent the mean and standard deviation for population parameters versus sample statistics?

For a population parameter, the mean symbol is $\mu$ (Mu) and standard deviation is $\sigma$ (Sigma). For a sample statistic, the mean symbol is $\bar{x}$ (X-bar) and standard deviation is $s$.

What is the difference between nominal and ordinal categorical variables?

Nominal variables consist of categories with no natural order (e.g., gender, religion), while ordinal variables consist of categories with a meaningful rank or order but unequal or unknown spacing (e.g., education level, satisfaction rating).

How do discrete and continuous quantitative variables differ?

Discrete variables take countable, whole number values only (e.g., number of children), whereas continuous variables can take any value within a range, including decimals (e.g., height, weight, age, income).

What distinguishes interval variables from ratio variables?

Interval variables have equal, meaningful intervals between values without a true zero (e.g., temperature in $0^\circ\text{C}$), while ratio variables have a true zero where $0$ indicates none (e.g., age, income, height).

Which measure of central tendency is best for skewed interval/ratio variables, and why?

The median is best because extreme outliers distort the mean, whereas the median is resistant to outliers.

Based on the provided distribution curves, how do the mean, median, and mode compare in right-skewed vs. left-skewed distributions?

In a right-skewed (positively skewed) distribution, $\text{mean} > \text{median} > \text{mode}$. In a left-skewed (negatively skewed) distribution, $\text{mode} > \text{median} > \text{mean}$.

What is the formula for calculating relative frequency percentage in a frequency distribution table?

$$\text{Relative Frequency (\%)} = \left(\frac{\text{frequency}}{\text{total number}}\right) \times 100$$

How is the location of the median score determined for an ordered dataset of size $n$?

The location of the median score is calculated as $\frac{n + 1}{2}$.

How is the Interquartile Range (IQR) calculated?

$\text{IQR} = \text{75th percentile} - \text{25th percentile}$, which measures the spread of the middle $50\%$ of observations.

What is the mathematical relationship between standard deviation ($s$) and variance ($s^2$)?

Standard deviation ($s$) is the positive square root of variance ($s^2$), and variance ($s^2$) is standard deviation squared.

What is the difference in representation between a bar chart and a histogram?

Bar charts display categorical data with spaces between bars to show order is arbitrary; histograms display interval/ratio variables with no spaces between bars.

How are independent and dependent variables defined and denoted?

The independent variable ($X$) is the predictor or explanatory variable, while the dependent variable ($Y$) is the outcome or response variable of interest.

What range of values can Pearson's correlation coefficient ($r$) take, and what do they indicate?

$r$ ranges from $-1$ to $+1$. Values near $-1$ or $+1$ indicate strong linear relationships, while values near $0$ indicate weak linear relationships.

What defines complementary events in probability?

Two mutually exclusive events whose probabilities sum to $1$ ($100\%$), with no other outcomes possible.

What is the difference between disjoint and non-disjoint events?

Disjoint (mutually exclusive) events cannot occur at the same time, whereas non-disjoint events can occur simultaneously.

According to the provided diagram, what is the formula for the probability of the union of two events, $P(A \text{ or } B)$?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

Based on the provided diagram, what is the formula for conditional probability $P(A|B)$?

$P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$, where the denominator represents the probability of the 'given' event $B$.

When are two processes or variables considered statistically independent?

Two processes are independent if knowing the outcome of one provides no useful information about the outcome of the other.

What information is visually represented in a boxplot?

A boxplot shows central tendency and dispersion, where the highlighted box region represents the Interquartile Range (IQR), the internal line indicates the median, and the plot displays the full range of data.