flashcard 4

Question 1

What is the main purpose of statistics in research?

Answer 1

To collect, analyze, interpret, and present numerical data in order to distinguish real patterns from random variation and make informed decisions.

Question 2

Name the four primary tasks involved in statistical analysis.

Answer 2

1) Designing experiments and collecting data, 2) Describing and summarizing data, 3) Testing hypotheses (inferential statistics), and 4) Building and evaluating predictive or explanatory models.

Question 3

Why is it important to design experiments carefully before collecting data?

Answer 3

Because a well-designed experiment ensures that data are representative, unbiased, and appropriate for answering the research question, making subsequent analysis valid.

Question 4

How does descriptive statistics differ from inferential statistics?

Answer 4

Descriptive statistics summarize and visualize the features of a dataset (e.g., mean, median, charts), whereas inferential statistics draw conclusions or make predictions about a population based on sample data.

Question 5

Explain what a random variable is in probability theory.

Answer 5

A random variable is a numerical representation of outcomes in an experiment, where each possible outcome is assigned a probability.

Question 6

What distinguishes a discrete random variable from a continuous random variable?

Answer 6

Discrete variables take on countable values (e.g., number of successes), while continuous variables can take any value within an interval (e.g., height or weight).

Question 7

How can probability be interpreted through the lens of long-run frequencies?

Answer 7

As the proportion of times an event occurs out of many repetitions of the same experiment, approaching a stable value as trials increase.

Question 8

Define sensitivity in the context of diagnostic testing.

Answer 8

Sensitivity measures the ability of a test to correctly identify individuals who have the condition (true positives) out of all actual positives.

Question 9

Define specificity in diagnostic testing.

Answer 9

Specificity measures the ability of a test to correctly identify individuals who do not have the condition (true negatives) out of all actual negatives.

Question 10

What do positive predictive value (PPV) and negative predictive value (NPV) convey about a diagnostic test?

Answer 10

PPV indicates the probability that someone with a positive test truly has the condition; NPV indicates the probability that someone with a negative test truly does not have the condition.

Question 11

Why does the prevalence of a disease in a population affect PPV and NPV?

Answer 11

Because PPV and NPV depend on the proportion of true cases versus non-cases; in low-prevalence settings, even tests with high sensitivity and specificity can yield a low PPV.

Question 12

Describe the key differences between randomized controlled trials (RCTs) and cohort studies.

Answer 12

In RCTs, participants are randomly assigned to treatment or control, controlling for confounders. In cohort studies, participants are followed over time based on exposure status without random assignment.

Question 13

What is the distinction between prospective and retrospective study designs?

Answer 13

Prospective studies collect data moving forward from a defined point, while retrospective studies analyze existing data that were collected in the past.

Question 14

Compare cross-sectional and longitudinal studies.

Answer 14

Cross-sectional studies measure variables at a single point in time, providing a “snapshot,” whereas longitudinal studies follow the same subjects over multiple time points to observe changes.

Question 15

What defines quantitative data versus qualitative (categorical) data?

Answer 15

Quantitative data are numerical measurements (either discrete or continuous), while qualitative data describe categories or attributes (nominal or ordinal).

Question 16

Give examples of nominal and ordinal qualitative variables.

Answer 16

Nominal examples: blood type, type of cuisine. Ordinal examples: pain severity scale, education level (high school, bachelor’s, master’s).

Question 17

What is a probability distribution, and why is it useful?

Answer 17

A probability distribution describes how probabilities are assigned to different values of a random variable, helping to understand the variable’s behavior and make inferences.

Question 18

Name three common probability distributions and their typical applications.

Answer 18

Normal distribution for continuous traits in populations; Binomial distribution for counts of successes in fixed trials; Poisson distribution for rare event counts over a fixed interval.

Question 19

Explain the concept of a normal distribution and its key characteristics.

Answer 19

A normal distribution is symmetric, bell-shaped, and defined by its mean (center) and standard deviation (spread); most values cluster around the mean.

Question 20

What does the empirical rule (“68–95–99.7 rule”) describe?

Answer 20

In a normal distribution, approximately 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three.

Question 21

Why might one choose the median over the mean as a measure of central tendency?

Answer 21

Because the median is less sensitive to extreme values or skewed data, providing a better “central” value when outliers are present.

Question 22

How do you interpret the standard deviation of a dataset?

Answer 22

Standard deviation quantifies the average distance of data points from the mean, reflecting the spread or variability in the dataset.

Question 23

What is the standard error of the mean (SEM), and how does it differ from standard deviation?

Answer 23

SEM measures the variability of sample means if the same experiment were repeated, whereas standard deviation measures variability of individual observations around the sample mean.

Question 24

Define skewness and explain what positive or negative skew indicates about a distribution’s shape.

Answer 24

Skewness measures asymmetry of a distribution. Positive skew (right-tailed) indicates a long tail on the higher side; negative skew (left-tailed) indicates a long tail on the lower side.

Question 25

What does kurtosis describe in a distribution?

Answer 25

Kurtosis measures the “tailedness” or “peakedness” of a distribution compared to a normal distribution, indicating the propensity for outliers.

Question 26

Why is it important to assess both location and dispersion when summarizing data?

Answer 26

Because measures of central tendency (location) alone don’t convey the spread or variability; dispersion measures (e.g., range, interquartile range, standard deviation) describe how data are distributed around the center.

Question 27

What is a contingency table, and when is it used?

Answer 27

A contingency table (cross-tabulation) displays frequencies of two categorical variables simultaneously, facilitating analysis of associations or interactions.

Question 28

Define the Pearson correlation coefficient (r).

Answer 28

A statistic that quantifies the strength and direction of a linear relationship between two continuous variables, ranging from –1 (perfect negative) to +1 (perfect positive).

Question 29

Under what circumstances might Pearson correlation be misleading?

Answer 29

When the relationship is non-linear, when outliers heavily influence the data, or when the variables are not measured on an interval/ratio scale.

Question 30

What is Spearman rank correlation, and why is it used instead of Pearson correlation in some cases?

Answer 30

Spearman correlation assesses the strength of a monotonic relationship using ranked data; it is robust to outliers and appropriate for ordinal data or non-linear (but monotonic) associations.

Question 31

Describe when you would use a histogram versus a boxplot to explore a dataset.

Answer 31

Use a histogram to visualize the detailed shape of a distribution (e.g., modality, skewness). Use a boxplot to summarize distribution in terms of median, quartiles, and identify outliers.

Question 32

In a boxplot, what do the box, whiskers, and outliers represent?

Answer 32

The box spans the interquartile range (Q1 to Q3) with a line at the median; whiskers extend to the most extreme values within 1.5×IQR; points beyond whiskers are outliers.

Question 33

How do sample size and variability affect the reliability of statistical estimates?

Answer 33

Larger sample sizes reduce the standard error, making estimates more precise. Greater variability in data increases uncertainty around estimates, requiring larger samples to achieve the same precision.

Question 34

Explain why random sampling is important in statistical studies.

Answer 34

Random sampling minimizes selection bias and ensures that the sample represents the broader population, allowing valid inferences and generalizations.

Question 35

What are type I and type II errors in hypothesis testing?

Answer 35

A type I error is incorrectly rejecting a true null hypothesis (false positive). A type II error is failing to reject a false null hypothesis (false negative).

Question 36

How does significance level (α) relate to type I error?

Answer 36

The significance level (α) is the probability threshold for rejecting the null hypothesis; setting α = 0.05 means there is a 5% chance of making a type I error.

Question 37

What is statistical power, and what factors influence it?

Answer 37

Statistical power is the probability of correctly rejecting a false null hypothesis (1 − type II error rate). It increases with larger sample size, larger effect size, and lower data variability.

Question 38

Define p-value in the context of hypothesis testing.

Answer 38

The p-value is the probability of observing data as extreme or more extreme than what was collected, assuming the null hypothesis is true.

Question 39

Why is it important to distinguish between statistical significance and practical significance?

Answer 39

A result can be statistically significant (unlikely due to chance) but have a trivial or clinically irrelevant effect size, so one must assess real-world impact.

Question 40

Describe the difference between one-sided and two-sided hypothesis tests.

Answer 40

A one-sided test assesses deviation in a specific direction (e.g., greater than); a two-sided test assesses deviations in both directions (greater or less than).

Question 41

What is a confidence interval, and how is it interpreted?

Answer 41

A confidence interval provides a range of plausible values for a population parameter (e.g., mean) with a specified confidence level (e.g., 95%), indicating that if the study were repeated, the true parameter would fall within that range most of the time.

Question 42

When might nonparametric methods be preferable to parametric methods?

Answer 42

When data do not meet parametric assumptions (e.g., normality, equal variances), have small sample sizes, or include ordinal/categorical variables.

Question 43

Give an example of a nonparametric test and its basic application.

Answer 43

The Wilcoxon rank-sum test (Mann–Whitney U) compares the central tendency of two independent groups when data are skewed or ordinal.

Question 44

Explain the purpose of analysis of variance (ANOVA).

Answer 44

ANOVA tests whether there are statistically significant differences among the means of three or more independent groups by comparing between-group variability to within-group variability.

Question 45

What is a chi-squared test used for?

Answer 45

To assess whether observed frequencies in categorical data differ from expected frequencies under a null hypothesis of no association or no difference.

Question 46

How does logistic regression differ from linear regression?

Answer 46

Logistic regression models the probability of a binary outcome using a logit link, whereas linear regression predicts a continuous outcome using a linear relationship.

Question 47

Why is it important to assess residuals after fitting a regression model?

Answer 47

Checking residuals helps verify model assumptions—such as normality, homoscedasticity, and independence—and identify potential outliers or influential observations.

Question 48

Define overfitting in the context of model building.

Answer 48

Overfitting occurs when a model captures noise or random fluctuations in the training data, performing well on that data but poorly on new, unseen data.

Question 49

What strategies can help prevent overfitting?

Answer 49

Use simpler models, cross-validation, regularization techniques (e.g., Lasso, Ridge), and ensure adequate sample size relative to the number of predictors.

Question 50

Why should descriptive plots always accompany numerical summaries in data analysis?

Answer 50

Because visualizations (e.g., histograms, scatterplots) reveal patterns, outliers, and distribution shapes that numerical summaries alone might obscure.