Introduction to Statistics and Levels of Measurement
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1
What is descriptive statistics?
The branch of statistics concerned with organizing, summarizing, and presenting observed data.
2
What is inferential statistics?
The use of sample data and statistical models to estimate population characteristics or test hypotheses while accounting for uncertainty.
3
What is a parameter in statistics?
A numerical characteristic of a population, such as its true mean or proportion.
4
What is a statistic in research?
A numerical quantity calculated from sample data, such as a sample mean or proportion.
5
What is nominal measurement?
Classification into categories that have no inherent numerical order, such as offense type or police district.
6
What is ordinal measurement?
Classification into categories with a meaningful order but without necessarily equal distances between categories.
7
What is interval measurement?
A numerical scale with equal units of measurement but without a meaningful absolute zero.
8
What is ratio measurement?
A numerical scale with equal units and a meaningful zero, allowing meaningful ratios.
9
What level of measurement applies to the number of reported thefts?
Ratio level, because counts have a meaningful zero and equal units.
10
What level of measurement applies to crime severity classified as low, moderate, or high?
Ordinal level, because the categories have a meaningful ranking.
11
What is a frequency distribution?
A summary showing how often each value or category occurs in a dataset.
12
What is relative frequency?
The frequency of a category divided by the total number of observations.
13
What is the arithmetic mean?
The sum of all observed numerical values divided by the number of observations.
14
What is the median?
The middle value of an ordered dataset, or the average of the two middle values when the number of observations is even.
15
What is the mode?
The value or category appearing most frequently in a dataset.
16
Which measure of central tendency is generally less affected by extreme outliers: mean or median?
The median.
17
What is the range of a numerical dataset?
The difference between its maximum and minimum observed values.
18
What is variance?
A measure of dispersion based on the average squared deviations from the mean, with the exact divisor depending on the population or sample formula.
19
What is standard deviation?
A measure of dispersion expressed in the original units of the data, equal to the square root of variance.
20
What is the interquartile range?
The difference between the third quartile and first quartile, describing the spread of the middle half of the data.
21
What is a percentile?
A value or position indicating the percentage of observations at or below a specified point, according to the chosen calculation method.
22
What is a z-score?
A standardized value showing how many standard deviations an observation lies above or below the mean.
23
What is probability?
A numerical measure of the likelihood of an event, ranging from zero for an impossible event to one for a certain event.
24
What is conditional probability?
The probability of an event occurring given that another specified event or condition has occurred.
25
What is the base-rate fallacy?
An error in reasoning that neglects the underlying prevalence of an event when interpreting evidence or predicting outcomes.
26
What is sampling error?
The difference between a sample estimate and the corresponding population parameter arising from random sample selection.
27
What is the standard error?
An estimate of the variability of a statistic across repeated samples under a specified sampling model.
28
What is a confidence interval?
An interval calculated by a method designed to contain the population parameter at a stated long-run frequency across repeated samples.
29
How should a 95% confidence interval be interpreted in frequentist statistics?
The procedure is designed so that approximately 95% of intervals constructed over repeated samples contain the true population parameter.
30
What is statistical significance?
A conclusion that observed data are sufficiently incompatible with a specified null hypothesis under a chosen significance threshold.
31
What is a p-value?
The probability, assuming the null hypothesis and statistical model are true, of obtaining a test statistic at least as extreme as the observed one.
32
Does a p-value of 0.03 mean there is a 3% probability that the null hypothesis is true?
No. A p-value is calculated assuming the null hypothesis; it is not the probability that the hypothesis is true.
33
What is the significance level, commonly represented by alpha?
The preselected threshold used to determine when a statistical test rejects the null hypothesis.
34
What is a Type I error?
Rejecting a true null hypothesis, also called a false positive in the hypothesis-testing context.
35
What is a Type II error?
Failing to reject a false null hypothesis, also called a false negative in the hypothesis-testing context.
36
What is statistical power?
The probability that a statistical test rejects the null hypothesis when a specified alternative hypothesis is true.
37
What is effect size?
A quantitative measure of the magnitude of a relationship, difference, or treatment effect.
38
What is the Pearson correlation coefficient?
A statistic ranging from minus one to plus one that measures the direction and strength of a linear relationship between two numerical variables.
39
What does a Pearson correlation coefficient of zero indicate?
No linear correlation in the measured data, although a nonlinear relationship may still exist.
40
What is Spearman's rank correlation coefficient?
A rank-based measure of the direction and strength of a monotonic association between variables.
41
What is regression analysis?
A statistical method for modeling the relationship between an outcome variable and one or more predictors.
42
When is logistic regression commonly appropriate in criminological research?
When modeling a binary outcome, such as whether a person reoffended during a defined follow-up period.
43
What is an odds ratio in logistic regression?
A measure comparing odds between conditions or associated with a change in a predictor, holding other modeled predictors constant when applicable.
44
What is multicollinearity?
A condition in which predictors in a regression model are strongly related, potentially making individual coefficient estimates unstable.
45
What is the ecological fallacy?
Drawing conclusions about individual people from relationships observed only in aggregated group-level data.
46
Scenario: A district records 240 crimes among 80,000 residents. What is the crude crime rate per 100,000 population?
300 crimes per 100,000 residents, calculated as 240 divided by 80,000 multiplied by 100,000.
47
Scenario: Five precincts report 4, 6, 6, 9, and 25 robberies. What are the mean, median, and mode?
Mean 10; median 6; mode 6.
48
Scenario: A sample has a mean response time of 12 minutes and standard deviation of 3 minutes. What is the z-score for 18 minutes?
Plus 2, calculated as (18 minus 12) divided by 3.
49
Scenario: A study reports p = 0.02 with alpha = 0.05. What is the conventional statistical decision?
Reject the null hypothesis at the 5% significance level, assuming the test and its assumptions are appropriate.
50
Scenario: A researcher finds that cities with higher unemployment have higher crime rates and concludes every unemployed person is more likely to offend. What reasoning error is illustrated?
The ecological fallacy, because an aggregate association does not establish the corresponding individual-level relationship.
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