Statistics II

Course Description

Statistics II covers mathematical derivation of standard statistical distributions along with their mean and variance, estimation and hypothesis testing of means, proportions, and variances, analysis of variance, simple and multiple linear regression, analysis of count data: chi-square and contingency tables, and nonparametric methods.

Within the SCNS taxonomy, STA is the Statistics prefix. Daytona State publishes this at 3 credits, offered spring, with MAC2311C, MAC2312C and STA2023 as prerequisites. ⚠ The single term of offering, behind a calculus sequence, is worth planning around.

The word "derivation" in the catalog description is what distinguishes this course from the introductory one, and it changes the subject completely. An introductory statistics course teaches you which test to run; this one asks where the distribution came from, why the test statistic has the sampling distribution it has, and therefore what happens when the assumptions behind it are not met. That is the difference between someone who can run a procedure and someone who can tell when the output is meaningless.

Daytona State does not publish a lecture and laboratory split for this course. It is an unsuffixed lecture course, and the institution's lecture convention is 15 contact hours per credit — PSY1012, AMH2010 and GEB1011 are all live at 3 credits and 45 hours. This course is priced at that convention.

Learning Outcomes

Required Outcomes

• Derive and describe standard discrete probability distributions.
• Derive and describe standard continuous probability distributions.
• Compute expectation and variance from a distribution.
• Describe moment generating functions and their uses.
• Describe sampling distributions and the central limit theorem.
• Describe the distributions used in inference and where they come from.
• Construct and interpret point estimates.
• Describe properties of estimators, including bias and efficiency.
• Construct confidence intervals for means, proportions, and variances.
• Interpret a confidence interval correctly.
• Formulate and test hypotheses about means.
• Test hypotheses about proportions and about variances.
• Describe type I and type II error and statistical power.
• Describe the assumptions underlying each procedure.
• Determine when an assumption violation matters.
• Perform and interpret analysis of variance.
• Conduct post hoc comparisons appropriately.
• Fit and interpret a simple linear regression.
• Assess regression assumptions using residual diagnostics.
• Fit and interpret multiple linear regression.
• Describe multicollinearity and its consequences.
• Analyse count data using chi-square and contingency tables.
• Apply nonparametric methods and describe when they are appropriate.
• Communicate statistical results accurately and without overclaiming.

Optional Outcomes

• Describe experimental design principles.
• Describe Bayesian inference at an introductory level.
• Describe logistic regression.
• Describe time series methods.
• Use statistical software for analysis.
• Describe reproducible analysis practice.

Major Topics

Required Topics

• Discrete distributions
• Continuous distributions
• Expectation and variance
• Moment generating functions
• Sampling distributions and the central limit theorem
• Distributions used in inference
• Point estimation
• Properties of estimators
• Confidence intervals
• Interpreting intervals
• Hypothesis tests for means
• Tests for proportions and variances
• Type I and II error and power
• Assumptions of procedures
• When violations matter
• Analysis of variance
• Post hoc comparisons
• Simple linear regression
• Residual diagnostics
• Multiple regression
• Multicollinearity
• Chi-square and contingency tables
• Nonparametric methods
• Communicating results

Optional Topics

• Experimental design
• Bayesian inference
• Logistic regression
• Time series
• Statistical software
• Reproducible analysis

Resources & Tools

• Your college library's science databases — free with enrolment, and the difference between citing the literature and citing a website.
• Your instructor's office hours — free, underused, and the fastest route past a concept you are stuck on.
• The tutoring centre — free, and used most heavily by the students who do best.
• Draw the mechanism yourself. Concept maps and hand-drawn diagrams outperform rereading substantially in science courses, and they show you where the gap is.
• Work problems continuously rather than before assessments. Science and mathematics are learned by doing, and reading a worked solution produces a convincing but false sense of understanding.
• R and RStudio, or Python with statsmodels — both free; learning one alongside the theory makes you employable in a way the theory alone does not.
• Your textbook's derivations, worked by hand — in this course the derivations are the content, and reading them is not the same as doing them.
• The American Statistical Association's statement on p-values — free, short, and the authoritative correction to the misuse described below.

Career Pathways

• Statistician — SOC 15-2041; strong projected growth, and generally requiring a graduate degree.
• Data scientist — SOC 15-2051; this course is the theory half that distinguishes a data scientist from a tool user.
• Data analyst and business intelligence roles — accessible with a bachelor's and strong software skills.
• Biostatistics and clinical research — a large, well-paid, and persistently short-staffed field.
• Actuarial science — examination-based, well paid, and built directly on this material.
• Quality engineering and process control — see this repository's ETS4502C guide.
• Market research and survey analysis — SOC 13-1161.
• Government statistical agencies at state and federal level.
• Transfer to a bachelor's or graduate programme in statistics, mathematics, or data science.

Special Information

⚠⚠ The p-value is the most misused number in science — know what it is not

• A p-value is the probability of data at least as extreme as yours, assuming the null hypothesis is true. Almost every popular misinterpretation comes from forgetting the second half of that sentence.
• ⚠ It is not the probability that the null hypothesis is true, and it is not the probability that your result is a fluke. Those are different questions requiring different machinery.
• ⚠⚠ It says nothing about effect size or importance. A large enough sample makes a trivial difference statistically significant, and a small sample can miss an important one entirely — which is why effect sizes and confidence intervals belong in every report and a bare p-value does not.
• A non-significant result is not evidence of no effect. Absence of evidence and evidence of absence are different conclusions, and conflating them is endemic.
• ⚠ The 0.05 threshold is a convention, not a law of nature, and treating it as a bright line between real and unreal is the root of a great deal of bad practice.
• ⚠⚠ Multiple comparisons inflate false positives. Test twenty independent hypotheses at the 0.05 level and you expect one significant result from pure noise — which is why post hoc corrections exist and why testing everything and reporting what worked is a serious methodological failure.
• Decide the analysis before seeing the data. Choosing the test, the subgroup, or the outcome after looking is how a null result becomes a publishable one, and it is not honest.
• Report everything you tested, not just what reached significance.
• Prefer estimation to testing where you can. "The difference is 4.2 units, 95% CI 1.1 to 7.3" tells a reader far more than "p < 0.05".

⚠ Assumptions are the point — that is what the derivations are for

• Every procedure in this course rests on assumptions, and the reason to derive the distributions is so that you can see which assumptions the derivation used and therefore what breaks when they fail.
• ⚠ Independence is the assumption most often violated and least often checked. Repeated measures on the same subject, clustered sampling, and time-ordered data all violate it — and violating independence is far more damaging than violating normality.
• Check the residuals in regression. Non-linearity, non-constant variance, and influential outliers are visible in a residual plot in seconds and invisible in the coefficient table.
• ⚠ Software will happily fit a model to data that violates every assumption, and it will return confident coefficients and small p-values. The output looks identical whether the model is appropriate or not.
• Know which violations matter. Many procedures are robust to moderate non-normality with reasonable sample sizes; few are robust to dependence or to a badly specified model.
• Use nonparametric methods when the assumptions genuinely fail, and understand what they give up in exchange.
• ⚠ Watch for influential points. A single observation can drive a regression line entirely, and identifying it is a diagnostic step rather than an excuse to delete it.
• Never delete data because it is inconvenient. Investigate it, and if you exclude anything, say so and say why.
• Plot the data before modelling it. Summary statistics conceal structure that a scatterplot reveals immediately.

⚠⚠ Report what you measured, not what you expected

• Results that disagree with the prediction are the interesting ones, and explaining the disagreement is the scientific work. Treating it as a mistake to be hidden is backwards.
• ⚠⚠ Never adjust data toward the expected answer, and never quietly drop an inconvenient reading. In coursework it is academic misconduct; in professional practice it is research fraud, and it ends careers.
• Record what you actually did, including the mistakes and the deviations from the protocol. A method section that describes an idealised procedure nobody followed is not reproducible.
• Quantify uncertainty rather than describing it. "Within experimental error" means nothing without the error.
• Distinguish systematic from random discrepancy. A consistent offset points at calibration or a modelling assumption; scatter points at technique.
• Say what your data cannot tell you. Stating a limitation is a strength, and overclaiming is the failure that damages credibility fastest.
• ⚠ Correlation is not causation, and an observational result is not an experimental one — this is where most over-interpretation of biological and environmental data happens.
• Keep a legible notebook. Contemporaneous notes are the record; reconstructed ones are a story.

How Florida course levels affect transfer

The first digit of an SCNS number denotes the year of offering, not transferability. Courses at the 1000 and 2000 levels transfer transparently between Florida public institutions, and 3000 to 4000 is unproblematic since both are upper division. The boundary that actually matters is 2000 to 3000, where lower-division credit generally cannot satisfy an upper-division requirement.

STA4024 is 3 credits and approximately 45 contact hours, offered spring only at Daytona State.

Learn R or Python alongside it. The theory plus the tool is what makes this material employable.