PSTAT 5LS – Intro to Data (Slide Set 1)

Course Logistics

• Welcome to PSTAT 5LS – Intro to Data (Slide Set 1, pp. 1–2)

• Today’s topic: Intro to Data

• Tomorrow (Wednesday): No lecture

• Thursday: continue Intro to Data

• Deadlines
  • Homework 1: Tuesday $\text{July 1, 11:59 PM}$
  • Homework 2: Friday $\text{July 4, 11:59 PM}$

• Office-hour schedule starts next week and is posted on Canvas
  • Instructor office hours: T & R, 2–3 PM (Zoom)

Core Questions for the Quarter (p. 3)

• How do we collect data that answer a research question?

• How do we summarize & display data so they can “tell their story”?

• What conclusions can legitimately be drawn from the data?

Working with Data (pp. 4–5)

• Real-world data are messy; course examples will be pre-cleaned “tidy” data.

• Three skill pillars introduced in this slide set:
  • Key terminology
  • Graphical displays that reveal structure
  • Numerical summaries that quantify insights

Hawks Data Set (pp. 6–8)

• Collected at a hawk blind near Lake MacBride, Iowa, by Cornell College students & faculty.

• Full data set >1000 hawks; we analyze a random sample of 50.

• Variables:
  • Year – year measured (quantitative)
  • BandNumber – ID band code (categorical, even though it looks numeric)
  • Species – CH (= Cooper’s), RT (= red-tailed), SS (= sharp-shinned) (categorical)
  • Wing – length of primary wing feather (mm) (quantitative)
  • Weight – body weight (g) (quantitative)
  • Culmen – upper-bill length (mm) (quantitative)
  • Hallux – killing-talon length (mm) (quantitative)
  • Tail – tail-length-related measure (mm) (quantitative)

• Data-table structure: one row = one hawk (individual, case, or observational unit); one column = one variable. Such rectangular structure makes it easy to add rows (new observations) or columns (new variables).

Types of Variables (pp. 9–12)

• Quantitative (numerical/measurement)
  • Values are numbers on which arithmetic makes sense (e.g., averages).
  • Ex: Year, Wing length, Weight, Culmen, Hallux, Tail.

• Categorical (qualitative)
  • Values are group labels; arithmetic is not meaningful.
  • Ex: Species, BandNumber.

• Converting quantitative → categorical
  • Possible by grouping continuous values into ranges (e.g., Age → Age Group 18–24, 25–34, etc.).
  • The reverse (categorical → quantitative) is not possible.
  • Numeric coding of categories (e.g., 1 = Yes, 2 = No) does not change variable type.

Exploring a Single Variable – Distributions (pp. 13–14)

• Distribution = values + how often they occur.

• Two complementary tools

  1. Graphical displays – show patterns, trends, outliers, and relationships.

  2. Numerical summaries – quantify center, spread, etc.

Graphing Categorical Variables (pp. 15–16)

• Bar Chart
  • Bars for each category; height = count or percentage.

• Pie Chart
  • Slice size = percentage of whole (must sum to $100\%$).

• Hawk-species example (sample $n=50$):
  • Cooper’s (CH) = 6, Red-tailed (RT) = 27, Sharp-shinned (SS) = 17
  • Either representation conveys relative frequencies.

Graphing Quantitative Variables (pp. 17–22)

• Dot Plot
  • Each observation = a dot on an axis.
  • Works best for small data sets and few unique values.
  • Demo: R’s $n=32$ mtcars dataset mpg values.

• Histogram
  • Breaks the numeric axis into bins/classes; bar height = frequency in bin.
  • Better for larger data sets and many unique values.

• Hawk-weight histogram (all species) reveals two main weight clusters → suggests two species share similar weight distribution, third species differs.

• Narrow focus: histogram of 69 Cooper’s hawks (full data set) used to practice interpretation.

Reading a Histogram (p. 23)

• Example questions asked of Cooper’s-hawks histogram:
  • “What % weigh $\le 200\text{ g}?$”
  • “What % weigh between $300$ and $600\text{ g}?$”
  ⇒ Estimate by comparing bar areas to total area (or counts to $n=69$).

Describing Shape (p. 24)

• Mode(s): number of peaks → unimodal, bimodal, multimodal.

• Symmetry:
  • Symmetric = mirror-image around mid-point.
  • Right-skewed (positive) = long right tail.
  • Left-skewed (negative) = long left tail.

Illustrative Shape Examples (pp. 25–26)

• Body Temperatures (n ≈ 1000): evaluate whether historic “$98.6^{\circ}\text{F}$” claim holds; histogram used to inspect center, spread, and potential outliers.

• Final Course Percentages for PSTAT 5LS (prior term): histogram demonstrates grade distribution; invites description (e.g., skew, modality, clustering).

Multimodal Distributions (pp. 27–29)

• Multiple peaks often signal hidden subgroups. Summarizing with a single mean/SD can be misleading.

• Golden retriever weights example (n=200)
  • Overall histogram is bimodal.
  • Separating into female vs. male produces two unimodal histograms.
  • Proper analysis requires stratifying by subgroup.

Outliers (pp. 30–31)

• Outliers = observations outside overall pattern.

• Never remove automatically—investigate first (data entry error? true unusual value?).

• Body-temperature histogram shows one reading $\approx 101.5{-}102^{\circ}\text{F}$.
  • Students are asked: Is that an outlier? Why/why not?

Center & Variability + Statistical Framework (pp. 32–35)

• Population = entire group of interest.

• Sample = subset actually measured.

• Parameter = numerical summary of a population.

• Statistic = numerical summary of a sample.

• Key principle: Sample statistics estimate population parameters.

Notation (p. 34)

• When writing results, always specify whether you report a statistic or a parameter and use correct symbol.

Practical & Ethical Implications (implicit throughout)

• Good data practice includes:
  • Ensuring representativeness of samples to support valid inference.
  • Being transparent about cleaning, transformations, and reasons for omitting data (e.g., outliers).
  • Choosing summaries appropriate to distribution shape (modalities, skewness) to avoid misleading conclusions.