Dr. Samir Orujov
ADA University - School of Business
Fall 2025
Define statistics and distinguish between descriptive and inferential statistics
Understand the relationship between populations, samples, and statistical inference
Classify studies as descriptive vs. inferential and observational vs. experimental
Master simple random, systematic, cluster, and stratified sampling techniques
Apply principles of control, randomization, and replication in experiments
Develop critical thinking skills for analyzing statistical information
Definition 1 (Plural): Facts or data, either numerical or nonnumerical, organized and summarized to provide useful information about a particular subject.
Definition 2 (Singular): The science of organizing and summarizing numerical or nonnumerical information.
Descriptive statistics consists of methods for organizing and summarizing information.
The Washington Senators played 153 games, winning 56 and losing 97. They finished seventh in the American League and were led in hitting by Bud Stewart (.279 average).
Key Point: This summarizes what actually happened - no predictions or inferences made.
Inferential statistics consists of methods for drawing and measuring the reliability of conclusions about a population based on information obtained from a sample.
The Gallup Poll predicted Truman would win only 44.5% of the vote and lose to Thomas Dewey. However, Truman actually won more than 49% and became president.
Key Point: Using sample data to make predictions about entire populations.
The collection of ALL individuals or items under consideration
That part of the population from which information is obtained
Researchers simply observe and take measurements
Data already exists
Can reveal: Association
Cannot establish: Causation
Researchers impose treatments and controls
Data created through intervention
Can reveal: Association
Can help establish: Causation
Researchers found 113 cases of prostate cancer among 22,000 men who had a vasectomy, compared to 70 cases per 22,000 among men who didn't have a vasectomy.
Result: About 60% elevated risk of prostate cancer for men with vasectomies.
Type: Observational Study
What it shows: Association between vasectomies and prostate cancer
What it cannot prove: That vasectomies cause prostate cancer
Why not: Other factors might influence both the decision to have a vasectomy and prostate cancer risk
4,753 women were randomly divided into two groups before conception. One group took daily multivitamins containing 0.8 mg of folic acid, the other received only trace elements.
Result: Major birth defects occurred in 13 per 1000 women taking folic acid vs. 23 per 1000 in the control group.
Type: Designed Experiment
What it shows: Association between folic acid and reduced birth defects
What it can suggest: Folic acid may cause reduction in birth defects
Why stronger evidence: Random assignment controlled for other factors
A simple random sample of size n from a population is a sample obtained in such a way that every collection of n members of the population has an equal chance of being selected.
Random numbers: 19223, 95034, 05756, 28713, 96409
Selected numbers: 19, 34, 05, 28, 09
Selected students: #5, #9, #19, #28, #34
Step 1: m = ⌊728/15⌋ = 48
Step 2: Randomly select k = 22
Step 3: Select students: 22, 70, 118, 166, 214, 262, ...
City divided into 947 blocks (clusters), each with 20 homes. To sample 300 homes:
Advantage: Reduced travel time for interviewers
| Method | How It Works | Advantages | Disadvantages |
|---|---|---|---|
| Simple Random | Every sample equally likely | Unbiased, straightforward | May be impractical for large populations |
| Systematic | Select every kth member | Easy to implement | Cyclical patterns can bias results |
| Cluster | Sample entire clusters | Cost-effective for scattered populations | Clusters may not represent population |
| Stratified | Sample from each stratum | Ensures representation of subgroups | Requires prior knowledge of strata |
Two or more treatments should be compared to isolate the effect of the variable of interest.
Experimental units should be randomly assigned to treatments to avoid selection bias.
Use sufficient experimental units to ensure reliable results and detect treatment differences.
The individual or item on which the experiment is performed
The characteristic measured or observed as the outcome
A variable whose effect on the response variable is of interest
The possible values of a factor
Each experimental condition (combination of factor levels)
The group receiving the experimental treatment
The group receiving a placebo or standard treatment
In a completely randomized design, all experimental units are assigned randomly among all treatments.
In a randomized block design, experimental units are assigned randomly among treatments separately within each block.
Advantage: Controls for gender differences that might affect driving distance
Scenario: A researcher wants to test whether a new teaching method improves student performance. She randomly assigns 200 students to either the new method or traditional method, then compares their test scores.
Questions to consider:
Answers:
The American Film Institute (AFI) conducted a poll of 1,500 film artists, critics, and historians, asking them to pick their 100 favorite films from a list of 400 films made between 1915 and 2005.
1. What is the population?
All film artists, critics, and historians who could potentially judge films
2. What is the sample?
The 1,500 individuals who participated in the poll
3. Is the study descriptive or inferential?
Could be either, depending on the statement made about the results
A researcher surveys 500 college students about their study habits and reports that 65% of surveyed students study more than 2 hours per day. This is an example of:
A pollster wants to survey voters in a city. She divides the city into neighborhoods, randomly selects 10 neighborhoods, and surveys ALL voters in those selected neighborhoods. This is:
Which of the following is NOT one of the three basic principles of experimental design?
What question are you trying to answer?
Apply appropriate statistical methods
Interpret results within the context of the study limitations
Just because two variables are related doesn't mean one causes the other.
Example: Ice cream sales and drowning deaths both increase in summer, but ice cream doesn't cause drowning.
When the sample doesn't represent the population of interest.
Example: Surveying only people with landlines in the age of cell phones.
Conclusions based on too few observations may not be reliable.
Rule of thumb: Larger samples generally provide more reliable results.
Understanding what statistics actually measure and their limitations.
Example: "Average" doesn't always represent typical values if there are extreme outliers.
Participants should understand the study's purpose, procedures, and potential risks before agreeing to participate.
Protect participant privacy and ensure data security. Aggregate data when possible to prevent identification.
Report results accurately, including limitations and potential biases. Don't cherry-pick favorable results.
Consider the potential impact of research on participants and society. Weigh benefits against risks.
A company reports "90% customer satisfaction" but only surveyed customers who made repeat purchases, ignoring dissatisfied customers who never returned.
Ethical issue: Misleading representation through biased sampling
Statistical thinking is essential for making informed decisions in all areas of life
Descriptive statistics summarize data; inferential statistics help us make predictions and decisions
The type of study (observational vs. experimental) determines what conclusions we can draw
Good sampling methods are essential for reliable statistical inference
Statistical practice requires integrity, honesty, and consideration of societal impact
In upcoming lectures, we'll dive deeper into:
Test your understanding of today's key concepts:
The Nature of Statistics - Complete
Ready for Advanced Statistical Methods
Complete textbook exercises 1.1-1.4
Find examples of statistics in current news
Review for upcoming data visualization lecture
Join the discussion forum for Q&A
Remember: Statistical literacy is not just about numbers - it's about making better decisions based on evidence!
Feel free to reach out during office hours or via email for any clarifications!
Office Hours: D312, by appointment
Email: sorujov@ada.edu.az