Exam 1 Flashcards
(62 cards)
Descriptive
-Descriptive Statistics Numbers that describe and summarize data
Ex: Unemployment rate in December 2024 was 4.1%
-Descriptive Statistics – “Just describing the data”
-Think of descriptive statistics as summarizing and organizing the information you already have. It doesn’t try to make predictions—just explains what’s in front of you.
-Example: You survey 100 students about their favorite ice cream flavor.
40 like chocolate
35 like vanilla
25 like strawberry
-That’s descriptive statistics! You’re just reporting what’s in the data.
- Other examples of descriptive stats:
The average test score in a class is 85.
The tallest player on a basketball team is 6’8”.
The most common car color in a parking lot is blue.
Inferential
-Inferential Statistics Make an inference from the data Infer from a sample what is going on with the population.
Ex. Political Polling
-Inferential Statistics – “Making guesses about a bigger group”
-Inferential statistics takes a small group (sample) and makes a prediction about a bigger group (population).
-Example: You survey 100 students at your school about their favorite ice cream flavor, and 40% say chocolate.
You then infer (or guess) that about 40% of all students in your school like chocolate, even though you didn’t ask everyone.
-Other examples of inferential stats:
A political poll surveys 1,000 voters and predicts that 55% of the whole country supports a candidate.
A researcher studies 50 patients and concludes that a new drug works for most people.
A scientist tests a few drops of ocean water and estimates how much pollution is in the entire ocean.
Descriptive vs. Inferential
The Key Difference
Descriptive Statistics = “Just the facts” (describing the data you collected).
Inferential Statistics = “Making an educated guess” (using a sample to predict something about a whole population).
Population vs. Sample
Population: Entire group you are interested in studying
Sample: Set of individuals selected from a population
Researchers analyze samples because studying an entire population is often impractical. The goal is to use inferential statistics to generalize findings from a sample to the full population.
Independent and Dependent variables
Independent variable (IV): manipulate
Dependent variable (DV): measure
Independent Variable (IV): The variable manipulated by the researcher (the cause).
Dependent Variable (DV): The outcome variable that is measured (the effect).
Example: A study tests the effect of sleep (IV) on test scores (DV).
Random Assignment
Assign participants to a group based on a random process Minimizes confounds Confound: extraneous variable that may influence the DV and explain the results
In an experiment, participants are randomly assigned to different conditions to ensure that groups are similar at the start.
helps reduce bias and increase the validity of research findings.
Random Sampling
Each member of the population has an equal chance of being in the sample Important for 2 reasons Estimate parameters of the population Confidence in the accuracy of your estimates
helps reduce bias and increase the validity of research findings.
Correlational Methods
Correlational designs are those that look at the relationships between two variables
Is your height related to your shoe size?
Variable: something that can be measured or counted
Laboratory Experiments
Examine causal relationships
Independent variable (IV): manipulate
Dependent variable (DV): measure
Variable
something that can be measured or
counted
measurement
The process of assigning numbers or categories to variables.
Scales of Measurement
Distinguish variables that have different
values
Four scales:
Nominal
Ordinal
Interval
Ratio
Nominal
Nominal Scale
What it is: Just names or labels for different groups.
Key idea: There’s no order or ranking.
Example: Sorting people by their favorite color (red, blue, green).
You can’t say one color is “more” than another: they’re just different.
Ordinal
What it is: Categories that do have an order.
Key idea: You can rank them (like 1st, 2nd, 3rd), but the difference between ranks isn’t always equal.
Example: A race where runners finish 1st, 2nd, and 3rd.
We know 1st is better than 2nd, but we don’t know how much better.
Interval
An interval scale is a way of measuring things where:
1️⃣ The difference between numbers is always the same (equal intervals).
2️⃣ There is NO true zero (zero doesn’t mean “nothing”).
3️⃣ You can add and subtract, but you can’t multiply or divide meaningfully.
Ex.1
Think of a Thermometer! 🌡️
Imagine a thermometer that shows temperature in Celsius or Fahrenheit:
The difference between 10°C and 20°C is the same as between 20°C and 30°C (equal steps ✅).
0°C doesn’t mean “no temperature”, it’s just another point on the scale (NO true zero ❌).
🔹 That’s why temperature in Celsius/Fahrenheit is an interval scale!
ex.2
✔️ IQ Scores – A person with 140 IQ isn’t “twice as smart” as someone with 70 IQ.
✔️ Years on a Calendar – The year 0 doesn’t mean “no time,” it’s just a point in history.
✔️ Shoe Sizes – The difference between size 7 and 8 is the same as between 10 and 11, but size 0 doesn’t mean “no shoe.”
Ratio
A ratio scale is a way of measuring things where:
1️⃣ The difference between numbers is always the same (equal steps).
2️⃣ There is a true zero (zero means “nothing” or “none of the thing”).
3️⃣ You can add, subtract, multiply, and divide (all math works!).
Think of a Measuring Tape! 📏
Imagine measuring height in centimeters:
The difference between 150 cm and 160 cm is the same as between 160 cm and 170 cm (equal steps ✅).
0 cm means “no height at all” (true zero ✅).
Someone who is 180 cm is literally twice as tall as someone who is 90 cm (multiplication makes sense ✅).
🔹 That’s why height is a ratio scale!
Operational Definition
Way to describe and define your variable in a clear and measurable manner
Example: Instead of defining “intelligence” abstractly, a researcher might operationally define it as a score on an IQ test.
Discrete Variables
1️⃣ Discrete Variables
🔹 Definition: Whole numbers; can be counted, but not divided into smaller meaningful parts.
🔹 Examples:
Number of students in a class (You can’t have 2.5 students!)
Number of pets (You can’t have 3.7 dogs.)
Number of cars in a parking lot
Continuous Variables
2️⃣ Continuous Variables
🔹 Definition: Can take any value within a range, including decimals and fractions.
🔹 Examples:
Height (Someone can be 170.5 cm tall.)
Weight (You can weigh 65.7 kg.)
Temperature (It can be 98.6°F.)
Discrete vs. Continuous variables
Discrete Whole numbers, counted People, pets, cars
Continuous Any value, measured Height, weight, temperature
Statistical Notation
X or Y variable
X: set of scores
N = number of scores in a population
n= number of scores in a sample
Σ (sigma) = Summation
μ (mu) = Population mean
M (or X̄) = Sample mean
σ (sigma) = Population standard deviation
s = Sample standard deviation
Summation
where x=[2,5,3,6].
E3x = (3×2)+(3×5)+(3×3)+(3×6)=6+15+9+18=48
Ex = 2+5+3+6=16
E(x-2) = (2−2)+(5−2)+(3−2)+(6−2)=0+3+1+4=8
Ex^2 = 2^2+5^2+3^2+6^2=4+25+9+36=74
where x=[2,5,3,6] and y=[1,4,2,3].
Exy = (2×1)+(5×4)+(3×2)+(6×3)=2+20+6+18=46
∑ 1/X = 1/2+1/5+1/3+1/6 =0.5+0.2+0.333+0.166=1.199
where A= [ 1 2 3]
[ 4 5 6]
∑ ∑ a = 1+2+3+4+5+6=21
Charts & Graphs:
simplify the organization and
presentation of data
Frequency Distribution Tables
A Frequency Distribution Table shows how often each value appears in a dataset.
🔹 The left column (X) lists the values (scores).
🔹 The right column (f) shows how many times each value appears.
✅ Used to: Organize data before making a graph.
