PSYC 210 setting up for midterm

lectures 1-6

what are variables

variables can be anything that can take on more than one value

What is an independent variable (IV) and what is another name for it

it is also called a predictor

it is a variable that is manipulated

what is a dependent variable (DV) and what is another name for it

it is also called a response

its a variable that is measured

what is a Quasi-independent variable

it is a variable that cannot be manipulated (it already exists)

examples are age, gender, a preexisting medical condition, eye colour

what is an extraneous/confounding variable

it is a variable that we are not investigating but affecting the results

population vs sample

population is the total pool a sample is a few pieces from that pool

what is statistical inference

the formal process of using data from a small sample to make educated guesses or draw conclusions about a much larger population.

• Inferential statistics is the toolkit (the spoon, the recipe, the rules of tasting).

• Statistical inference is the actual act of tasting that one spoonful and declaring, "The whole pot needs more salt."

what is an experimental designs characteristics

manipulation, randomization, and comparison/control

what is an experimental design

a carefully planned test where a researcher changes one specific thing to see if it directly causes a change in something else.

example Imagine you invent an energy drink called RocketJuice and want to prove it causes people to run faster.

what is a quasi-experimental design

a research method that looks a lot like a true scientific experiment, but it lacks one crucial feature: random assignment it uses preexisting groups and use the information that is already there

what are the characteristics of a quasi-experimental design

includes a quasi-independent variable (cannot be manipulated) and/or (2) lacks a comparison/control group

what is a correlational design

looking at the relationship between two or more variables without any manipulation remember correlation does not equal causation

what is a notation

it is the way in which we symbolize aspects of data, such as variables, scores/measurements/values, etc.

• upper or lower case letters

• numerical subscript

• general index

what is “X“

it represents the variable

what is “i“

it represents the observation

what does X_{i mean}

it represents the variable for observation i

what does this image mean

find the sum of numbers between 0 and 2 so you start at 0 and stop at 2

what is rule 1 for summing a constant

number of times it appears multiplied by the constant

the key idea is to count how many times c appears, then multiply by c

what is a constant

it is a value that does not change

what is the rule for summing cX

cX is a constant multiplied by a variable

because the constant is constant and the variable can change for each operation you add the values of X then multiply by c

what is the distributive laws over addition and subtraction

for example if you have E(X_i + Y_i - c) you sum the X’s + sum the Y’s - sum the constant

summation CAN distribute over + and -

what is the non distributive laws over multiplication and division

sum of products does not equal product of sums for example product of sums is E(X_i x Y_i) which multiplying the the products and adding it with the other observation and product of sums is (E X_i)(E Y_i) which is adding the products and multiplying the result between the observations

what is descriptive statistics

the branch of statistics that simply summarizes, organizes, and describes the data you already have

example if you have soup and you take a spoonful You aren't guessing about the rest of the pot; you are just saying, "This spoonful has three carrots, two peas, and is 60 degrees Celsius.descriptive statistics is just describing exactly what is on your spoon.

what is inferential statistics

a branch of statistics that uses data from a small, random sample to make predictions, test claims, or draw conclusions about a much larger [population]

example: Imagine you are cooking a massive pot of soup for a party. You cannot drink the entire pot just to find out if it needs more salt. Instead, you use a small spoon to taste one sip.

what is the difference between data and raw score

Data is a broad collection of information or facts, while a raw score is a single, specific, and unaltered measurement from that collection

by definition how is sample related to population

a smaller, manageable subset drawn from a larger population

what are three commonly used research methods in behavioural science

experimental research, observational studies, and survey research

how do you find the median

line all numbers up from lowest to highest and find the number exactly in the center of the number line if there are two then you find the mean of those two numbers

how do you find the mode

you look for the number that shows up the most in the sequence it helps to line them up

how do you find the mean/average

you add all the numbers up and divide by the number of numbers

how do you find the range

you find the lowest number in the set and you subtract it from the largest number in the set

what is PEDMAS/BEDMAS

it is the order of operations: Parentheses/Brackets → Exponents →

Division/Multiplication → Addition/Subtraction

why is it important to follow order of operations

if you do not follow them and you mess up the order that calculations are meant to be done in the results will be off

meaning of square brackets

Also group things together, especially when parentheses are already being used.

• Example: 2[3 + (4 × 2)]

• They help make complicated expressions easier to read.

meaning of parentheses

Group things together

• Example: 3(2 + 4) = 18

• Means: calculate 2 + 4 first.

meaning of line brackets

Absolute value

• Example: |-7| = 7

• Means the distance from 0, so the answer is always positive or zero.

what does this mean x > y

x is greater than y

what does this mean x < y

y is greater than x

when working with fractions explain how to add and subtract

what does a negative times a positive produce

negative

what does a negative times a negative produce

positive

what does 3^{2 mean}

3×3

what does the √9 mean

what times itself is equal to 9

what does Σ mean

add together

what is another name for Σ

sigma

what does index mean and what is the symbol for it

the symbol is “i“ and it is the position/number of a particular observation in a dataset.

what is something to be cautious about with summation notation

Sometimes the answer might be ambiguous! For instance:

there can be multiple interpretations example:

∑( xⁱ+ 2) = 3 + 7 + 12 = 22

(∑ xⁱ) + 2 = (1 + 5 + 10) + 2 = 16 + 2 = 18

In both scenarios, parentheses are implied but the equation on the bottom would

generally be considered “more” correct.

The take away: Always include parentheses to avoid confusion!

what do levels or scales of measurement refer to

The Levels or Scales of Measurement refer to the relationships between what is

being measured and the numerical values we use to represent it.

Broadly speaking, variables are either categorical or continuous.

what are categorical and discrete variable and what are they made up of

Categorical or discrete variables are made up of categories. The simplest form has only

2 levels (e.g., Do you live on campus? Do you own a waffle maker?) and are called binary

variables.

There are two levels of categorical variables:

Nominal Variables: name distinct entities

There is no order to the levels of a nominal variable - one is not necessarily better

or ‘bigger’ than another just different.

e.g., favorite type of animal or genre of show, political affiliation.

what is a bar chart

discrete; non-touching bars (grouped/ungrouped)

what is a histogram

continuous; touching bars (grouped/ungrouped)

what are frequency polygons

uses points and lines instead of bars

what is something to note sum of products and product of sums

sum of products does not equal product of sums

what is something to note for sum of quotients and quotient of sums

sum of quotients does not equal quotient of sums

what does sum of products look like

∑(X_i xY_i ) → (1×3) + (2×4)

(1×3) is observation 1

(2×4) is observation2

what does product of sums look like

(∑ X_i) (∑ Y_i) → (1+2)(3+4)

(1+2) is all of x

(3+4) is all of y

what are the methods for Psychology + Statistics

1. psychological concepts

2. measure and describe

3. identify patterns

4. make informed predictions

5. understand - communicate - intervene

what is the point of variables

• psychology studies concepts that are often abstract

• Variables make these concepts observable or measurable

• Variable must be able to take on different values

Examples:

Stress • Anxiety • Memory • Age • Treatment condition

what is an example for the Operationalization of Variables

Concept: Stress

How can we measure it?

• Questionnaire score: 0–40

• Stressful events: 0, 1, 2, 3...

• Categories: Low / Moderate / High

Same concept ≠ same variable

Define it clearly → Measure it consistently

what is a discrete variable

what is a continuous variable

what is NOIR

Nominal

Ordinal

Interval

Ratio

explain nominal

name

Categories with NO meaningful order

Examples:

Eye colour: Brown / Blue / Green

Condition: Control / Treatment

Numbers can be labels:

Control = 0, Treatment = 1

1 does NOT mean “more” than 0

explain ordinal

= Order

• Categories WITH a meaningful order

Examples:

Grades: A > B > C > D

Satisfaction: Low < Moderate < High

But: distance between categories is

not necessarily equal

explain interval

Equal Distance

Equal differences between values are meaningful

Example: Celsius temperature

10°C → 20°C = +10°C

20°C → 30°C = +10°C

• the + 10 represents the same level of change

But 0 is arbitrary

20°C ≠ “twice as hot” as 10°C

• “0” isnt an absence of a thing its just a point on the number line ex: 0^o is still a temp

explain ratio

= Equal Distance + True Zero

Examples: Age • Height • Weight • Reaction time

0 = absence of the quantity

→ Meaningful to describe ratios

which NOIR variables are discrete

Nominal and Ordinal

which NOIR variables are continuous

Interval and ratio

what are the three scales of measurement used to characterized by

order, difference, and ratio

what are the three ways of describing data and summarizing empirical distributions

1. Tables - Organize values and frequencies

2. Graphs - Show patterns visually

3. Descriptive statistics - Summarize data with numbers

Same data → Different ways of describing it

what does frequency =

how often something occurs

what is ungrouped frequency

- Keep each value/category separate

Example: Relationship status

Best when: Few values or categories

what is grouped frequency

Combine values into ranges

Example: Test scores

Best when: Many possible values

what is the purpose of the levels of measurement

the relationship between the variables and the number we use to measure it

what is the formula for proportion

also written as P = f/n

what is the formula for percentage

also written as %= f/n x 100

what does cumulative frequency (cf) mean

the frequency of the current and lesser values

example : how many values are at that value and lower

what is cumulative relative frequency (CRF)/ Percentile Rank

CRF = cf/N x100

what does f mean on a table

how many observations in that group

what does f_R mean on a table

the ratio between 0 and 1

what does f_% mean on a table

percentage of that frequency

what do you do when you see f_c on a table

you add the add the numbers together by row so for example if the row looked like

4

7

5

in the f column

the f_c column would look like

4

4+7= 11

4+7+5=16

what do you do for the CRF section on a table

you multiply the f_r by 100

what are apparent limits

- The values written for each interval

0–4 | 5–9 | 10–14

the left side is the lower limit and the right side is the upper limit

what are real limits

- The actual boundaries separating intervals

−0.5 to 4.5 | 4.5 to 9.5 | 9.5 to 14.5

how do you find the mid points

you take the lower limit and the upper limit and add them together and divide by 2 to get the midpoints

what is a bar graph best for what does it show and list a key feature

Discrete / categorical data

Frequency of each category

Bars are separated

what is a histogram best for what does it show and list a key feature

Continuous numerical data

Frequency across values or intervals

Bars touch

what is a frequency polygon best for what does it show and list a key feature

Continuous numerical data

Shape of a distribution

Midpoints connected by lines

why is it important to select a proper graph

Choosing a graph depends on how the variable is represented

Continuous data can sometimes be converted into categories:

Age: 18, 19, 20, 21... → Histogram

Age groups: 18–24, 25–34, 35–44... → Bar graph

But: Converting continuous data into categories loses info

State the four scales of measurement. Which scale of measurement is the most informative?

Nominal Ordinal Interval Ratio

Ratio is the most informative b/c it adds a true zero plus all of the properties of NOIR

Can a nominal variable be numeric? Explain.

yes- numbers can be used as category labels for example 0= control 1=treatment

the numbers do not represent quantity or rank

A study is conducted to test whether rewarding children in a cheer camp intermittently (4

times during the camp) or once at the end of the camp differentially bolsters how much they

enjoy cheering.

1. Identify the independent and dependent variable in this study.

2. What is the scale of measurement of the independent variable?

1. independent - rewarding intermittently or at the end

dependent - how much they enjoy cheering

2. Nominal - the two rewards continue with no numerical ranking

Rank the scales of measurement in order from least informative to most informative.

1. Nominal

2. Ordinal

3. Interval

4. Ratio

what are the measures of central tendency

mode median and mean/average

what is x̄

sample mean

what is μ

population mean

why do we use a weighted mean

is used when some numbers in your data are more important or happen more often than others.

why do we need the median

The median is not drawn out by outliers or extreme scores.

why do we need the mode

it is not affected by scale so it can be used with discrete/categorical scales