Stats Midterm

How to get the mean?

Sum of all scores ÷ sample size (N)

Whats the median and mode?

• median middle score

• mode = most common

• these are known as central tendency (including mean)

Define nominal, rank order, equal interval, discrete, and continuous variables?

• nominal: CATEGORIES with NO ORDER

  • eye colour, gender

• rank order: categories with an order but distance between levels is arbitrary

  • A, B , C (grades), 1ST, 2ND, 3RD (race)

• Equal interval: ORDERED values with EQUAL gaps in between

  • IQ test (never an absolute zero)

• Descrete: separate, COUNTABLE, WHOLE NUMBERS

  • # of people in a class

• Continuous: DECIMALS AND ABSOLUTE 0

  • weight, height, reaction time, temperature

How to get degrees of freedom?

N - 1

How to get deviation?

X - Mean

How to get variance

Sum of squares (SS) ÷ Degrees of freedom (DF)

How to get standard deviation?

√variance

How to get Z score?

X-M ÷ SD = Z score

→ or deviation ÷ standard deviation = Z score

How to get z cross product?

Z-score(X) multiplied by Z-score (Y)

How to get correlation from Z scores?

Sum of Z-score cross-products ÷ degrees of freedom

How do you get standard deviation if you only have deviation and z-score from one participants score

deviation ÷ Z-score = standard deviation

→ standard deviation can be used to find missing Z-scores if needed

How to get the Z-score back into raw data?

Mean + {Z-score x SD} = raw data

What are quartiles and IQR?

divide ordered set of scores into 3 quarters (Q1, Q2, Q3)

• IQR is the distance between q1 and q3

What is Q1, Q2, Q3?

Q1 = first quartile; 25% of scores fall below it

Q2 = second quartile; MEDIAN of total score, 50% fall below

Q3 = third quartile; 75% of scores fall below

→ you can think of Q1 and Q3 as a median for each quarter to represent it

How to determine IQR?

Q3 - Q1 = IQR

→ median of q3 - median of q1 = IQR

How to determine if they are outliers?

An outlier is any score that is far away from the rest of the scores

• 1.st: multiply IQR with 1.5

  • trick IQR + Half of itself

• 2.nd: Lower boundary (Q1) SUBTRACTION

  • Q1 - # from 1st step

• 3.rd: Upper boundary (Q3) ADDITION

  • Q3 + # from 1st step

• Any numbers smaller than lower boundary is an outlier

• Any numbers higher than upper boundary is an outlier

What is regression?

Way to predict one variable using another

• predictor: information we KNOW

• criterion: information we WANT to know

Define all variables of regression formula

Y = a + bx

• Y = predicted score/criterion

• a = intercept (Y score when x = 0)

• b = slope (How much Y changes when X increases)

• X = Predictor score (what we know)

Regression constant vs. regression coefficient

Regression constant = intercept (a)

Regression coefficient = slope (b)

What are residuals/errors and what is the main rule about them?

How far the predicted score is from the actual

• rule: the stronger the correlation (-1.00 or + 1.00) the less residual/error there is.

What is the equation for residual?

Actual score - Predicted = residual

What is proportional reduction in error? What is the rule?

Tells you the percentage of prediction in error that is REDUCED when using regression

→ the HIGHER the PRE percentage is the LESS error

• ex: 25% PRE = 25% of error is reduced

  • The stronger the correlation, the higher the PRE

What is the PRE formula?

r2 = PRE

• correlation x correlation = PRE

How to get total error

total error is the overall amount of error across ALL people you’re predicting

• square individual residuals

• sum of squared residuals = total amount of error

SStotal vs SSerror

SStotal = error before regression

SSerror = error remaining

→ Total - error = total error reduction

• idk if this is needed but just in case

Sampling distributions vs. regular distributions

Sampling = means of MULTIPLE different samples taken from the POPULATION

→ used to understand how sample averages vary

Regular = Set of scores from individual people in a group

What are the 3 rules of Sampling distributions?

1. Mean always stays the same

2. SD gets SMALLER as sample size INCREASES

3. variance gets SMALLER as sample size INCREASES

How to get SD of sample means?

Population SD ÷ √sample size = SD sample means

What does a negative, positive, and zero Z-score mean

• positive = above the mean

• negative = below

• zero = exactly the mean

How do we find the second Z-score (predicted) ?

Correlation x known z-score = predicted z-scroe

→ ALWAYS REFER TO THIS EQUATION NEVER GUESS

What is the predicted z-score if the correlation is 0?

the best predicted z-score is always going to be the average

formula for deterring slope and intercept

intercept = y - (slope multiplied by x)

slope = y2 - y1 ÷ x2 - x1