final exam

Question 1

what do we use when we want to test if two variables are different from each other

Answer 1

two-way chi-square

Question 2

formula for chi-square

Answer 2

TOTAL OF (Observed - Expected)2 / Expected

Question 3

when you run the formula for X2 (chi-square) and you get the final number, what is that called

Answer 3

test statistic

Question 4

degrees of freedom for two-way chi-squared

Answer 4

(number of rows minus 1) * (number of columns – 1)

Question 5

what do you plug into R-Studio to check p-value for two way chi-square

Answer 5

pchisq(X2 , df = x , lower.tail = F)

then check if the p-value is greater or less than 0.05. If it’s lower, you reject the null hypothesis.

Question 6

What does “power” mean?

Answer 6

it’s the likelihood of finding a particular difference as statistically significant

Question 7

what variable are you trying to find in power analysis?

Answer 7

what is n (sample size) you need to reject the null hypothesis and the findings to be significant

Question 8

Why do you want to aim for ~ 80% for power?

Answer 8

you want a 80% probability of rejecting the null hypothesis with a 95% confidence

Question 9

when we want an area to be 80%, the z value that corresponds with that is

Answer 9

qnorm(0.8) = 0.84

Question 10

formula for SE

Answer 10

σ/n(squarerooted)
​

Question 11

what are we trying to minimize in power analysis?

Answer 11

Type II error (β): This error occurs when the test fails to reject the null hypothesis when it is actually false. To minimize this, we aim to decrease the overlap between the two distributions (the H0 and Ha curves)

Question 12

what are we trying to maximize through power analysis?

Answer 12

Distance between the null hypothesis and alternative hypothesis distributions

Maximizing the area of the alternative distribution that falls in the rejection region of the test (where we reject the null hypothesis) increases the chances of detecting a true effect.

Question 13

what does ANOVA stand for?

Answer 13

ANalysis Of VAriance

Question 14

What is ANOVA used for?

Answer 14

ANOVA is used to determine if a numeric variable differs across different groups

Question 15

What are the three assumptions for ANOVA?

Answer 15

The observations are independent within and across groups

The data within each group are nearly normal

The variability across the groups is about equal

Question 16

Hypothesis testing for two-way chi-squared and ANOVA – what null are they testing?

Answer 16

chi-square Ho = there is no meaningful difference between observation and expected value (from random chance)

ANOVA Ho = all group means are equal
𝜇_x=𝜇_y=𝜇_c

Question 17

when we reject the null hypothesis in ANOVA it doesn’t mean every mean is different from one another it just means

Answer 17

that there is at least one difference.

Question 18

Mean Squared Between Groups (MSG) in ANOVA

Answer 18

conceptually represents the amount of variation between groups (how much group means deviate from the overall mean).

If it’s high, there’s more of a difference. If it’s low, the group means are similar to the overall mean - the groups aren’t different.

Question 19

Mean Square Error (MSE) in ANOVA

Answer 19

measures how much the data points within each group deviate from their respective group mean. This is an estimate of the variance within the groups.

Question 20

how do you calculate test statistic (F-Value) in Anova?

Answer 20

F = MSG/MSE

Question 21

F distributions (ANOVA) take on two degrees of freedom, which are

Answer 21

DF1 = k – 1
DF2 = n - 1

Question 22

(ANOVA) on R studio, how do you calculate the mean and standard deviation for particular groups within the dataset?

Answer 22

dataset %>%
group_by(pos_group) %>%

Question 23

(ANOVA) on R studio, how do you create multiple histograms for the particular groups of the dataset?

Answer 23

facet_wrap(~pos_group)

Question 24

how do you do an ANOVA analysis on R-studio

Answer 24

anova <- aov( variable1 ~ pos_group, data = dataset)
summary(anova)

Question 25

how do you examine the structure of a dataset in R

Answer 25

str(dataset)

Question 26

how do you look at the number of observation in dataset

Answer 26

nrow(dataset)

Question 27

how do you look at the number of variables in dataset

Answer 27

ncol(dataset)

Question 28

how do you look at the mean of a specific variable but you want to eliminate the missing values?

Answer 28

mean(variable1, na.rm = T)

Question 29

Pearson’s R/Correlation

Answer 29

one number to describe a relationship in linear regression.

Ranges from -1 to a 1

Question 30

coefficient of determination

Answer 30

when you square the correlation coefficient (R). This represents how well the linear model
predicts the data, ranging from 0 to 1. (how much the variation in a variable is explained by another variable)

Question 31

what minimizes the RMSE (root mean square error) and what is that line called?

Answer 31

the mean of the different datapoints minimizes RMSE, and the line is called “best fit line”

Question 32

Why is it called OLS regression (ordinary least squares)?

Answer 32

because it finds the line with the least root mean squared error

Question 33

What are the four assumptions of linear regression?

Answer 33

Linearity – the data have a linear trend
Nearly normal residuals
Constant variability
Independent observations

Question 34

RMSE

Answer 34

a measure of how well a predictive model’s predictions match the actual data. It quantifies the average magnitude of the residuals

Question 35

how to create a scatter plot with a regression in R

Answer 35

ggplot(dataset, aes(x = independent, y = dependent)) + geom_point + geom_smooth (method = “lm”)

Question 36

how to construct an OLS regression model in R

Answer 36

lm(dependent ~ independent, data = dataset)

Question 37

when do you use chi-square, anova, and OLS regression

Answer 37

categorical - categorical = chi-square
independent variable is categorical and the dependent is numeric = ANOVA
numeric - numeric = OLS Regression

Question 38

High leverage

Answer 38

in regression analysis, a point with a very high or low value on the independent variable (X) is said to have “high leverage”

Question 39

Influential point

Answer 39

a data point that has an extreme value on both the independent (X) and dependent (Y) variables such that its inclusion meaningfully changes the regression line

Question 40

How do you deal with outliers? (3)

Answer 40

1. Check to make sure they are real and not data entry errors
2. Don’t automatically exclude them – sometimes outlies can hold important insights
3. be cautious about interpreting a relationship if it’s solely the product of an outlier

Question 41

How do Calculate RMSE

Answer 41

1. find the SE by summing up all the squared distances between each point
2. find the mean of the SE by sum of SE squared / # of points
3. find the root of this number by square rooting the mean

Question 42

Binary variables can take on exactly…

Answer 42

two values, 1 or 0
In R, TRUE or FALSE

Question 43

With binary variables, what’s the difference between when x = 0 and when x = 1

Answer 43

x = 0 : y = b or y = Bo
x = 1: y = mx + b or y = Bo + Bx

Question 44

what are the three criteria for causality again?

Answer 44

1. plausibility
2. time order
3. non-spuriousness

Question 45

Multiple regression

Answer 45

is a way of mathematically controlling for variables to eliminate spuriousness

Question 46

how would you make this regression equation to a multiple regression equation?

crime = Bo + B1 * icecream eating + E

Answer 46

crime = Bo + B1 * icecream eating + B2 * summer + E