Stats and Probability

Question 1

What is Data that can be named called?

Answer 1

Categorical Nominal.

Question 2

What is Data that can be put in an order called?

Answer 2

Categorical Ordinal.

Question 3

What is Data that increases at set intervals called?

Answer 3

Discrete Numerical.

Question 4

What is Data that can be measured to any degree of accuracy called?

Answer 4

Continuous Numerical.

Question 5

What is Systematic Sampling?

Answer 5

Each member of the population is numbered, and a system is used to draw the sample.

Question 6

What is Stratified Sampling?

Answer 6

The population is organized based on known characteristics and samples drawn from sub-groups.

Question 7

What is Cluster Sampling?

Answer 7

Where the population is already organized into groups and areas.

Question 8

What is Non-Random Sampling?

Answer 8

May include advertising for volunteers or using an opportunity sample.

Question 9

How to load a dataset on RStudio -

Answer 9

Session > Set Working Directory > Choose Directory.

Question 10

How to calculate proportions-

Answer 10

prop.table(table(X))
(to display this as a percentage, *100)

Question 10

What to do when you are finished with a dataset-

Answer 10

detach(name)

Question 11

How to produce a pie chart for (categorical) data -

Answer 11

pie(table(X), main=”Title”)

Question 12

How to produce a bar chart for (categorical) data -

Answer 12

barplot(table(X), main=”Title”, xlab=”Categories”, ylab=”Frequency”)

Question 13

How to produce scatter plot for (numerical) data -

Answer 13

plot(X-bottom, Y-side, main= “X and Y”)

Question 14

How to produce histogram for (numerical) data -

Answer 14

hist(X)

Question 15

How to produce box plot for (numerical) data -

Answer 15

boxplot(Y,X, main=”Y and X”, horizontal=TRUE, names=c(“Y”,”X”))

Question 16

What does a box plot tell us?

Answer 16

• The box shows the interquartile range (IQR) – the middle 50% of the data (from Q1 to Q3).
• The line inside the box shows the median.
• The whiskers extend from the box to the minimum and maximum values (excluding outliers).

Question 17

Data Distribution skewed to the right-

Answer 17

Positive Skew - Most of the data values are clustered toward the lower end (left side), and a few larger values (high outliers) pull the tail to the right.

Question 18

Data Distribution skewed to the left-

Answer 18

Negative Skew - Most of the data values are clustered toward the higher end (right side), and a few smaller values (low outliers) pull the tail to the left.

Question 19

Correlation Coefficient Test-

Answer 19

cor.test(X,Y)

Question 20

Strong Negative Linear Relationship -

Answer 20

A correlation coefficient between -0.75 and -1 is a strong negative relationship.

Question 21

Strong Positive Linear Relationship -

Answer 21

A correlation coefficient between 0.75 and 1 is a strong positive relationship.

Question 22

Moderate Negative Linear Relationship -

Answer 22

Values between -0.3 and -0.75 are considered a moderate negative relationship

Question 23

Moderate Positive Linear Relationship -

Answer 23

Values between 0.3 and 0.75 are considered a moderate positive relationship.

Question 24

No Linear Relationship -

Answer 24

Values close to zero (between -0.3 and 0.3) indicate that there is no relationship between variable X and Y.

Question 25

Line of Best Fit -

Answer 25

lm(Y~X) write the line of best fit as Y=X(x) - Intercept

Question 26

Applying the Line of Best Fit -

Answer 26

abline(lm(Y~X))

Question 27

Null Hypothesis-

Answer 27

The null hypothesis (H₀) is a statement that there is no effect, no difference, or no relationship between variables. It represents the idea you’re testing against.

Question 28

Alternative Hypothesis-

Answer 28

The alternative hypothesis (H₁) is a statement in statistics that contradicts the null hypothesis (H₀). It proposes that there is a real effect, a difference, or a relationship between variables.

Question 29

p-value -

Answer 29

If the p-value is less than 0.05, we can reject the null hypothesis, thus the results are statistically significant.

Question 30

95% confidence interval -

Answer 30

Tells us with 95% certainty that the 'true' difference between the means lies between the given confidence intervals. If it does not include a 0, there is a less than 5% probability that the difference between the samples is 0. This confirms that the result is statistically significant.

Question 31

t-test -

Answer 31

t.test(X,Y) Used to compare numerical data that is normally distributed.

Question 32

Paired t-test -

Answer 32

t.test(paired="TRUE") Used when there is meaningful pairing between numerical data samples.

Question 33

z-test -

Answer 33

prop.test(x=c(a,b), n=c(n1,n2)) Used to compare categorical data. The 'prop 1', and 'prop 2' can be used to compare percentages between the two samples.

Question 34

type 1 error -

Answer 34

Known as a false positive. This occurs when results appear to be significant, but in fact there is no real difference.

Question 35

type 2 error -

Answer 35

Known as a false negative. There is a real difference, but the statistical test did not reflect on this.