Theory

Question 1

What is nominal data?

Answer 1

Assigns observations to unordered categories. Examples include hair colour, political party etc. They can be graphed with a pie or bar chart (being discrete) and summarised with number/percentages

Question 2

What is ordinal data?

Answer 2

Assigns observations to ordered categories. Examples include level of education, meaningfullness categories etc. They can be graphed with a pie or bar chart (being discrete) and summarised with number/percentages

Question 3

What is interval/ratio data?

Answer 3

Assigns scores on a scale with quantitative information, with outcomes of calculations being sensible. Ratio scale also has a true meaningful zero-point. Examples include reaction time, IQ scores etc. They can be graphed with a histogram and boxplot and summarised with a 5 number summary and mean+stdev

Question 4

What are the special features of mode?

Answer 4

It is not sensitive to outliers, making it a resistant measure. There can also be multiple modes in a data set

Question 5

What are the special features of median?

Answer 5

It is a resistant measure

Question 6

What are the special features of mean?

Answer 6

It is not a resistant measure

Question 7

What are the special features of range?

Answer 7

it is not a resistant measure

Question 8

What are the special features of variance?

Answer 8

It is not a resistant measure and it is often expressed in the square of the unit of the variable (ie. cm^2)

Question 9

What are the special features for standard deviation?

Answer 9

It is not a resistant measure and is expressed in the same unit as the variable

Question 10

What is the 1.5 x IQR rule?

Answer 10

If a value is higher than 1.5 x IQR + Q3 or lower than 1.5 x IQR - Q, the value is an outlier

Question 11

What are some characteristics of a density curve?

Answer 11

1. The curve is always above the horizontal axis
2. The total area under the curve is equal to 1
3. The area under the curve and above any range of values is the proportion of all observations that fall in that range

Question 12

When does the empirical rule apply?

Answer 12

When the distribution is normal

Question 13

What is the z-score?

Answer 13

The number of stdevs that an observation is from the mean

Question 14

What is a correlation as a measure?

Answer 14

It is a measure that indicates how strong a linear relationship is between 2 quantitative variables. It is sensitive to outliers.

Question 15

Why is it always beneficial to create a scatterplot before calculating a correlation?

Answer 15

To check whether the association is linear and whether there are outliers present in the data set.

Question 16

What is an independent variable?

Answer 16

A variable that explains or causes changes in the response variable

Question 17

What is a dependent variable?

Answer 17

A variable for which a predication is made

Question 18

What is a regression line?

Answer 18

A straight line in a scatterplot that is as close as possible to the points in the graph

Question 19

What is the meaning of the slope and intercept in a regression line?

Answer 19

Slope is the amount by which y changes when x increases by 1 unit
Intercept is the value of predicted y when x = 0

Question 20

What is a residual and what is its correct notation?

Answer 20

The difference between the observed score yi and the predicted score y(hat)i that reflects the “error” you make in the prediction of observation i:

yi - y(hat)i

Question 21

What is the principle of ordinary least squares regression?

Answer 21

The best line is the line with the smallest sum of the squared residuals (vertical distances from the points to the regression line):

min∑(yi - y(hat)i)^2

Question 22

What is the meaning of correlation coefficient in relation to the regression line?

Answer 22

A measure of the linear association between x and y which indicates how well the point in a scatterplot follows the straight line.

Question 23

How can you use R^2 to examine the fit of the regression model?

Answer 23

The square of the correlation determines the percentage of variance in y that is explained by changes in x (percentage explained variance). The higher this percentage, the better prediction of y

Question 24

What is a residual plot and how can you use it to investigate the fit of the regression model?

Answer 24

A graphical representation (scatterplot) of the residuals with on x-axis, the value of the independent variabel x, and on the y-axis, the value of the residuals. In case of a good model fit, the residuals are small and have a value around 0; in case of perfect model fit, all residuals are equal to 0

Question 25

What is an outlier?

Answer 25

It is a value that appears to be unusually large or small, compared to the rest of the data

Question 26

What is an influential observation?

Answer 26

An observation that affects the results of the statistical outcomes considerably, with its removal resulting in considerable differences in the outcomes.

Question 27

What is a lurking variable?

Answer 27

A variable that is not among the explanatory or response variables in a study and yet may influence the interpretation of relationships among those variables.

Question 28

What is a prediction model?

Answer 28

The equation of the regression line that is used to predict scores on a dependent variable y based on a score on an independent variable x: y(hat) = a + bx

Question 29

What is Simpson's paradox?

Answer 29

A situation in which a trend or relationship is observed between different groups, which disappears when the groups are combined. Depending on how the groups are combined, the conclusion is different and sometimes even the opposite.

Question 30

What are the similarities and differences between covariance and correlation coefficient?

Answer 30

They are both measures that indicate how strong two variables are linearly associated. However, covariance can be all values between -infinity to infinity as it is not standardised

Question 31

What is a monotonic graph?

Answer 31

One where as a value increases, its next value should increase.

Question 32

What are disjoint events?

Answer 32

Two events A and B are disjoint if they have no joint outcomes and can never happen at the same time

Question 33

What are independent events?

Answer 33

Two events A and B are independent if the knowledge about A's performance does not say anything about the probability of performance B

Question 34

What are independent trials?

Answer 34

Two (or more) draws (of a random phenomenon) are independent if the outcome of one draw is not affected by the outcome of another draw

Question 35

What is the Central Limit Theorem?

Answer 35

If X has a normal distribution, the sampling distribution of the sample mean will also have a normal distribution. If X has a population mean and population standard deviation, the sampling distribution of the sample mean has an approximate normal distribution.

Question 36

When is binomial probability addressed?

Answer 36

When there are a fixed number of observations that are independent, fall into either success or failure and if the probability if a success is the same for each observation