Quantative methods

Variable

Something that can be measured or manipulated

Dependent variable

What is measured (the outcome) (The y axis)

Independent variable

What is changed (predictor variable) (The x axis)

Ordinal

Measured on a scale

Continuous

Measured with numbers

Model

Simplified representation of a system

Frequency distribution (empirical)

Associates each possible outcome with a frequency value

Uniform distribution (theoretical)

Probability is uniformly spread across all atcomes

Normal distribution

Aka the bell curve OR the Gaussian distribution - for continuous data, symmetrical around the mean.

Standard deviation

Quantifies degree of dispersion

Parameters (normal distribution)

The mean and standard deviation, it is a property of a distribution

Mode

Most frequently occurring value, peak value in frequency distribution.

Median

Value in the middle. If in even number it is the mean of the two middle numbers. It is a theoretical value.

Mean

Sum of all the values divided by the number of values.

Bimodal graph

Has 2 modes, median and mode are within them

Kurtosis

Fancy word for now spiky the distribution is, the higher the spike, the more the mean will fit.

Bar plot

X is categorical, Y is categorical

Box plot

X is categorical, y is numerical

Scatterplot

X is numerical, y is numerical

Conditional means

Means that shift depending on what valve some other piece of data assumes

Bivariate statistics

Describing the relationship between 2 variables

Regression line

Represents the average which is the relationship between the x and y axis

Slopes

The change in y over the change in x

Intercepts

The point where the line starts on the y-axis

Coefficients of the regression model

Slope and the intercept

Fitted value

A prediction of a different value by fitting a regression model onto a dataset.

Residuals

Represent information that is left over after removing the effect of explanatory variables. (Represented by the e at the end of the regression equation to show error)

Observed values =

Fitted values plus residuals

Null model

Residuals are from the mean of the dependent variable.

Residuals

The difference between a plot of data and the coefficient.

SSE

Squared sum of error

R squared

1- SSE model / SSE null

What does r squared show?

Closer to 1, there is less error, closer to 0, lots of error

Residual formula

Observed value - fitted value

Correlation

Not equal to causation- but variables do have a relationship

Positive correlation

Relationship is linear and is going up

Negative correlation

Relationship is going downwards

Persons R

A number that tells you how strongly correlated results are

What does Pearson R show?

Goes from 1 to 1, negative correlation is minus and vice versa close to zero - not much correlation

Centering

Linear transformation, center a predictor variable by subtracting the mean of it from each datapoint

Z -score

A value that has been transformed to a unit that quantifies how far it is from the mean (during centering)

Linear transformation

Changing all the numbers, values aren't changed

Log-transformation

The power to which a base most be raised to yield a given number - logarithms need bases

Non-linear transformations

Large numbers are affected more than small ones

Log e

2.72

R: mutate ()

Computes all linear transformations and makes another column for the Z -scores

Log transformations in r

Log ()

R: manually adding slope and intercept

Geom_abline(aes(intercept = x, slope = x))