DAPR 1 sem

categorical data types

nominal, ordinal and binary

numeric data types

interval or ratio, continuous, discrete(count)

what is categorical data

variables with a discrete number of response options (usually written answer)

what is numeric data

variables which can take any real number value within the specified range of measurement (eg height in cm)

what is count data

variables which can only take non-negative integer values (0,1,2,3)

what are the four levels of measurement

nominal, ordinal, interval and ratio

what is nominal data

binary or categorical variable where the numerical markers share no relationship. no meaningful order. eg 1= brown 2= blonde, this doesnt suggest brown is better than blonde

what is ordinal data

binary or categorical variable where there is a meaningful way to rank order responses. you can say one is greater than the other, however cannot meaningfullt quantify the differences. eg - likert scale (agree, strongly agree)

what is interval data

variables where the numerical value have meaning but there is no true 0 point, can consider differences. eg - IQ

what is ratio data

variables where the numerical value have meaning and there is a true 0 point, can multiply and divide variables and legitimately talk about double X. eg - degrees kelvin.

data types key in R

what is frequency distribution

a plot showing the number of instances of each value of a variable

what are bar plots used for

used to show frequency distributions of categorical variables. x axis - values of variable. y axis - frequency

what is the central tendency

a set of statistics that describe the central point of frequency distributions. typically known as averages

what is dispersion

a set of statistics that describe the variation of frequency distributions

what central tendency and variability to use for nominal data

mode and relative frequency

what central tendency and variability to use for ordinal data

mode or median and range or inter-quartile range

what does a frequency table show

possible outcomes and count of number of observations per outcome

what is mode

mode is the most commonly observed value in the data set

what is median

the value for which half the data falls above and half below the given value. to calculate - rank order the data, find middle value

what is range

the value between two points, max-min

inter-quartile range (IQR)

the difference between first and third quartile. steps - rank data, split into four equal clocks, iqr is diff between 25% and 75%

what data is a histogram used for

continuous data

how to label x and y axis of histogram

x - possible values of a variable (height) y - frequency of a given value occurring

what are bins in a histogram

the number of columns

what is the optimal measure for continuous data

mean (sum of all values, divided by total number of observations)

what is the sum of deviations and what will it always equal

the amount each observation differs from the mean, will always be 0 and positives and negatives cancel eachother out

what is variance

the average squared deviation from the mean. σ(^2)

what is standard deviation

the square root of the variance

what central tendency do you use for categorical (nominal) data?

mode (+frequency table)

what central tendency do you use for categorical (ordered) data?

mode or median (+range)

what central tendency do you use for continuous data?

mean (+variance and sd)

what central tendency do you use for count data?

mode (+range so variance and standard deviation)

skew

measure of the asymmetry of a distribution

kurtosis

measure of the flatness of the peak, and fatness of tails of the distribution

what is a dependent variable?

the thing we want to predict, referred to as the outcome, and y in stats

what is an independent variable?

the things we hypothesize to influence the dependent variable, the explantory varible, and x in stats

what is a covariate?

things that will influence the outcome but we may not have a hypothesis about, also known as nuisance variables we try to control them to minimise their effect

when trying to describe two categorical variables what do we use?

contingency table

what does a contingency table show?

shows the frequency of one level within levels of the other

what do we use mosaic plot for?

to visualize a contingency table (categorical-categorical data)

how do we examine relationship between categorical and continuous data?

we look at stats (mean, sd, distribution shape) of the continuous variable at each level of categorical variable

what does group_by do

splits the data by the categorical variable data

what does facet_wrap do?

produces a plot per value of the variable given

how do we visualise continous-continous data?

scatterplots

scatterplot going from left to top right?

positive relationship

scatterplot going from top left to bottom right?

negative relationship

what is covariance?

the numerical value that represents the degree to which variables vary in the same way.

what does a function do?

takes an input, does something, provides an output

what does a linear function look like when plotted?

straight line

what do non-linear functions contain?

powers or roots

what are the uses of functions?

for data transformations and describing formal models

what is standardising?

putting all variables into the same scale to compare them

what is a standardised variable referred to as?

z-score

eg of standard way to interpret z score?

if z score is 1.2 this means respondent is 1.2 SD above the mean

what is the purpose of probability?

to help make inferences about the truth of the world from data we have

what is probability?

the likelihood of an events occurrence

probability formula

P(X) = (a)/(a+b) where a = ways event x can occur and b = ways event x can fail to occur

what is a set?

a well-defined collection of objects, composed of elements

what does x ∈ A mean

x is an element of set A

what does x ∉ A mean

x is not an element of set A

what does B ⊆ A mean

B is a subset of A

what does B ⊂ A mean

B is a proper subset of A (at least one element of A is not a member of B)

what does A ⊄ B mean

A is not a subset of B

in probability, what is a union?

an object is a member of either set A or B A⋃B

in probability, what is an intersection

an object is a member of set A and set B A⋂B

in probability, what is difference

when an object is a member of set A but not set B A-B

in probability, what is an empty set

when set A and B are mutually exclusive, when A occurs B cannot occur A⋂B = ∅

what is sample space

all the possible outcomes of a random experiment

what is the compliment of set A

the probability of not A

mutually exclusive events

if A occurs B cannot occur

independent events

the occurance of A does not impact B

dependent events

the occurance of event A does impact B, therefore changing the probability of event B

sampling with replacement

replacing the item sampled so that sample number stays the same

sampling without replacement

not replacing used sample meaning number of sample gradually decreases

conditional probability

probability of B given A p(B|A)

three features of statistical experiment

more than one possible outcome, outcomes specified in advance, each outcome has probability

random experiment

sampling simple events from a sample space, to produce an outcome

random variable

set of values that quantify the outcome of the random experiment

discrete random variable

can assume only a finite number of values

continuous random variable

arbritarily precise, can take all infinite values in a range

cumulative distribution function

provides an easy way to see the total probability of all values before or after a given point

continuous probability distribution

a random variable that produces a continuous set of outcomes

when is the probability density function used (PDF)

when describing continuous probability distributions

what is the mean and SD in a standard normal distribution

mean  μ=0 and SD σ=1

what happens when you adjust μ (mean) in the probability density function (PDF)

the curve shifts left or right

what happens when you adjust σ (SD) in the probability density function (PDF)

the curve changes shape

where should 68% of the area of a normal distribution fall

1 SD either side of mean

where should 95% of the area of a normal distribution fall

2 SD either side of the mean

where should 99.75% of the area of a normal distribution fall

3 SD either side of the mean

what does a z score do?

standardise the values of x

what is the z score formula?

Z=(x−μ)/σ

numerator - converts x to deviations from mean

denominator - scales values based on spread in data (SD)

difference from standard normal and t distribution

standard normal - uses σ which is actual population value, t - uses sd which is an estimate

curve difference - tails of t are higher due to variability/uncertainty from sd estimate

what is a population

a group of people whom youd like to make inferences abouts

sample

a subset from the population whom you will collect data on to make inferences

what is a population parameter

a measure that describes the entire population

what is a sample parameter

a proportion of our sample which have identified characteristics

what is sampling distribution

a probability distribution of some statistic obtained from repeatedly sampling the population

what is a benefit of having a large sample

our estimates from those samples are likely to be closer to the population value

what is the formula for standard error (SE)

### **SE=(σ)/√N**