descriptive statistics

data

Facts and statistics collected together for reference or analysis

data set

all the data collected in a particular study

Types of Measurement Scales

1. Nominal

2. Ordinal

3. Interval

4. Ratio

nominal

no 'favourite' option (better than), No ordering

nominal variable type

Discrete (i.e., categorical)

nominal examples

university you attend, favourite colour

Ordinal

Non-consistent ordering, doesnt require consistency between each scale points (1st and 2nd place may be decided by a minute, 15th and 16th maybe 3 seconds)

ordinal variable type

Discrete or Continuous

ordinal example

rank in army, race position, school grade (C+)

Interval

Consistent ordering, no true zero

interval variable type

Discrete or Continuous

interval example

degrees Celsius, time of day, ATAR

Ratio

Consistent ordering, true zero

ratio variable type

Discrete or Continuous

ratio example

degrees Kelvin, height, reaction time (ms)

statistics

Numerical statements about data from a sample, and the scientific discipline associated with making and understanding those statements; used to communicate important information about our data

descriptive statistics

statistics that describe the characteristics of our sample

measures of central tendency

mean, median, mode; describe the "typical" score / data-point from our sample

mode

the most frequently occurring score(s) in a distribution

median

the middle score in a distribution; half the scores are above it and half are below it

how to calculate the median

Put all the numbers in numerical order.

If there is an odd number of results, the median is the middle number.

If there is an even number of results, the median will be the mean of the two central numbers.

mean

average

how to calculate the mean

add up all the numbers, divide by how many you added

shape distributions

symmetric or skewed

symmetric shape

Right and left side are symmetric; Mean, Median and Mode will be equal (rare)

skewed shape

If a distribution is squished to one side (skewed), then the mean, median and mode will not be the same; Like a mouse, a distribution has a body and a tail; The mean gets dragged towards the "tail", The median also is slightly dragged, The mode stays pretty resilient:

negatively skewed data

distribution's tail extends to the left, in a negative direction

positively skewed data

distribution's tail extends to the right, in a positive direction

measures of dispersion

Range, Variance, and Standard Deviation; describe the "spread" of scores / data-points from our sample

range

the difference between the highest and lowest scores in a distribution

variance

"average" of the squared distances between each score and the mean

(score - mean)^2

standard deviation

a measure of variability that describes an average distance of every score from the mean; Variance of the dataset, but in the context of the original measurement scale.

types of stats summary

-Descriptive Stats → Describe your SAMPLE

-Inferential Stats → Use your sample to describe the POPULATION

-Statistical inference → Making statements about the population, from what the sample tells us.

statistical inference

The process of using data obtained from a sample to make estimates or test hypotheses about the characteristics of a population.

bell curve

distribution of scores in which the bulk of the scores fall toward the middle, with progressively fewer scores toward the "tails" or extremes

normal distribution

A function that represents the distribution of variables as a symmetrical bell-shaped graph.

population standard deviation symbol

σ

population mean symbol

μ

sample mean symbol

x̅

sample standard deviation symbol

SD or Sx

how to bias-correct stats

n-1 in denominator

descriptive vs. inferential statistics

-Descriptive statistics use numbers to describe data collected from your sample

-Inferential statistics estimate what the “population” is like, using your sample data.