Research Methods (2) - Descriptive Statistics and Exploring Data

Population

A group that shares a common characteristic of interest for the research question.

Sample

A smaller group of members from a population selected to represent that group.

Central tendency

A value that represents a typical score in a data set.

Dispersion

A value that describes how spread out a set of data is.

Standard deviation

The square root of the variance.

- the most popular measure of dispersion

-represents the average deviation of scores from the mean

Outlier

A data point/observation that differs significantly from other observations.

Kurtosis

Describes how pointy or flat the distribution is.

Experimental design

Systematically manipulating one variable to observe its causal effect on other variables.

Between subjects design

Participants are randomly assigned to different conditions or groups.

Within subjects design (repeated measures)

Each participant takes part in all conditions.

Quasi experimental design

Between groups design where participants are not randomly allocated to different conditions.

- ivs we cannot directly manipulate e.g gender

parameters

describe populations e.g mean of a population

statistics

describe samples e.g mean value of a sample

population

-The measurable quality is called a parameter

-The population is a complete set

-Reports are true representation of opinion

-Contains all members of a specified group

sample

-The measurable quality is called a statistic

-The sample is a subset of the population

-Reports have a margin of error and confidence interval

-its a subset that represents the entire population

measures of central tendency

mean, median, mode

mean (most sensitive)

arithmetical average, sum of scores divided by the number of scores

median (Extreme scores)

middle score when scores are ordered

mode (least sensitive)

score that occurs the most often in the data set

when should mean be used

interval or ratio data

limit of the mean

can be a problem when outliers in data

when should median be used

if you have extreme scores, can be used on interval, ratio and ordinal data

when should mode be used

- nominal data

limits of mode

-The most common score may be at one end of the distribution

-There may be more than one mode (Bimodal distribution)

limit of measures of dispersion

cannot provide a full description of a data set

range

simplest measure of spread

highest score minus lowest score

limit of range

- only based on 2 scores

-ignores any information thats available in other scores

- very sensitive to outliers

limits of IQR

-Not based on all the observations

-The first 25% and last 25% are completely ignored in its calculation

variance

-Uses information from all scores in data set

-Tells us the degree to which scores vary around the mean

-To work the variance out we square the deviations (multiply them by themselves) -to remove negative values

Variance - sum of the squared deviations/ (n-1)

limits of variance

-Does Not describe the amount of variability in the same units as the original data (due to squaring values)

-We got an overall variance of 2.84 but the biggest deviation from the mean was 2.375

Large SD

scores are very spread out

small SD

scores are very close to the mean

exploratory data analysis

- first step after data collection

- aims to determine the main characteristics of data

- exploring data using descriptive statistics

- summarising and condensing data using graph (box plots and histograms)

histograms

-represent distribution of data

-values divided into intervals called bins

normal distribution (bell shaped curve)

- mean divides data in half

- symmetric

- unimodal curve (one peak)

- the curve approaches but never touches the X axis

skewed distributions

bimodal/multimodal distributions

Random selection

Equal probability, unbiased selection of participants from a population.

Representative sample

A sample that accurately represents the population.

Parameters

Measurements that describe populations.

Statistics

Measurements that describe samples.

Descriptive statistics

Measures of central tendency and dispersion that summarize data.

Measures of central tendency

Mean, median, and mode that represent typical scores in a data set.

Mean

Arithmetical average of scores in a data set.

Median

Middle score when scores are ordered.

Mode

Score that occurs most often in a data set.

Range

Simplest measure of spread, highest score minus lowest score.

Interquartile range (IQR)

Range that represents the middle 50% of scores, less sensitive to outliers.

Variance

Degree to which scores vary around the mean, calculated by summing squared deviations.

Standard deviation (SD)

Square root of the variance, represents the average deviation of scores from the mean.

Exploratory data analysis

First step after data collection, aims to determine the main characteristics of the data.

Box plots

Graphical representation of data using quartiles and outliers.

Histograms

Graphical representation of data using intervals called bins.

Normal distribution

Symmetric, bell-shaped curve with a mean dividing the data in half.

Skewed distributions

Distributions that are not symmetric, can be bimodal or multimodal.