Correlation and Distribution Flashcards
what are scatterplots used to display?
relations between two quantitative variables
positive relationship
both variables increase
negative relationship
variables change in opposite directions
strong relationship
points lie close to a line
weak relationship
points are widely scattered
perfect relationship
often appears when cheating has occurred, or when the same thing is being measured
what is the purpose of correlational analysis?
- determine whether there is a linear relationship between variables
- the direction and strength of relationships
pearson correlation coefficient
r
spearman correlation coefficient
rs
what do correlations make no distinction between?
the IV and DV
how can linear relationships be measured?
by correlations
correlations and non-linear relationships
correlations cannot be used, and data may need to be transformed
pearson correlation
- calculated directly from the raw score
- suitable for interval or ratio data
- highly affected by outliers
- not suitable for skewed data
spearman correlation
- calculated from the ranking of the raw scores
- suitable for ordinal data
- marginally affected by outliers
- suitable for skewed data
issues with sample size
small samples can indicate a pattern when there is no real relationship
when are density curves useful?
when dealing with lots of data, that can be distributed normally and generalised to the population
what do density curves use?
a mathematical model to describe a histogram distribution of scores
_______ and _______ ______ should be ignored
outliers, extreme values
normal distribution
perfectly skewed data
positively skewed data
right f
negatively skewed data
left f
what do density curves display?
the overall pattern of a distribution, as all the data is under the curve
when can predictions be made for distribution?
if certain values of the model are known, e.g., mean or SD
what can normal distributions be used to describe?
lots of naturally occuring data that is distributed similarly around a single measure of central tendency
what can observed data be fit to?
the normal curve
how can distributions be described?
using different parameters of mean and SD
mean of the sample
x̄
mean of the population
μ
SD of the sample
S
SD of the population
σ
what is normal distribution described by?
a normal curve
- symmetrical, single-peaked, and the tail meets at the x-axis at infinity
- the higher the mean, the further along the axis it is
- shape is determined by SD
what do statistical tests assume?
data is normally distributed
what happens if data is not normally distributed?
parametric tests must be used
what do standard scores allow us to do?
compare values from different datasets
how can different datasets by translated into a standard normal distribution?
they can be standardised by calculating z-scores
z-score
(deviation of x from mean) / standard deviation
(x - x̄) / S
what is the z-score
the number of standard deviation that the observation deviates from mean
what is created when z-scores are plotted?
a normal distribution
mean and SD of z-score
mean = 0
SD = 1
mean and SD of standard normal distribution
μ = 0
σ = 1
how are normal datasets standardised into standard normal distributions?
by calculating the z-score
what does the area under the standard normal distribution curve represent?
the percentage of participants (100%) and equals 1
what does the table entry indicate?
the area under the curve to the left of the line
