Correlations and Inferential Stats Tests

Includes distribution, references and peer review

Differences between a correlation and an experiment

• Difference between two conditions of an IV, relationship between two co variables

• IV is manipulated, DV measured, no IV or DV but covariables

• Cause and effect, no cause and effect

• Uses graphs and bar charts, uses scatter graphs

• Both use a null hypothesis which aims to be disproven

Features of a correlation

• Stats tests can be applied: Spearmans, Pearsons

• Correlation coefficients can be established- these tell us the strength and direction of the relationship

  • Ranges from -1 to +1

  • Closer to -1 is strong negative, closer to +1 is strong positive

• Strengths: doesn’t require the IV to be manipulated- more ethical and in further research the correlation can be demonstrated experimentally

• Weaknesses: cannot establish cause and effect and self report data (people could lie- data is unreliable and meaningless)

• Hypothesis: there will be a (positive) relationship/correlation between the two co variables

• A perfect correlation goes straight from the middle

What are descriptive statistics?

• Allow us to summarise a set of data:

• Measures of central tendency

  • Mean, median, mode

• Measures of dispersion

  • Range, standard deviation

What are inferential statistics?

Used to draw conclusions about a null hypothesis- accept or reject

Inferential stats tests

What are the level of measurement data?

Nominal data: frequency count

Ordinal data: rating or ranking

Interval level data: universally recognised units of measurement with equal units between each measure eg speed, weight, seconds

How to choose a stats test?

• Level of measurement (nominal, ordinal, interval)

• Correlation or experiment (if correlation use Pearson’s if both sets of data are interval level, use a Spearman's test if not) - looking for a difference or association

• If experiment, independent groups of repeated measures design

How to carry out a Spearman’s Rho stats test?

• Decide whether the hypothesis requires one tailed or two tailed test + how many participants

• Assume p=0.05 unless stated otherwise

• Find the critical value from the Spearman’s Rho table

• Decide whether the calculated value is significant (if it is more than the critical value)

• Accept or reject the null hypothesis

How to carry out other stats tests?

• Use the same method

• Some may use N₁ and N₂ for the number of ps which need to be cross-referenced, chi-squared uses degrees of freedom (df)

• Different tests may require the calculated value to be more or less than the critical value

The significance statement framework

The calculated value is ___. The critical value is ___ (N= ,__-tailed, __%). The calculated value is greater/less than the critical value so the null hypothesis is accepted/rejected. Therefore we can conclude (reinstate the hypothesis you are accepting-either null or alternative)

What does the p=0.05 mean in inferential stats tests?

• Psychologists are 95% sure that the manipulation of the IV has caused the change in DV

• 5% chance that other factors eg extraneous variables influenced our findings

What are the symbols for each statistical test?

• Chi-squared X₂

• Spearman’s r_s or rho

• Wilcoxon T

• Mann-Whitney U

• Sign test S

• Pearson’s R r

• Related T t

• unrelated T t

What are type 1 errors?

• This is when the null hypothesis is falsely rejected due to a mistake telling you the result is significant

• A false positive where the researcher incorrectly concludes there is an effect

• This could be due to too lenient of a significance level e.g. 10% or confounding variables

• e.g. caffeine and coffee in IG design on memory test- people recalled better due to participant variables (people with better memories in one group) not caffeine

What are type 2 errors?

• The null hypothesis is falsely accepted - a false negative where a real effect exists but is undetected

• Could be due to too strict a significance level eg 1% or confounding variables

• Ps given 3 minutes to learn list of words which is too long- caffeine would have no effect but it would if the study had been planned better, too small sample

Difference between a parametric and non-parametric statistical test

• A parametric test is used to identify differences between two related conditions using interval level data

• A non-parametric test is used when data does not meet the assumptions required for parametric tests

Describe how to carry out a sign test

• Used for nominal level data and repeated measures design and experiment (difference)

• Convert raw data to nominal by recording a positive or negative sign

• Ignore any 0 values (stay the same) and exclude these from the n value

• If using a table, see if the values have increased (+) or decreased (-) and count the number of times the signs appear

• Calculate the value of S- this is the number of times the less frequent sign or value occurs (this is the calculated value)

• Compare this with the critical value and accept or reject the null

What are normal and skewed distributions?

• Normal distribution: mean, median and mode are in the middle

• Positive skewed: P that has fallen backwards with mode at the hump, then median, then mean further down

• Negative skewed: mode at hump, then median and mean down the curve