statistical tests Flashcards
define null hypothesis
this is the prediction you want to test
you assume the null hypothesis is true
define significance level
this is the level of proof you are looking at before you read into your results
the smaller the significance level, the stronger the evidence you’re looking for that your results are not just down to chance
if the probability of your results being a fluke is less than the significance level…
you can suggest that your null hypothesis was not true. you can then assume that the difference between groups was down to the change you made in your independent variable.
you reject the null hypothesis and assume your alternative hypothesis is true.
your results are therefore statistically significant
if the probability of your results being a fluke is more than the significance level…
you accept the null hypothesis and reject the alternative hypothesis as it means that your results could have occurred by chance.
assumptions of the sign test
- test of difference
- repeated measures
- nominal data (categories)
how to carry out the sign test
- Calculate difference between before and after.
- Add up positive signs and negative signs, ignore no change.
- The smallest one is the observed value.
what key pieces of information do you need for the sign test?
- significance level desired
- number of participants (N value)
- identify whether its a two-tailed or one-tailed test
assumptions of the Mann Whitney test
- test of difference
- independent groups
- ordinal data (scores)
how to carry out the Mann Whitney U test?
- rank both sets of data together (1 being the lowest)
- add up the sum of both groups
- work out value of U –> U = sum - (N(N+1))/2
- use smallest value
- use critical value table to find critical value
- draw conclusion: if the U value > critical value = must accept null hypothesis
what key pieces of information do you need for the sign test?
- no. of participants for both groups
- value of U
- critical value table
assumptions of the Wilcoxon test
- test of difference
- repeated measures
- ordinal data
how to carry out the Wilcoxon test?
- calculate the difference before and after
- rank the absolute difference (leaving out differences of 0)
- calculate value of T –> T = sum of the less frequent sign
- draw conclusions: T value < critical value = accept the null hypothesis
what key pieces of information are needed to carry out the Wilcoxon test?
- critical value table
- table of results
- significance level
- one or two tailed tests
- no. of participants
assumptions of spearman’s rho
- test of relationship/ association
- ordinal data
- correlation
how to calculate spearman’s rho?
- rank both columns from N (no of participants) - 1 (1 being the largest)
- calculate the difference between the two and square each value
- find the sum of D^2
- calculate value of Rho –> Rho = (1-6Σd^2)/ (N^3-N)
- draw conclusions: Rho > critical value = data is significant
what key pieces of information is needed to calculate spearman’s rho?
- number of participants
- critical value table
- significance level
- table of results
- one or two tailed test
assumptions of pearson’s r
- looking for a relationship/ association
- interval or ratio data
- correlation
- parametric test
how to calculate pearson’s r
- calculate mean of X and mean of Y
- for each value find the value of (x-x̄) and (y-ȳ)
- square those values
- find the value of (x-x̄) times (y-ȳ)
- calculate r value: r=Σ(x-x̄) x Σ(y-ȳ) /
what key pieces of information do you need to calculate pearson’s r
- degrees of freedom: N-2
- table of results
what is a parametric test?
it is robust
it uses interval data as it contains a true zero value
it can be a test of difference or relationship
parametric tests are pearsons r, related and unrelated t tests
assumptions of related t-tests
- parametric test of difference
- repeated or matched pairs design
- interval data
assumptions of unrelated t-test
- parametric test of difference
- independent groups
- interval data
assumptions of chi-squared test
- test of difference/ association
- independent groups
- nominal data - recorded as a frequency
- data is presented in a contingency table
type I error
this is when the null hypothesis is rejected and the alternative hypothesis is accepted, but it should be the other way around; in reality the null hypothesis is true
this is referred to as an optimistic error or false positive as the researcher claims to find significance that does not exist.
type II error
when the null hypothesis is accepted but the alternative hypothesis should have been.
pessimistic error or false negative
