Statistical Tests Flashcards
2 types of statistics
descriptive statistics — such as averages and graphs
inferential statistics — calculated using inferential tests which allow researchers to work out the probabilities of certain results so they can decide whether to accept or reject a null hypothesis
they are inferential because they involve making an inference about whole populations based on smaller samples
what are statistical tests?
procedures for drawing logical conclusions and inferences about the population from which the samples are drawn
why are statistical tests needed?
researchers may find a difference or correlation between samples but the difference needs to be big enough so we can be sure that there is a real difference in the population from which the samples were drawn
we use inferential statistical tests to find out if the result is significant using tables of critical values
what is significance?
the statistical term indicating that the research findings are sufficiently strong to enable the researcher to reject the null hypothesis and accept the alternative hypothesis
difference between parametric and non parametric tests
parametric tests are preferred because they are more powerful, however they can only be used if certain criteria are met
parametric tests concern interval and ratio data, non-parametric tests concern nominal and ordinal data
parametric tests concern data drawn from populations within normal distribution, non-parametric tests concern data drawn from populations with skewed distributions
parametric tests involve variances between samples that are not significantly different, non-parametric involve variances between samples that are significantly different
why are parametric tests powerful?
they make calculations using the mean and standard deviation of a dataset
whereas nonparametric tests use ranked data. thus losing some of the detail
parametric tests can detect significant in situations when nonparametric tests cannot
criteria for parametric tests
the level of measurement is interval or better
the data is drawn from a population that has a normal distribution
variances of the two samples are not significantly different
define levels of measurement
refers to the different ways of measuring items or psychological variables
NOIR (nominal, ordinal, interval or ratio)
the lower levels are less precise (nominal and ordinal)
how to decide if a test is parametric?
use a parametric test if….
- the data is interval or ratio (the intervals between the data are truly equal)
- the data has a normal distribution (when most items cluster around the mean with an equal number of items above and below the mean)
EXAMPLE = we might expect many physical and psychological characteristics to be normally distributed, such as height, shoe sizes, IQ and friendliness (the characteristic being measured is assumed to be normal)
• the variance is a measure of how spreadout the data is around the mean, it is the square of the standard deviation — for repeated measures, any difference in the variances should not distort the result but for independent groups, the variance of one sample should not be more than four times the variance of the other
types of parametric test
pearson’s r
related t test
unrelated t test
how to decide if a test is non-parametric?
if the data is in categories (nominal) or ordered in some way (ordinal)
the data has a skewed distribution
the variances of the two samples are significantly different
types of non parametric test
chi squared
sign test
spearman’s rho
wilcoxon
mann whitney
when to use….
pearson’s r test
parametric (interval or ratio data)
correlation
when to use….
related t test
parametric (interval or ratio data)
not a correlation
test of difference
repeated measures / matched pairs
when to use….
unrelated t test
parametric (interval or ratio data)
not a correlation
test of difference
independent groups
when to use….
chi squared test
nominal data
independent groups
when to use….
sign test
nominal data
repeated measures / matched pairs
when to use….
spearman’s rho
ordinal data
correlation
when to use….
wilcoxon test
ordinal data
not a correlation
tests of difference
repeated measures / matched pairs
when to use….
mann whitney test
ordinal data
not a correlation
test of difference
independent groups
define calculated and critical values
calculated value = the value of a test statistic calculated for a particular set of data
critical value = the value of the test statistic that must be reached to show significance
calculated and critical values
each statistical test involves taking the data collected in a study and doing calculations which produce a single number called the test statistic
for example, in spearman’s test the test statistic is RHO but in the mann whitney test it is U
the test statistic value calculated for any set of data is called the calculated value because it’s based on the calculations made
to decide if the calculated value is significant, it is compared to a critical value
critical value is the value that a test statistic must reach in order for the null hypothesis to be rejected and the alternative hypothesis to be accepted
what is a test statistic?
the name given to the calculated value, calculated using a statistical test
for each test, this value has a specific name such as S for the sign test
how to find the critical value
- identify the significance level, which is usually p < 0.05
- identify the type of hypothesis used (a one-tailed test is used for a directional hypothesis, a two-tailed test is used for non-directional hypothesis)
- identify the value of N (the number of participants in the study) — for independent groups there are two values for N, one for each group of participants which are called NA and NB
in some tests such as t tests and chi squared tests, you calculate degrees of freedom (df)
what are degrees of freedom?
the number of values that are free to vary given that the overall total values are known
they are used instead of N for some tests, such as t-tests and chi squared test
how to know if a test is significant?
some tests are significant if the calculated value is equal to or greater than the critical value
other tests are significant when the calculated value is equal to or less than the critical value
if the name of the test has a letter R in it, then the calculated value should be greater than the critical value — e.g. spearman’s, pearson’s, chi squared and related and unrelated t tests
if there is no R in the name of the test, then the calculated value should be less than the critical value — e.g. sign test, mann-whitney and wilcoxon
when to use a one-tailed test and two-tailed test
one tailed test is used with a directional hypothesis
two-tailed test is used with a non-directional hypothesis
