Statistical Tests

Question 1

2 types of statistics

Answer 1

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

Question 2

what are statistical tests?

Answer 2

procedures for drawing logical conclusions and inferences about the population from which the samples are drawn

Question 3

why are statistical tests needed?

Answer 3

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

Question 4

what is significance?

Answer 4

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

Question 5

difference between parametric and non parametric tests

Answer 5

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

Question 6

why are parametric tests powerful?

Answer 6

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

Question 7

criteria for parametric tests

Answer 7

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

Question 8

define levels of measurement

Answer 8

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)

Question 9

how to decide if a test is parametric?

Answer 9

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

Question 10

types of parametric test

Answer 10

pearson’s r

related t test

unrelated t test

Question 11

how to decide if a test is non-parametric?

Answer 11

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

Question 12

types of non parametric test

Answer 12

chi squared

sign test

spearman’s rho

wilcoxon

mann whitney

Question 13

when to use….

pearson’s r test

Answer 13

parametric (interval or ratio data)

correlation

Question 14

when to use….

related t test

Answer 14

parametric (interval or ratio data)

not a correlation

test of difference

repeated measures / matched pairs

Question 15

when to use….

unrelated t test

Answer 15

parametric (interval or ratio data)

not a correlation

test of difference

independent groups

Question 16

when to use….

chi squared test

Answer 16

nominal data

independent groups

Question 17

when to use….

sign test

Answer 17

nominal data

repeated measures / matched pairs

Question 18

when to use….

spearman’s rho

Answer 18

ordinal data

correlation

Question 19

when to use….

wilcoxon test

Answer 19

ordinal data

not a correlation

tests of difference

repeated measures / matched pairs

Question 20

when to use….

mann whitney test

Answer 20

ordinal data

not a correlation

test of difference

independent groups

Question 21

define calculated and critical values

Answer 21

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

Question 22

calculated and critical values

Answer 22

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

Question 23

what is a test statistic?

Answer 23

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

Question 24

how to find the critical value

Answer 24

1. identify the significance level, which is usually p < 0.05
2. 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)
3. 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)

Question 25

what are degrees of freedom?

Answer 25

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

Question 26

how to know if a test is significant?

Answer 26

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

Question 27

when to use a one-tailed test and two-tailed test

Answer 27

one tailed test is used with a directional hypothesis

two-tailed test is used with a non-directional hypothesis