inferential stats tests

descriptive statistics

techniques such as calculating percentages, graphs, measures of dispersion and central tendency

inferential statisitcs

techniques used to analyse a set of data to measure if there is significant difference or correlation between them

significance

the difference or correlation between 2 sets of data is greater than what could occur by chance i.e. its a meaningful result

3 criteria for selecting a statistical test

1. difference or correlation (what the hypothesis predicts)

2. is experimental design used related (repeated measures, matched pairs) or unrelated (independent groups)

3. level of measurement/ data collected (nominal, ordinal, interval)

criterial for choosing a stats test- hypothesis

• H1 is the alternative hypothesis, reflects the researchers prediction

• H0 is the null hypothesis, states there’s no effect or relationship between variables

• H1 and H0 cant both be true, researchers make decisions on what must be retained and rejected using an inferential stats test

• does the hypothesis predict difference or correlation/relationship, eg there will be a significant difference between IV and DV

criterial for choosing a stats test- related or unrelated

• related designs- participants are the same or similar across conditions

• unrelated designs- participants are different and not matched across conditions

levels of data- nominal data

• each item can only appear in one category, there is no order

• eg favourite colour

levels of data- ordinal data

• data in the form of scores, collected on an ordered scale but intervals aren’t equal so a score of 8 isn’t 2x a score of 4, data lacks precision as its based on subjective opinion

• eg rating something from 1 to 10

levels of data- interval data

• data in the form of scores based on numerical scales with units of equal, precisely defined size

• eg any public unit such as time, temperature or counting observations in observational studies, 8 tallies is 2x as many as 4

how are stats tests chosen?

use the 3 criteria and find the suitable test from the table

how to conduct the sign test

1. enter pairs of related data in a table

2. for each pair, the score from condition B is subtracted from condition A to produce the sign of difference- plus, minus, equal

3. participants who achieved the same in both are deducted from the N value

4. calculated value (S) is the total of less frequent sign

5. compare calculated value with critical value using the critical value table

6. if S is less than or equal to the critical value, then it is significant and the null hypothesis is rejected and the alternative hypothesis accepted

type I error (false positive)

• the null hypothesis is rejected even though its actually true

• concluding there is a significant difference or correlation when there actually isn’t, optimistic error

• cause by using a significance level that is too lenient eg 0.5

type II error (false negative)

• the null hypothesis is accepted when in reality the alternative hypothesis is ‘true’

• concluding there is no significant difference or correlation when in reality there is one, pessimistic error

• caused by using a significance level that is too stringent eg 0.0005

calculated values

a value achieved by carrying out an inferential stats test that represents data from an investigation

critical value

a value taken from a statistical table which, when compared with calculated value, tells us if results are significant

how is critical valued identified?

1. direction of the hypothesis- one tailed (directional) or two tailed (non directional)

2. amount of data collected- number of participants (N) or degrees of freedom (df), df always given

3. significance level chosen by the researcher- usually 0.05 or 5%, means there’s a 5% chance the results occurred even if there was no real difference in the population, very occasionally 0.01 or 1%

how do you check for statistical significance?

• the calculated value is compared with the critical value in a table of critical values based on probabilities

• based on the test the calculated value needs to be greater than or less than the critical value to achieve significant results, says at bottom of the table

relationship between significance and hypothesis

• if the stats test is not significant, the null hypothesis is accepted

• if the stats test is significant, the alternative hypothesis is accepted