Week 1: Independent t-tests and null hypothesis testing

differences between groups question (choosing which statistical test to use)

• DV often continuous

• IV often categorical

-can use between-participants or within-participants design

→ use an independent t-test for between-participants

→ use a paired t-test for within-participants

relationship between variables question (choosing which statistical test to use)

• two continuous variables

→ use Pearson’s correlation

• two categorical variables

→ use Pearson’s Chi-Square

independent t-test

• between-participants

-comparing the difference between the means of two independent groups

95% confidence interval

-the more similar the data points within a group are, the more precise you can be in predicting where the mean would be in the population

-use standard deviation to predict how reliable our mean score is

-when there is more standard deviation in a set of results, the 95% confidence interval is larger

→ this shows more variation in results and makes it harder to predict the mean in the actual population

mean difference

-subtracting the mean from one group from the mean of another group

null hypothesis testing

-if the probability is less than 0.05 (5%) 1 then we believe it is small enough

-so, we reject the null hypothesis in favour of the experimental hypothesis

-therefore, we believe there is a significant effect in the population

95% confidence interval around mean difference

-indication of the importance of the effect

-calculates with 95% certainty what the difference in the population will be

t value

-represents the mean difference between two scores

p value

-probability of finding a difference in the sample if there is no difference in the population

calculation of p value

-based on the calculation of the t value

-if the mean difference increases, then t value increases, then p value increases

assumptions that need to be met in order to use independent t-test analysis

• data is approximately normally distributed

• no outliers/extreme scores

• variance is relatively equal in both groups

distribution (assumptions that need to be met in order to use independent t-test analysis)

-data is approximately normally distributed

-assessed via a histogram by looking for a clear skew

-take into account sample size

-if not normally distributed, use non-parametric test

outliers/extreme scores (assumptions that need to be met in order to use independent t-test analysis)

-assessed using a box plot

-looking for points that fall outside box and whiskers on box plot

-dots count as outliers but not immediately problematic

-stars count as extreme scores and should be further investigated

z-scores

-assessing for outliers

-based on standard deviation s

-uses the principles of the 68-95-99 rule

-z score of 2 = 2 SDs from mean = outlier

-z score of 3 = 3 SDs from mean = extreme outlier

-can only be used for normal distributions

what to do with extreme scores

-perform analysis with extreme score

-non-parametric test

-perform analysis without extreme scores

assumption of equal variance (assumptions that need to be met in order to use independent t-test analysis)

-the spread of scores is relatively equal in both groups

• Levene’s test:

  -if not equal, it affects the accuracy of the t-test

  -but alternative test possible

-if levenes test is non-significant (p>0.05) means no significant difference in variance of scores in each group → so use parametric test

-if there is a significant difference then use non-parametric test

reporting results from an independent t-test

-information to report in your results paragraph:

• descriptive statistics

• inferential statistics

• interpretation of results

descriptive statistics (reporting results from an independent t-test)

-which groups did you compare (IV) on what measure (DV)

-direction of effect if significant

-means and SDs

inferential statistics (reporting results from an independent t-test)

-difference between groups significant or not

-t(df) = (t value), p = (p value)

interpretation of results (reporting results from an independent t-test)

-link back to terms stated in the research question

non-parametric independent t-test

-when we have a participants design that does not meet the assumptions to conduct a t-test → carry out Mann Whitney U test, non-parametric equivalent

parametric tests

-used when data is normally distributed

-use actual scores

-more powerful

non-parametric test

-used when data is not normally distributed

-use ranks → focusses on difference in mean ranks

-less powerful

non-parametric test descriptive statistic

-use the median

Mann-Whitney test

-use median

-order all participants according to liking score (merge two groups)

-rank scores in order from lowest to highest

-average ranks of any duplicate scores

-separate into two groups again

-calculate mean ranks for each group

descriptive statistics (reporting results from a Mann-Whitney test)

-which groups did you compare (IV) on what measure (DV)

-medians for each group

inferential statistics (reporting results from a Mann-Whitney test)

-difference between groups significant

interpretation of results (reporting results from a Mann-Whitney test)

-make sure to link back to the terms in the research question