statistical tests

what is the typical p value used? what does this mean?

• p = 0.05

• there is a 5% probability that the results of a study are due to random chance

what is a null hypothesis (H₀)?

a hypothesis in which the results of a scientific investigation will no produce no statistical significance

what does Student’s t-test determine?

if there is a significant difference between the mean values of a particular variable across two populations

when should you use Student’s t-test?

• data must be continuous and normally distributed

• variances (SDs²) of the populations should be equal (? never heard of this)

• samples must be independent of each other

in the formula for the t-test (which you don’t need to learn), what do each of the symbols represent? 

how do you calculate the degrees of freedom for the t-test?

df = (n₁ + n₂) - 2

give a conclusion for if the value of t is greater than the critical value:

• the value of t exceeds the critical value, so we reject the null hypothesis

• this suggests that there is a significant difference between the means (specify)

• ∴ there is a low probability (p < 0.05) that the difference between the means (specify) is due to chance

give a conclusion for if the value of t is lower than the critical value:

• the value of t is lower than the critical value, so we accept the null hypothesis

• this suggests that there is no significant difference between the means (specify)

• ∴ there is a high probability (p > 0.05) that the difference between the means (specify) is due to chance 

what does the Chi-squared test determine?

looks for a significant difference between the frequencies of individuals in different categories

when should the Chi-squared test be used?

• used for categorical data where the no. of individuals/events are counted

• ∴ calculates the probability that the difference between the your data and the expected frequencies is due to chance

in the eqn for the Chi-squared test (which you don’t need to learn), what do each of the symbols represent? 

(∑ = sum of)

how do you calculate the degrees of freedom for the Chi-squared test?

df = n - 1

give a conclusion for if the value of Chi-squared is greater than the critical value:

• my value of Chi-squared is greater than the critical value, so we accept the null hypothesis

• so there is no significant difference between X and Y (specify)

• ∴ there is a high probability (p > 0.05) that the difference between X and Y (specify) is due to chance 

give a conclusion for if the value of Chi-squared is smaller than the critical value:

• my value of Chi-squared is smaller than the critical value, so we reject the null hypothesis

• so there is a significant difference between X and Y (specify)

• ∴ there is a low probability (p < 0.05) that the difference between X and Y (specify) is due to chance

what does Spearman’s rank determine?

looks for a correlation between 2 sets of continuous on a scatter graph

when do we use Spearman’s rank?

2 sets of normally distributed continuous data

in the Spearman’s rank formula (which you don’t need to learn), what do each of the symbols represent?

D = diff in ranks

n = no. of pairs

how do you calculate degrees of freedom for Spearman’s rank?

df = n - 2

give a conclusion for if the value of r_s is greater than the critical value:

• the value of r_s exceeds the critical value, so we reject the null hypothesis

• so the correlation between X and Y (specify) is significant

• ∴ there is a low possibility (p < 0.05) that the correlation between X and Y (specify) is due to chance

• (comment on +ve/-ve correlation)

give a conclusion for if the value of r_s is smaller than the critical value:

• the value of r_s is lower than the critical value, so we accept the null hypothesis

• so the correlation between X and Y (specify) is not significant

• ∴ there is a high possibility (p > 0.05) that the correlation between X and Y (specify) is due to chance

• (comment on +ve/-ve correlation)

what does an r_s value near +1 indicate?

strong +ve correlation

what does an r_s value near -1 indicate?

strong -ve correlation

what does an r_s value around 0 suggest?

no correlation