Inferential statistics

what is the difference between descriptive and inferential statistics?

• descriptive summarise the data

• inferential uses data to make inferences about relationships/effects

what is Ho?

null hypothesis: there is no effect, difference or relationship

what is H1?

alternative hypothesis: an effect, difference or relationship exists

what does a p-value represent?

• the probability of obtaining a test statistic at least as extreme as the observed statistic, assuming Ho is try

• a small p value indicates that the observed result would be relatively unusual under Ho

what is a type 1 error?

false positive

what is a type II error?

false negative

what is statistical power?

• power is the probability of correctly detecting a real population effect

• higher power reduces the probability of a type II error

what is effect size?

• quantifies the magnitude of an observed or population effect

• communicates how large or practically meaningful an effect is

how does sample size affect statistical inference?

• larger sample generally produce more precise estimates and increase statistical power/reduce sampling variability

• small samples provide less precise estimates and can increase risk of type II errors

what is a point estimate?

a single sample based estimate of a population parameter

what is a confidence interval?

• gives a range of plausaible values for a population parameter

• communicates uncertainty around point estimate

what determines sample size in an a priori power analysis?

• the chosen significance level, a

• the desired power, which is determined by B

• the expected effect size

what is a sensitivity power anaylsis?

• useful when the sample is already fixed, such as with an existing dataset

• estinates the samllest effect that can be reliably detected

• answers a different planning question from an a priori power analysis

what are nominal and ordinal variables?

• nominal- categories without meaningful order

• ordinal- ordered categories (scales)

• measurement level affects which statistical procedures are appropriate

what distinguishes interval from ratio data?

• inteval data have equal distances between values but no meaningful absolute zero

• ratio data have equal intervas and a meaningful zero point

• ratio sales allow meaningdul statements such asa ‘twice as large’

when is a cross tabulation X2 test appropriate?

• when examining the association between two categorical variables

• data is organised as frequencies in a contingency table

• test assesses whether the distribution of one categorical variable differs according to the levels of another

what is the null hypothesis for a cross tabulation X2 test?

• Ho states that the two categorical variables are independant in the population

• If Ho, is true, observed frequencies should be reasonably close to the frequencies expected under independance

what does a cross tabulation X2 test compare?

• observed frequencies in each contingency table cell

• expected frequencies calculated under the assumption that the variables are independant

• large discrepancies

what are the key assumptions of a cross tabulation X2 test?

• both variables must be categorical

• observations must be independant

• cells in the contigency table mut be mutually exclusive

• EF must be sufficiently large

ow are expected frequencies interpreted in a contingency table?

• expected frequencies are the numbers of cases predicted in each cell if the categorical variables were independent

• they are determined from the marginal totals and the assumptions of indepedance

• they provide the bench mark against which observed frequencies are compared

How is X2 calculated conceptually?

• For each cell, calculate observed frequency − expected frequency.

• Square the difference so positive and negative deviations do not cancel.

• Divide the squared difference by the expected frequency.

• Sum the resulting values across all cells.

• The formula is χ² = Σ[(O − E)²/E].

How are χ² degrees of freedom calculated?

• df = (number of rows − 1) × (number of columns − 1).

• For a 2 × 2 contingency table, df = 1.

• Degrees of freedom determine the relevant reference distribution for evaluating χ².

How is a χ² result interpreted against a critical value?

• Compare the obtained χ² statistic with the appropriate critical value for the chosen α and df.

• If χ² exceeds the critical value, reject H₀ in favour of H₁.

• If χ² does not exceed the critical value, retain/fail to reject H₀.

• A significant result indicates an association, not necessarily a causal relationship.

What does Cramer’s V measure?

• Cramer’s V is an effect-size measure for a cross-tabulation χ² test.

• It quantifies the strength of association between categorical variables.

• It complements statistical significance by describing magnitude.

How is the relevant df term for Cramer’s V selected?

• Use the smaller of the number of columns − 1 and the number of rows − 1

• This minimum determines the dimensional term used in the Cramer’s V calculation.

What must contingency table cells contain?

• Cells must contain frequencies or numbers of cases.

• They should not contain percentages or ratios.

• Each participant should appear in only one mutually exclusive cell