Stats

-flashcards made so far from lecture 1 to 4-

IV, DV and CV

Independent → The thing that is changed

Dependent → The thing that is measured

Control → Everything that should remain the same between test

Which types of data are continuous and which are categorical?

Continuous → Interval and Ratio

Categorical → Nominal and Ordinal

Interval data

Quantitative data measured along a scale where each point is placed at an equal, standardized distance from adjacent values, but has no true or absolute zero point

Ratio data

Quantitative data measured along a scale where each point is placed at an equal, standardized distance from adjacent values, and has a meaningful zero (where zero represents a complete lack of something)

Nominal data

Qualitative, categorical data used to label or name variables without any quantitative value, ranking, or natural order

Ordinal data

Qualitative, categorical data used to label or name variables with a natural order (e.g. disagree, neutral, agree)

Correlational design

All variables are measured to examine a relationship between variables → non of the variables are manipulated

Experimental design

An experimental design involves manipulating an independent variable and measuring its effect on a dependent variable. Random assignment and appropriate controls strengthen causal conclusions.

Between vs within subjects

Between-subjects (Independent groups) → Different participants in different groups

Within-subjects (Repeated measures) → Same participants in one group

Inferential statistics

Using research methods and statistical analyses, we can infer information about a population based upon the findings of our sample. We can generalise the findings from our sample to a population.

Descriptive statistics

Tells us information about our specific group (our sample). Helps us to explore, summarise, organise and simplify data.

Unimodal, bimodal, and multimodal distribution

What is skewed data? What are the types?

A set of data where the distribution is asymmetrical instead of forming a balanced bell curve

What is kurtosis? What are the types?

A statistic used to describe the shape of a distribution of continuous data. It measures the tendency of the data to be distributed toward the tails, or ends, of the distribution versus toward the middle.

What is the difference between a one tailed and two tailed hypothesis

One tailed → One population mean is greater than or less than the other → Example: Drug A will be better than Drug B (direction)

Two tailed → Two populations are different from one another → Example: Drug A and B will have different effects (no direction)

What is a type one and a type two error

Type 1 error → We believe there is an effect, but in reality there isn’t. → Rejection of a true null hypothesis

Type 2 error → We believe there is no effect, but in reality there is. → Failing to reject a false null hypothesis

What is meant by the statistical power of a test?

Statistical power is the probability that a statistical test will correctly detect a real effect or difference when one actually exists

Define standard deviation

A measure of how spread out a set of scores is around the average, or mean

What does a high or low standard deviation mean?

Low Standard Deviation: Scores cluster around the mean, meaning participants behaved very similarly.

High Standard Deviation: Scores spread out across a large range, meaning there is high variability among participants.

Define a T-test

An inferential statistical test used to determine whether there is a statistically significant difference between the means of two groups

What is standard error?

A statistical measure that tells you how far your sample mean (average) is likely to be from the true average of the whole population

It is inversely proportional to the (square root of the) sample size, meaning that smaller samples tend to produce greater standard errors

What is the standard error of the differences in means?

How much we expect the means of different samples, drawn from the same distribution, to differ from each other

What is the difference between an independent and dependent t-test

What are the three types of t-test

One sample	One sample, compared with known population mean	Comparing the acidity of a liquid to a neutral pH of 7
Independent sample (Between subjects)	Different samples of participants experience each level of IV	Comparing the academic performance of online vs. on-campus students
Paired/dependent sample (Within-subjects)	Same or related samples of participants experience each level of IV	Comparing the happiness score before and after eating chocolate

What is a p-value? (t-tests)

A measure of how likely your observed results (or more extreme ones) would be if the null hypothesis were true. e.g. null hypothesis = no relationship so if it is likely a statistical relationship is shown when null hypothesis is true this means results can’t be trusted

How do we know if a t-test is statistically significant?

Statistically Significant (p ≤ 0.05): If your p-value is lower than or equal to 0.05, the result is considered statistically significant.

Not Significant (p > 0.05): If the p-value is higher than 0.05 there is insufficient evidence to reject the null hypothesis

What is a z-score? (t-tests)

A statistical measure that describes the position of a raw score in terms of its distance from the mean

What are the four assumptions of data in a t-test

1. Are independent

2. Are (approximately) normally distributed (no outliers!)

3. Have a similar amount of variance within each group being compared (i.e. homogeneity of variance; for between subjects)

4. DV needs to be continuous; IV needs to be categorical

What is a parametric test?

A type of statistical hypothesis test that assumes the underlying data follows a specific probability distribution (most commonly a normal or bell-shaped distribution) and makes inferences about population parameters like the mean and standard deviation

What is a non-parametric test?

A statistical hypothesis test that makes few or no assumptions about the underlying population distribution

How are t-test assumption checked?

Define degrees of freedom

The number of scores that are free to vary when estimating a population parameter from a sample

What is ANOVA

Analysis of Variance (ANOVA) is a family of statistical tests that are useful when comparing several sets of scores → means of three or more groups

The basic idea behind ANOVA is a comparison of the variance between the groups and the variance within the groups

(NOTE: No restriction on number of means (as many groups as you wish)

NOTE: Allows us to use more than one independent variable)

What are the null and alternative hypotheses for ANOVA

Null hypothesis → there is no significant difference among the groups

Alternative hypothesis → assumes that there is at least one significant difference among the groups

What is the F statistic? (ANOVA)

The ratio of the Between Group Variation to the Within Group Variation

(If the Between Group Variation is significantly greater than the Within Group Variation, then it is likely that there is a statistically significant difference between the groups)

What are the assumptions of data of an ANOVA

What is sphericity?

A key assumption in a repeated-measures ANOVA (with three or more levels). It means that the variances of the differences between all pairs of within-subject conditions are equal

If an assumption is violated, what do you do?

• Data transformation

• Use a non-parametric test instead

• Alternative test

Define post-hoc tests

Statistical follow-up tests used after an omnibus test - such as an Analysis of Variance (ANOVA) - shows a statistically significant overall difference among three or more groups, but does not specify which particular groups differ from one another

What is a factorial design?

An experiment containing two or more independent variables (factors).

What is a factor, and what is a level?

A factor is a major independent variable; a level is a subdivision or condition of that factor.

What does a two-way ANOVA test?

The effects of two factors on a continuous dependent variable (DV), including their interaction.

What is a main effect in factorial ANOVA?

The effect of one factor on the DV, considered independently of the other factor.

What is an interaction effect?

When the effect of one factor on the DV changes across levels of another factor.

What hypotheses are tested in a two-way ANOVA?

Three pairs: the main effect of factor A, the main effect of factor B, and the A × B interaction.

What is a repeated-measures two-way ANOVA?

A two-factor ANOVA in which both factors are within-subjects factors.

What is a mixed ANOVA?

An ANOVA combining at least one between-subjects factor and one within-subjects factor.

When must sphericity be checked?

For a within-subjects factor with three or more levels; it is automatically met with two levels.

What do interaction plots tell us?

Non-parallel lines suggest an interaction; parallel or nearly parallel lines suggest little or no interaction.

What does a 2 × 2 factorial design mean?

Two factors, each with two levels.

What are the three effects in a two-way ANOVA?

Main effect A, main effect B, and the A × B interaction.

What is the null hypothesis for a two-way ANOVA interaction?

There is no interaction between the two factors.

What is the alternative hypothesis for a two-way ANOVA interaction?

There is an interaction between the two factors.

How is variance partitioned in a two-way ANOVA?

Into factor A, factor B, their interaction, and error variance.

What are the assumptions of an independent-groups two-way ANOVA?

Independent observations, approximate normality, homogeneous variances, a continuous DV and categorical factors.

Why is sphericity not an issue with two repeated-measures levels?

With only two levels, there is only one pair of conditions to compare.

What assumptions matter in a mixed ANOVA?

Check homogeneity of variance for between-subjects factors and sphericity for within-subjects factors with three or more levels.

What is an N-way ANOVA?

An ANOVA with three or more factors, such as age, gender and handedness.

What is Tukey's HSD used for?

Post-hoc pairwise comparisons between group means, with adjustment for multiple comparisons.

When might Bonferroni adjustment be used?

To adjust significance thresholds or p-values when conducting multiple comparisons.

What is long-format data?

Each observation has its own row, with columns identifying the participant and condition.

What is wide-format data?

Different measurements or conditions are usually stored in separate columns for each participant.

How do you interpret F(1, 39) = 5.03, p = .031?

F is the test statistic; 1 and 39 are numerator and denominator degrees of freedom; p = .031 is significant at .05.

What should an APA-style ANOVA report include?

The design, assumptions, F statistic, degrees of freedom, p-value, effect size and relevant descriptive or follow-up results.

How do you interpret a significant interaction in a repeated-measures ANOVA?

The effect of one factor depends on the level of the other; follow-up comparisons can show where the differences occur.