What is descriptive research?

- **Aim**: to **describe characteristics** of a * sample* (what kind, how much etc)

- Used to **summarise**, **organise** and **simplify** sample data

- Often based on **measurement of a single variable** (univariate statistics)

- Relies on measures of central tendency, frequencies, spread, distributionel shape, etc

What is inferential research?

- **Null hypothesis testing **

- Aim: to **infer** characteristics of the **population**

- Often interested in **multiple variables **(bivariate, multivariate) - Relies on a** wide range of different tests** (e.g. correlation, regression, t-tests, ANOVA, chi square etc.)

- Allows us to make **probability statements** about how confident we can be that our sample findings reflect the ”true” of things

Level of measurement: What are the two main types of variables?

- **Categorical**

- **binary** (2 levels)

- **nominal** (3+ levels)

- **ordinal** (ordered, no equal intervals)

- **Continuous** (Interval, ratio)

- **Interval** (ordered, equal intervals, **no absolute zero**)

- **Ratio** (ordered, equal intervals, **absolute zero**)

How can you keep error to a minimum?

- By making sure we use careful sampling strategies and use measures that are **valid** and **reliable**

- Validity+reliability=credibility

What are the critical values of z-scores?

- 95% of z-scores lie between **-1.96** and **1.96 **

- 99% of z-scores lie between **-2.58** and **2.58 **

- 99.9% of z-scores lie between **-3.29** and **3.29**

What does the z-score represent?

- The distance a particular observation is away from the mean, measured in **standard deviations **

- The **standard normal distribution** has a **mean of 0 **and a **standard deviation of 1**

What are the two ways you can carry out inferential hypothesis-based research?

- **Correlational research **(observing **what naturally happens** without interfering)

- **Experimental research** (manipulationg one variable and observing the effect on another variable – can be used to **infer cause/effect**)

What are the two types of experimental designs?

- **Independent/between subject** (different participants in different groups)

- **Dependent/repeated measures **(same participants exposed to all conditions)

What is systematic variance?

- **Variation due to genuine effect **

- Variance that can be explained by our model

- **Signal/effect** - What we want to measure

What is unsystematic variance?

- **Noise/error **

- Small differences in outcome due to **unkown factors**

What is the most important formula of all? :-)

- **outcome=(model)+error **

- the way that effect and error is measured varies for each type of statistical test

- But for a test to be ”significant”, **effect should be considerably greater that error (chance)**

What is the null hypothesis?

- What we actually tests in statistics

- Assumes that there is no effect, then **try to reject this **

- **H0: no effect in the population**

What is the alternative hypothesis?

- What **we’re really interested in**, when trying to reject the null hypothesis

- Can be:

- **Non-directional: H1: **There is an effect in the population

- **Directional: H1: **There is this effect in the population

What are significance tests for?

- For determining whether to reject or fail to reject the null hypothesis

- For determining **by how many percents confidence we reject the null hypothesis **(typically **95%, 99% or 99.9%**)

What are the z-distribution, t-distribution, F-distribution etc?

- **Test statistics **

- A statistic for which we know **how frequently different values occur **

- Theoretical sampling distributions that assume the null hypothesis

- **Test statistic=variance explained by the model (effect)/variance not explained by the model (error)**

What is the confidence level for p<.05 p and>

- P<.05>

- P<.01>

- P<.001>

If p is high (p>.05)…

- … the null applies! :-)

If p is low (p<.05>

- … the null must go! :-)

What is the relationship between critical values, significance and confidence?

- As **critical value increase** (gets further away from null), **confidence increases**

- As **confidence increases**, p **(probability of making a type 1 error) decreases**

- Confidence+p=1.0 or 100%

What are critical cut-offs dependent on?

- **Type of test** - 1 vs 2 tailed significance

- **P level **

- **Degrees of freedom** (calculated different for different tests)

What is a type I error?

- **False positive **

- Saying there is an effect when there isn’t

- ”You’re pregnant” to a man :-)

What is a type II error?

- **False negative **

- Saying there isn’t an effect when there is

- ”You’re not pregant” to a pregnant woman :-)

What is NHSTP?

- Null Hypothesis testing procedures

- Black and white thinking -> limitations

- We should** take a middle ground**, **combining NHSTP and effect sizes**

What is the point of confidence intervals?

- Can be useful in **helping us to estimate the range within which the true population mean **(or some other parameter) **would fall in most samples **

- Typically **95% (p<.05>**

What is an effect size?

- A **standardized measure of the size of an effect **

- Comparable across studies

- Not as reliant on the sample size

What are the effect sizes we’ve learned?

- Pearson's *r*

- Cohen's *d *

- *R ^{2}*

- Odds ratio

- Cramer’s V

When and how should we test for **normality**?

- For **all parametric tests **

- Using the K-S/Shapiro-Wilks test

When and how should we test for **homogeneity** of variance?

- Independent t-test

- Independent ANOVA

- Using **Levene’s test**

When and how should we test for **sphericity**?

- Dependent ANOVA

- Using **Mauchly’s test**

What do you usually assume, when assuming normality?

- That** the sampling distribution of the parameter (**e.g. means, or mean differences for a dependent t-test), **or the residuals for regression, are normal in shape **

- **Not** that the distribution of the sample data must be normal

What does the K-S and Shapiro Wilks tests tell you?

- Significant test at **p<.05 of normality>**

- Non-significant test at **p>.05= normality is OK **

- **We want a non-significant test!**

What do you do, if there’s a difference between K-S and Shapiro-Wilks?

- Use shapiro-wilks :-)

What is the central limit theorem?

- **As sample size increases, the random sampling distribution tends towards a normal distribution regardless of the shape of the sample data **

- The tendency increases as sample size increases

- **Can usually be argued with a sample size of >30 **

- For independent tests: at least 30 in each group

- For dependent tests: at least 30 overall!

- Can also be argued if K-S/Shapiro Wilks tests show problems with normality

What if there’s a problem with normality? :-(

- If **large** **sample** **size**, argue to meet normality assumptions on the basis of the **central limit theorem **

- If not: Use a **transformation** (consider **bootstrapping**)

- Or: **use a non-parametric test**

What is the **homogeneity of variance**?

- The assumption that **the variance in the outcome variable is approximately equal at all levels (groupings) of the independent variable **

- If variance is approximately equal for all groups, there is **homogeneity** of variance

- If variance is not equal across groups, there is **heterogeneity** of variance, and the assumption is vioalted

When is the homogeniety of variance relevant?

-** Independent designs **

- For independent t (**independent t-tests**)

- For F tests (**independent ANOVA**)

How can we assess homogeneity of variance?

- Using **Levene’s test **

- Non-significant Levene’s test at p>.05=homogeneity of variance

- **We want a non-significant Levene's test!**

What if we violate the assumption of homogeneity?

-** For independent t-tests**: if Levene’s test **is** significant, meaning there is heterogeneity of variance, we should **report the t-statistic and degrees of freedom from the equal variances NOT assumed row in SPSS output **

- **For Independent ANOVA**: If Levene’s test **is** significant, meaning there is heterogeneity of variance, **report corrected F and df values such as Welch’s F**

What is the assumption of **Sphericity**?

- Similar to the assumption of homogeneity, but **for repeated measures designs **

- The variances of the differences between groups are expected to be equal

How do you test for sphericity?

- Calculating **the differences between each pair of conditions** - Calculating **the variance of these differences **

- **Determining if the variances are approximately equal **

- (If variance 1=variance 2=variance 3…., the assumption of sphericity is met)

How can we assess sphericity?

- Using **Mauchly’s test **

- Non-significant Mauchly’s test p>.05=sphericity

- **We want a non-significant Mauchly's test!**

What if there’s a violation of sphericity?

- If Mauchly’s test for sphericity is significant at p<.05>you should report your findings from a corrected row in the SPSS output

**- **(e.g. **Greenhouse-Geisser** or **Huynh-Feldt correction**)

Why do assumptions matter?

- Many of the most common statistical tests (parametric tests) are only reliable if these assumptions are satisfied or corrections are made

- If we use **uncorrected parametric tests with problematic data, there is a greater risk of drawing inccorect conclusions **(type I error, especially)

What has more power? Non-parametric or parametric tests?

Parametric tests!

What are the key factors in determining which test to use?

- **Aim of research **

- **Level of measurement of IV and DV** (categorical vs continuous)

- **Research design** (for group tests - **independent** vs **repeated measures**)

- **Normality** (e.g. K-S tests)

- **Sample size** (to argue CLM for independent tests: 30 in each group, to argue CLM for dependent tests: at least 30 overall)

- **Homogeneity** of variance and **Sphericity**

- **Post hoc tests (if ANOVA)**

What is correlation?

- **Determining how two continuous variables are related **

- E.g. what relationship, if any, exists between number of hours spent studying for an exam and exam performance?

- **Correlation DOES NOT equal causation** :-)

What is the most widely used correlation coefficient?

- **Pearson' r **

- Ranges from -1 (perfect negative relationship) to +1 (perfect positive relationship

What is Cohen's rule of thumb for Pearson's r?

r__>__.1 (**small** effect)

r__>__.3 (**medium** effect)

r__>__.5 (**large** effect)

What is Cohen's rule of thumb for Cohen's d?

d__>__0.2 (small effect)

d__>__0.5 (medium effect)

d__>__0.8 (large effect)

What is Cohen's rule of thumb for Odds Ratio?

OR __> __1.49 (small effect)

OR __>__ 3.49 (medium effect)

OR __>__ 9.0 (large effect)

How do you generally report results using APA format?

1: State the type of analysis you conducted

2: state the overall finding in normal words (including mean or Mdn, SD)

3: report the DF and test statistic (F, t etc)

4: report the significance level (p)

5: report effect size (including direction) (fx r, d, OR)