Are you looking at news articles differently after this introduction to statistics?

Sometimes you don’t need to be a statistician to call BS!

• We can perform a linear regression
• We can interpret the output of a linear regression
• We know what assumptions to check for (and how)
• We know how to report the results of a linear regression analysis
• We can plot the results of a linear regression
• We can predict a y value based on any x value, the intercept, and the slope

• Revision questions
• old lab reports
• SPEQ: please fill in the questionnaire online!

• COME TO YOUR LECTURES/LABS: those who are present tend to do well
• Have the right attitude (YOU are responsible for your learning)
• Be organised, time yourself: Revise your labs every single week!
• Be creative, inquisitive, ask questions, don’t let loose!
• Be realistic: 102 hours self-directed learning (as per paper descriptor) equates to 8.5 hours per week, that’s 2 afternoons/week!
• Don’t get lost in the ocean of available resources, choose one, stick to it, read!

Type of variable	Categorical (Binomial)	Categorical (Nominal)	Categorical (Ordinal)	Continuous
Predictor	smoker, gender, handedness	state of mind, hair colour	age class, rank	long jump results, body weight
Response	survival, handedness	employment type, hair colour	income bracket, clutch size	cholesterol level, body weight

A variable has got a name, and values, examples:

• Variable name: handedness, values: left, right
• Variable name: body weight, values: 63.4, 88.2, …
• A categorical predictor variable is often called a ‘factor’, its values ‘factor levels’

• The variance has one problem: it is measured in units squared
• This isn’t a very meaningful metric so we take the square root value
• This is the standard deviation (\(s\), sometimes \(sd\)):

\[s = \sqrt{\frac{\sum(x_i-\bar{x})^2}{n-1}} = \sqrt{\frac{5.2}{4}} = 1.14\]

In R:

friends = c(1, 2, 3, 3, 4)
sd(friends)
[1] 1.140175

We can commit 2 types of errors:

We need a metric (a test statistic!) that puts the difference between the samples into perspective with

• the difference between the samples that we would expect by chance, and
• the standard deviations of the two samples

This is called the t-statistic:

\[t = \frac{\text{observed difference - expected difference}}{\text{estimate of the standard deviations}}\]

In fact, the expected difference is mostly zero (this is the case in the following examples)

There is a trade-off between sample size, standard deviations, expected difference, type-I error probability (\(\alpha\)) and type-II error probability (\(\beta\) or power, \(1-\beta\))!

• It is an effect size
• ± 0.1 = small effect
• ± 0.3 = medium effect
• ± 0.5 = large effect
• The correlation coefficient, \(R\) shows us how strongly two variables are correlated.
• It ranges from -1 to 1, a negative sign means a negative correlation

• t-test (incl. power t-test)
• Wilcoxon test
• Shapiro-Wilk test
• Correlation test (Pearson, Spearman, Kendall)
• Chi-squared test
• Linear regression

1. variation caused by random effects in any direction
2. variation coming from a factor that introduces bias in one direction only
3. always deflating the standard deviation
4. all of the above

1. the frequencies
2. the scores
3. any metric
4. none of the above

1. equals the standard deviation divided by the square root of the sample size
2. estimates the correlation between two variables
3. equals the mean in most cases
4. often equals the standard deviation

1. Rank in a 100 m race
2. Civil status
3. Numbers of cigarettes smoked per day
4. Cholesterol level in blood samples (in mg/ml)

1. An independent variable is the same as a predictor variable
2. A predictor variable can be a factor
3. A response variable is the same as a factor
4. A factor can have two or more factor levels
5. A response variable can be categorical or continuous

1. Squaring the sum of the differences between observations and the mean
2. Dividing by the degrees of freedom
3. Summing up the differences between observations and the mean
4. All of the above is correct

1. the median is 20
2. the first quartile is 11
3. the third quartile is 30
4. the interquartile range is 19
5. all of the above are correct
6. only (1) is correct

1. About 95%
2. About 50%
3. About 4%
4. less than 4%
5. Almost zero

1. A two-tailed Wilcoxon test
2. A two tailed t-test
3. A correlation analysis
4. A regression approach

1. you increase your power
2. you increase your type I error probability
3. you decrease your type II error probability
4. you improve your chances to find a difference, should there be one
5. All but (2) are correct

1. whether the residuals are continuous
2. whether the residuals are homogenous along the fitted values
3. whether the residuals are normal
4. all of the above
5. only (2) and (3) are correct

1. It ranges from -1 to 1
2. It is not necessarily associated with a p-value
3. It has nothing to do with the t-statistic
4. It is the normalised covariance
5. All of the above is correct

1. the same as sampling a value lower than -2
2. quite low, maybe a few percent
3. around 30%
4. infinitely small
5. 1 and 2 are correct

1. minimise the sum of squared differences between the observed values and the mean
2. minimise the distances between the fitted values and the observed values
3. minimise the sum of squared differences between the fitted values and the observed values
4. maximise the sum of squared differences between the fitted values and the observed values

1. your p-value is extremely low
2. your p-value is clearly not significant (i.e. not below 0.05)
3. your p-value is above 1
4. given the information, it is impossible to make a statement on the p-value

1. Describe an experimental setting that would require you to conduct a t-test

2. Make up the according data frame and conduct the test

3. Describe a situation in which you need a power test to determine the sample size. Come up with some numbers and perform the test.

4. Describe a setting in which you best use a linear regression model. Invent the numbers, conduct the complete analysis, including checking for the model assumptions and interpretation of the coefficients for the intercept and the slope.