lectures 7 & 8

Question 1

Issue with observational research:

Answer 1

Confounding variables (spurious causation)

Question 2

Causal effect of the treatment

Answer 2

the difference within and between groups

Question 3

Advantages of experiments (3)

Answer 3

1. Standardisation i.e. the same : stimuli, procedure, responses, variables
2. Random assignment → controls for confounding variables
3. Time order i.e. exposure to treatment (X) precedes the change in the outcome (Y)

Question 4

disadvantages of experiments (5)

Answer 4

1. Feasibility
2. Unrepresentative subject pool
3. Artificial environment
4. Noncompliance and attrition
5. ethical considerations

Question 5

natural experiments

Answer 5

Natural experiments are close to experiments but without the researcher’s ability to assign subjects to one group or another.
→ take advantage of situations in the real world, in which a treatment has been assigned at random, or as-if random, to a group of individuals by nature, politicians, etc.
We can compare the outcomes of the treatment and control groups.
E.g. lotteries

Question 6

difference in difference studies limitations

Answer 6

1. Parallel trends assumption: in the absence of treatment, the two cases would have followed the same path
2. There is no other relevant factor that also changed between the two cases in the period.
3. There is no interference between the cases

Question 7

probability distributions

Answer 7

A mathematical function that gives the probabilities of occurrence of different possible outcomes.
can be:
Symmetric
Bimodal
Skewed right
Skewed left

Question 8

Properties of the normal distribution:

Answer 8

1. The probability is highest at the mean
2. The distribution is symmetric around the mean
3. It is defined by two parameters: µ (the mean) and σ (the standard deviation)
4. Two parmeters → infinite number of normal distributions

Question 9

Proportions under the normal distribution

Answer 9

68% of the observations fall within one standard deviation above and below the mean.
95% of the observations fall within two standard deviations above and below the mean
99.7% of the observations fall within three standard deviations above and below the mean.

Question 10

standard deviations measures are often called

Answer 10

z scores

Question 11

z scores

Answer 11

indicates how many standard deviations a score is above or below the mean of its distribution, regardless of the original units of measurement.
Z = (X - µ) / σ
X Is the original score, µ is the mean, and σ is the standard deviation. The z-score tells you how many standard deviations it is above or below the mean.

Question 12

Z-scores: The standard normal distribution

Answer 12

The standard normal distribution is a special case of the normal distribution, for which µ = 0 and σ = 1
If the original distribution approximates a normal curve, then the shift to z-scores will produce a standard normal distribution, i.e., it has a mean of 0 and a SD of 1.

Question 13

Parameters

Answer 13

numerical measures that describe certain characteristics of a population

Question 14

Sample statistics

Answer 14

using estimates to describe the population
→ used to estimate a parameter, we rely on the sample mean to estimate the population mean

Question 15

The sampling distribution

Answer 15

a probability distribution of a statistic that is obtained through repeated sampling of a specific population.
It describes a range of possible outcomes for a statistic, such as the mean or mode of some variable, of a population.

Question 16

Sampling distribution of the sample mean

Answer 16

represents the mean of the overall population.

Question 17

central limit theorm

Answer 17

the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough.
NB: there are exceptions (e.g. highly skewed distribution)

Question 18

standard error

Answer 18

The standard deviation of the sampling distribution
Sample standard deviation / square root of n (size of sample) → SE = s / √ n

Question 19

properties of the standard error

Answer 19

→ will always be smaller than the standard deviation.
→ It allows us to assess whether a particular sample mean is rare (i.e. “abnormally” low or high).
→ it tells us how frequently we would get a sample that deviates from the hypothesized mean
→ low SD and a narrow distribution means that a sample is rare, and did not come from the general population

Question 20

Why do we need the standard deviation of the sample?

Answer 20

It tells us something about the population this sample came from. A sample with a large standard deviation, probably comes from a population that has a large standard deviation itself.
Hence, every time you take a sample, you are likely to get a pretty different mean.
A sample with a small standard deviation will instead have means that are more or less always the same.

Question 21

Why do we need the size of the sample?

Answer 21

Suppose you have a small sample size. Say, n = 2. Then by chance you are likely to get means that are all over the place.
If instead you have a larger sample size, you will get different means but these will average to something close to the population mean.
Moreover, you will get a mean that is more or less the same each time. I.e., a small standard error!

Question 22

how to increase confidence in a confidence interval

Answer 22

increase the sample size

Question 23

null hypothesis

Answer 23

Written H0
indicates that there is NO difference between groups (or NO relationship between the variables).
The results of the hypothesis test will indicate whether we reject or fail to reject the null hypothesis.

Question 24

alternative hypothesis

Answer 24

Written H1
The alternative hypothesis (H1) asserts the opposite of the null hypothesis:
H1 : µ ̸= (not equal) 100
Rejecting H0 implies support for H1.

Question 25

the decision rule

Answer 25

specifies precisely when H0 should be rejected. i.e., how rare a sample mean should be to conclude that our sample is special (i.e. different)?
We need to choose a level of significance (α).
A 5% significance level implies that values occurring by chance in only 5% of cases would be considered rare.