Semester 1 Flashcards
(62 cards)
1
Q
What is important to consider when looking at sample size?
A
- Size matters
- Sampling error can result if your ample is not large enough
- Trade off between size and time/cost
2
Q
Factors in deciding sample size?
A
o Design
o Response rate
o Heterogeneity of population
3
Q
What is a population parameter?
A
- a quantity that describes some characteristic of a population with respect to a specific variable
- E.g., population mean, population range etc.
- Not usually possible to calculate
- Might be given to you if available
4
Q
What is a sample statistic?
A
– a quantity that describes some characteristic of a sample with respect to a specific variable
- E.g., sample mean, sample range etc.
- We can always calculate these from a sample
- Sample statistics provide an estimate of population parameters
5
Q
Why is it important to summarise data?
A
- Data can be very complex and therefore it is useful to summarise it
- Allows for interpretation
6
Q
What are measures of central tendency?
A
They provide an indication of a “typical” score in the data set
7
Q
What is the mean?
A
o Provides and estimate of the average score in the data set
o Is affected by extreme data points
8
Q
What is the median?
A
o Is insensitive to extreme scores in the data set
o Doesn’t reflect the shape of the scores e.g., doesn’t care how far away the extreme scores are
9
Q
What is the mode?
A
o Easy to calculate from a histogram and easy to understand – the most common value
o Data might have more than 1 mode or no mode at all
10
Q
What is the range?
A
o Difference between min and max scores
o Range doesn’t always change for distributions with different shapes
11
Q
What is a deviation?
A
o The signed distance of a score from the mean
12
Q
How to calculate simple variance?
A
o Calc mean
o Calc deviations
o Square deviations
o Calc a slightly adjusted average squared deviation
- You divide by n-1
13
Q
What is the danger of bimodal data?
A
- Danger – mean is not representative
- Tends to suggest an issue with your experiment – more than one underlying population
14
Q
What is the normal distribution?
A
- Bell-shaped
- Symmetric about the centre
- Tails never reach 0 – go towards infinity
- The area under the centre is always equal to 1
- Very close to 0 by the time it gets to 3 SD from the mean – can use this to draw a rough idea of a normal distribution
15
Q
What is probability?
A
– a measure of how likely it is that an uncertain event will occur
16
Q
What is conditional probability?
A
- Probability of an event given that something else is known/assumed e.g., A|B
17
Q
What is a z-score?
A
- Z measures how far away your sample is from the population mean in multiples of the SD
- If you were to find z-scores for all points on a normal distribution, you would find that it would form a normal distribution with mean 0 and SD 1 – N (0, 1)
- The area underneath a normal distribution above/below some variable value of x EQUALS the area underneath N (0, 1) above/below z
18
Q
How do you obtain a z-score?
A
- Obtained by subtracting the population mean from x and then dividing by the population SD – (x-µ)/σ
19
Q
What is a sampling error?
A
Sampling error – the error associated with examining statistics calculated from a sample rather than the population
20
Q
Why do sampling errors occur?
A
- It occurs because in our sample we don’t have all the members of the population
21
Q
What does the magnitude of a sampling error depend on?
A
The sample size
- Bigger sample = big sampling error less likely
- Smaller sample = big sampling error more likely
22
Q
How do we generate a sampling distribution?
A
- Take a sample (size N) from a population
- Calculate a sample statistic (e.g., mean, SD etc.)
- Add the new statistic to a frequency plot (a histogram) of the sample statistic
- Repeated the above 3 steps multiple times
23
Q
What does the sampling distribution tell us?
A
- Tells us important info about how a statistic changes from sample to sample
- What is the mean value of the statistic over all samples?
- How variable is the statistic over all samples?
- What shape is the distribution of the statistic over all samples?
24
Q
What are the properties of the sampling distribution of the mean (SDM)?
A
- Mean which is the same as the parent population
- SD is different to that of the parent population – find by calculating σ (of p pop)/√N (sample size)
- SD is called the standard error of the mean (s.e.m.) or standard error (s.e.)
- S.e.m. must be smaller than SD of the parent population because you are diving by something that is bigger than one
25
What is a parent population a distribution of?
Parent population is a distribution of individual scores x (e.g., from an individual person or thing)
26
What is SDM a distribution of?
SDM is a distribution of sample means for samples of size N drawn at random from the parent population
27
What is central limit theorem?
- Given a population with a mean and SD, the sampling distribution of the mean approaches a normal distribution with a mean and SD sigma/ square root N as N increases
- This is true regardless of the underlying distribution – so even if your population is not normal, the distribution of means sampled from it will be
28
How do you find a z-score for a SDM?
z-score = (x-µ)/(σ/√N)
29
What is a point estimate?
– a single value estimate of a population parameter e.g., sample mean
30
What is an interval estimate?
– a range of possible values of a population parameter e.g., confidence interval
31
What is a confidence interval?
– describes an interval (e.g., a range) of values for our population parameter, together with a specified level of confidence that the parameter is in that range
32
For a sample drawn at random from a normal population N (µ, σ) with known s.d. σ ,the 95% CI for the population mean is centred on the sample mean m and goes from?
m – (1.96 x σ√N) to m + (1.96 x σ√N)
33
What does a 95% confidence interval mean?
A 95% confidence level means that if we repeated our sampling many times and worked out a new CI each time centred on our new sample mean we would expect the population mean to be in the interval on 95% of those repeats
34
True or False, if centred on sample mean, there is a 95% chance that the population mean is also in the range and vice versa (if looking for a 95% confidence interval)?
TRUE
35
True or False, if centred on sample mean, there is a 5% chance that the population mean falls outside of this range and vice versa (for a 95% confidence interval)?
TRUE
36
What are the steps for null hypothesis testing?
```
- Formulate research hypothesis
o Null hypothesis (H0)
o Research hypothesis (H1)
- Collect data
- Evaluate inconsistency with H0 and data
o How inconsistent are the data with H0?
- Reject or fail to reject H0?
- Interpret in context
```
37
True or false, If we were able to reject the null (H0) in favour of the research hypothesis (H1) then we can claim to have evidence for the research hypothesis?
True
38
True or false, If we fail to reject the null (H0) then we can claim to have evidence for the null hypothesis?
False
39
What do values of p > α suggest?
suggest not inconsistent with H0: fail to reject null
40
What do values of p > α suggest?
suggest not inconsistent with H0: fail to reject null
41
What do values of p < α suggest?
suggest inconsistent with H0: reject the null
42
What is the value of α in stats?
α = 0.05
43
What is the p-value?
p-value = the conditional probability associated with your sample statistic
44
How do you conduct a z-test?
- Use NHST framework
- Calculate inconsistency with mean by calculating the z-score, use the table to find the associated p-value and compare this to 0.05 to decide whether to reject or fail to reject the null hypothesis
45
When is a z-test used?
- To check if a sample mean that has been obtained is different from some population mean
46
What is a 1 tailed hypothesis that is right hand tailed?
- Something is better than the population
- H1: sample mean > population mean
- Looking for p-value above score
47
What is a 1 tailed hypothesis that is left hand tailed?
- Something is worse than the population
- H1: sample mean < population mean
- Looking for p-value below score
48
What is a two tailed hypothesis?
- Something is different than the population
- H1: sample mean =/= to population mean
- Looking for p value above and below score – have sample mean and then also find another value the same distance away from the population mean but on the other side. E.g., population mean = 67.5, sample mean = 70.7, the difference is 3.2 so the other value you should consider is 64.3 (z-score will be the same for the two)
- Conditional probability = 2 x p-value
49
When can you formulate a 1 tailed hypothesis?
- There is previous research
| - You can predict the effect
50
What is a type I error? Why does it occur?
- Rejecting the null hypothesis when it was correct – occur due to sampling error
51
What is a type II error? Why does it occur?
- Failing to reject the null hypothesis when it was incorrect
- Arise due to a number of reasons such as a biased sample, an error in the experimental task, sample size was too small etc.
52
Why do we use α = 0.05?
- It is small so it is difficult to reject the null hypothesis but not so small that it is impossible to do so
- It is a compromise between type I and type II errors
53
How is a student's t distribution similar to SND?
- Bell-shaped, symmetric, uni-modal
54
How is a student's t distribution different to SND?
- Has a lower peak, higher tails, have more variance
55
When is a student's t distribution used?
- When population s.d. is unknown
56
Does student's t distribution include a variety of t tests?
yes
57
How do you find the t statistic?
T(m) = (m-µ) / (s/√N)
58
How do you find the estimated standard error?
(s/√N) – estimated standard error
59
When using t distribution table, what value should you use for v?
When using t table – t (v = N-1) – subtract 1 off of sample size
60
How do you find confidence intervals when population s.d. is unknown?
- For 95% of repeat sample mean m would be within:
o Some number c e.s.e.’s of µ
o (µ- (c x s/√N) to µ+ (c x s/√N))
- To find c:
o Find t value for 0.025% in one tail (or 0.05% for 2 tails)
61
How do you conduct a 1 sample t test?
- Same as a z test except:
- Work out e.s.e.
- Find t statistic
- Find if t stat is inconsistent with critical value for corresponding t(n) and significance level
- Reject or fail to reject H0
- Interpret in context
62
When do you use a 1 sample t test?
- Use to test whether sample mean you have is different from some given or hypothetical population mean
