Inference Flashcards
What is a latent variable?
Latent variables are things that are not directly measurable such as attitudes, beliefs, perceptions and so on.
What is psychometrics? And Galton’s theory
Psychometrics is the field of study concerned with
psychological measurement. Psychometrics are concerned with measuring latent variables. In order to measure latent variables, which are not directly observable, we measure a co-related observable variable which allows us to draw inferences. These co-related variables are referred to as ‘items’. An example would be measuring aggression, the item would be seeing if someone uses violence.
When we look at a sample and take the mean/SD/SE/etc. we are are looking at …….
However, when we look at a whole population’s mean/SD/SE/etc. we are looking at ……….
Statistics
Parameters
The statistic is the estimator of the model parameter
How can a statistic and a parameter be distinguished visually?
Statistic uses latin symbols
Parameter uses greek symbols
Why is it that 3 different samples will have different means? Why would each mean from each different sample, but different to the population mean?
This is due to ‘random error’
If we are looking at ‘how often do people exercise per week’ and we take a sample of people on the street. However, we are taking this sample on the street but outside of a gym. Why would this sample have a different mean to the population mean?
This is due to a systematic error! This is a bias sample
When we describe data, if there is a small random error this means our data is more ….
If there is a small systematic error this means our data is more …..
- small random error - more reliable
2. small systematic error - more valid
What do we mean by ‘reliability’?
Every time you reproduce the same test, you will receive the same result. The reproducibility of a result. Reliability is about the reproducibility, the consistency, and the precision of a measurement.
What do we mean by ‘validity’?
The validity is our ability to compare the result to a ‘gold standard’, and if it is close to this gold standard then it is valid (accurate). Validity is about the accuracy of the measurement, based on the current knowledge.
Are results always valid and reliable at the same time?
No - A result can never be valid without also being reliable.
However, a result can be reliable but does not mean it is valid (e.g. could get the same result 100 times, but the scales you are using to measure are wrong).
What are the key features of random error? And, what does it mean if the random error is small?
- Unpredictable
- It can go up or down on either side
- It is due to completely random factors
- If small, it is more RELIABLE
What are the key features of systematic error? And, what does it mean if the systematic error is small?
- Consistent
- You always underestimate or overestimate the true value
- Due to factors which can be traced
- If small, then we have more VALIDITY
What is the ‘sampling distribution of the mean’? (if normally distributed, random error)
The sampling distribution is the distribution of multiple sample’s mean. It is the “distribution of the estimated means from different samples”
How does the sampling distribution of the mean fit into the central limit theorem? (if normally distributed, random error)
Theory states that if we take more and more and more samples from the same population, then the sampling distribution of the statistic mean will be a normal distribution
What is the mean of the sampling distribution? (if normally distributed, random error)
The mean of the sampling distribution is the mean of the population which the sample came from. The mean of all the sample means is the population mean! All sample means should come under this population mean.
In normally distributed data,
the population mean is …..
the population variance is ….
- mean of the sample means - mean of sampling distribution
2. The variance of the samples’ means is actually the population variance, divided by the sample size
What is the ‘population variance’ and how do we work this out?
The variance of the samples’ means is actually the population variance, divided by the sample size.
What is the standard error? Write the formula for this
The standard error is a measure of how much an estimate (sample mean) will vary over repeated sample. It is the standard deviation of the sampling distribution (mean of means).
- square root the sample size
- divide the SD by the ^above answer (square root the sample size)
- the answer is the SE
The sd of the sampling distribution is equal to…
…the sd of the population divided by the square root of the sample size.
Fill in the blanks:
The ‘…’ sample mean is the … of the population ‘…’ mean
Statistics
Estimator
Parameter
A researcher estimated the expected mean age in a population of interest to be 20 (sd = 5), with 95% CI to be (17.8, 22.2). If the researcher would have calculated the 99% CI then this would be …
WIDER as 99%
Two researchers used two samples and studied the expected hours of sleep in the population. They both came up with the same mean = 8.5 and sd = 2 hours. The 95% confidence interval for Researcher A was (7, 9) and the 95% confidence interval for Researcher B was (6, 11). Which of the two researchers had the larger sample size?
Researcher A
In terms of standard error - The bigger the sample, what will happen?
The larger the sample size, the smaller the standard error (random error). Thus, we have greater precision in our estimation.
In terms of standard error - The smaller the variability of our sample, what happens to the SE?
The smaller the variability in our sample, the smaller the standard error (random error). Thus, we have greater precision in our estimation.
What is a confidence interval? Why would we calculate this?
The confidence interval is the plausible range in which the sample point estimate should almost always fall in (depends if 90%, 95%, or 99%).
Rather than estimating a single value for the population mean & sd (parameters) estimating a plausible range would be more sensible to take account of the random error from one sample to the next.
Write the formula for working out the 95% confidence interval…
Step by step:
- Work out the SE (SD divided by the square root of the sample size)
- Now for the lower: mean - (1.96 * SE)
- Now for the upper: mean + (1.96 * SE)
What is the number for 90% CI?
95% CI?
99% CI?
- 65
- 96
- 58
Which CI has the most precision and which has the least? Why might we choose a CI with more precision?
90% (1.65) has less precision, 95% (1.96) middle, 99% (2.58) most precision
Depends on the varible, for example something like could be life-threatening or potenitally dangerous (e.g. violent crime stats) we want to be very precise!
What does BIDMAS stand for?
Brackets Indicies Division Multiply Addition Subtract
