Week 4: Quantitative Methods I

In the context of statistics, what is a sample?

• is a smaller group that has been drawn from the population

  • the existence of stats is related to the existence of samples

  • informs us of the population — generalisation

In the context of statistics, what is a population?

• is to use a sample to understand something about the population it is drawn from

  • we have access to samples but not exactly populations

What is sampling with replacement?

once a member of the population has been sampled they can be sampled again

What is sampling without replacement?

once a member of the population has been sampled they cannot be sampled again

What are some non-random sampling methods?

• convenience sampling

• snowball sampling

• stratified sampling

What is convenience sampling?

• where units are selected for inclusion in the sample because they are the easiest for the researcher to access

  • adverts 4 participation

What is snowball sampling?

• one participant provides contact details for another participant

  • useful for recruiting hard-to-reach/hidden populations

  • advantage — allows for sampling from populations that might otherwise be unreachable

  • disadvantage — resulting sample is highly non-random

What is stratified sampling?

• deliberately sampling more from sub-populations — strata

  • people with schizophrenia and people who don’t have schizophrenia

  • sampling equal numbers from each group — we have oversampled people w/ schizophrenia relative to the general population

    • resulting sample is non-random — but may be well suited for asking other research questions

what is meant by a probability distribution?

a mathematical function that describes the probability of different possible values of a variable—how surprised should we be of the results?

How is a normal distribution defined?

described by its mean and standard deviation

In relevance to distribution, what is the mean?

It is the most likely value—the average score

In relevance to distribution, what is the standard deviation?

how spread out; how far away do values fall from the mean

Which graphic shows the same mean but different standard deviations?

B

Which graphic shows the different mean but same standard deviations?

A

Which graphic shows the different mean and different standard deviations?

C

What do norms have to do with normal distribution?

if scores are distributed normally then we can interpret a single measurement with reference to the norms of the scale

What is a percentile?

tell you what percentage of the population has a score or value that’s lower/same than yours

What is a percentage and how is it different to a percentile?

A percentage represents the ratio expressed in terms of 100 and it tells an individual score, while a percentile is relative to the score that others made and it tells the score or rank as compared to the others

What are the types of statistics we’ve gone through this semester?

• descriptive

• inferential

What is descriptive statistics?

• are used to describe a population or a sample

  • “how much does an adult red heeler typically weigh?”; asking about the centre — central tendency

  • “how much do different red heelers differ in how much they weigh”; spread of the distribution

What is inferential statistics?

• are used when we want to use data from a sample to draw conclusions about a population

  • to make a conclusion

What are the two types of descriptive statistics?

• measures of central tendency

• measures of spread

What is covered in the measures of central tendency?

• mean

• median

• mode

What is the mean?

• is the average or the most common value in a collection of numbers

  • arithmetic average of a distribution

What is the median?

the middle number in a sorted list of numbers

What is the mode?

the value most common in the distribution

How do you know which measure of central tendency to use?

• it depends on the shape of the underlying distribution

  • when data is normally distributed — all 3 three should give the same answer

  • when data is skewed — the median is preferred

    • median is less affected by high values — comparative to the calculation of the mean

  • categorical data — mode is the most useful

    • data measured on a nominal scale

What is covered in the measures of spread?

• variance

• standard deviation

• range

• inter-quartile range

What measures of the spread of the data around the mean?

variance and standard deviation

What is variance?

calculates the average squared difference of observations from the mean

In relevance to measures of spread, what is standard deviation?

is the square root of the variance

What is range?

• is the difference between its highest and lowest values

  • highest value — lowest value = range

What is inter-quartile range?

is the difference between its first and third quartile

What are some other ways to conceptulising data?

• continuous — observations can take on any value within the range of measurement

• discrete — there are only some values that observations can take

  • integers, categories

What are the 4 measurement scales?

• nominal

• ordinal

• interval

• ratio

What is a nominal scale?

• where the data is assigned to different categories and there is no systematic relationship between the different category labels

  • ethnicity, gender, brand etc

  • assesses differences between groups

What is an ordinal scale?

• data where there is an inherent rank/order between categories

  • levels (1, 2, 3) , types of difficulties (easy/med/hard)

  • wouldnʼt make sense to average them

What is an interval scale?

• numerical data with equal spacing between each number

  • temperature (farenheit), credit score

  • but the scale does not have a 0 point that indicates an absence of the quantity measured (0 is arbitrary)

What is a ratio scale?

THE BEST ONE—data have a meaningful numerical value, the intervals between different numbers are equivalent, and the scale has a true 0 point (absolute)

• weight, height, length, time

• can add, multiply, subtract, divide

• makes sense to average