PSYC20008 Lecture Notes - Lecture 6: Chi-Squared Distribution, Fruitarianism, Categorical Variable
14 Jun 2018
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Lecture 6 - Thursday 16 March 2017
PSYC20006 - DEVELOPMENTAL PSYCHOLOGY
LECTURE 6
CHI SQUARE
MEASUREMENT
•Putting numbers to a construct helps us to measure that construct
•Think about something you would like to measure:
•How many stars are in the sky?
•Is that pigeon dead or alive?
•How many people in the lecture are omnivores, vegetarians, vegans or fruitarians?
•How anxious is that person over there?
•Who received a H1, H2A, H2B, H3, or a Pass in last semester’s exam?
•“The relationship between what is being measured and the numbers that represent what is being
measured is known as the level of measurement” Field (2013)
•Variables can be split into:
•Categorical
•Continuous
•Within these types of measurements are different levels of measurement;
•Categorical
•Binary, nominal, ordinal variables
•Continuous
•Interval, ratio
TYPES OF DATA
CATEGORICAL DATA
•Entities are divided into distinct categories
•Binary variable: there are only 2 categories
•(e.g. dead or alive; yes or no)
•Nominal variable: there are more than two categories
•(e.g. vegan, omnivore, vegetarian, fruitarian)
•Ordinal variable: A nominal variable that has a logical, ordered order
•(e.g. H1, H2A, H2B, H3, Pass)
CONTINUOUS DATA
•Entities receive a distinct score on a measurement scale
•Interval variable: equal intervals on the variable represent equal differences in the property being
measured.
•(e.g. difference between 2 and 4 is the same as the difference between 20 and 22)
•Ratio variable: Same as interval variable but the ratios are meaningful, with a true zero point
•(e.g. response times to the appearance of a target)
DISTINCTION?
•We can measure continuous data as categories
•Age (years)
•We can treat categorical variables as if they were continuous
•Average number of boyfriends that women in their 20s have is 4.6 (.6 of a boyfriend?)
ANALYSING CATEGORICAL DATA
•We want to quantify the relationship between two categorical variables
•(We can’t use the mean because a mean of categorical data is meaningless)
•We analyse the number of things that fall into each category,
•i.e. the count
•Also known as the frequency
Lecture 6 - Thursday 16 March 2017
PSYC20006 - DEVELOPMENTAL PSYCHOLOGY
DIFFERENT TYPES OF DISTRIBUTIONS
•http://en.wikipedia.org/wiki/List_of_probability_distributions
•When measuring something in a population, there is typically a spread of scores in the data
•Almost all measures are made with some error (random errors and uncertainty about the
measure*)
•Statistics is the science of measurements and their errors.
•Data can follow certain patterns (or distributions)
•Mathematicians have described many different distributions, which have their own properties
•We can use these distributions to our advantage...
FREQUENCY PERSPECTIVE
•Frequency perspective: take a population and measure each person’s height.
•Graph this data on a histogram (or frequency distribution).
•Height follows a normal (bell-shaped) (Gaussian) curve/distribution
PROBABILITY PERSPECTIVE
•Probability perspective: take a person at random and measure their
height.
•What is the probability that they will be ~170cm tall?
•Another way of asking this question is “How big is the blue area
compared with all the values of the bars?”
•Total count: 53,298 people
•170cm people: 8,700
= !8,700 !
53,298
= !0.16
= !16% is the height between 170-180cm tall.
•Size of the bars relate directly to the probability of an event occurring.
•Probability of an event occurring ranges from 0 to 1.
ADVANCED SLIDE: NOT NEEDED FOR EXAM. TYPES OF DISTRIBUTION
•For any distribution of scores we can calculate the probability of obtaining a score of a certain
size
•Statisticians have done this for us, by:
•Identifying several common distributions of data (e.g. Gaussian, chi, t, F)
•Working out probability density functions that specify idealised versions of these distributions
•If you plot the value of the variable (x) against the probability of it occurring (y), the resulting
curve is a probability distribution
•The normal curve is a probability distribution
•Probability distributions come in many different shapes
•These shapes can be described mathematically and have assumptions associated with them
•We can use these distributions to calculate the precise probability of obtaining a given score
Z SCORES
•Distributions of data will have different means and SDs. If we want to make use of a distribution
that we already know the characteristics of, we can convert our distribution of data onto the
Gaussian curve, to hep us understand the probability of something occurring.
•We can make use of the already calculated probabilities associated with the normal/Gaussian
distribution (phew!)
•To do this, we need to convert our data so it has a mean of 0 and a SD of 1. Form here we can
find our probabilities of something occurring.
•Z = each score – group mean
group standard deviation
Document Summary
Distinction: we can measure continuous data as categories, age (years, we can treat categorical variables as if they were continuous, average number of boyfriends that women in their 20s have is 4. 6 (. 6 of a boyfriend?) Frequency perspective: frequency perspective: take a population and measure each person"s height, graph this data on a histogram (or frequency distribution), height follows a normal (bell-shaped) (gaussian) curve/distribution. = 16% is the height between 170-180cm tall. Z scores: distributions of data will have different means and sds. If we want to make use of a distribution that we already know the characteristics of, we can convert our distribution of data onto the. Form here we can find our probabilities of something occurring: z = each score group mean group standard deviation. Psyc20006 - developmental psychology: our data is now fitted onto the normal curve. We assume the null hypothesis is true (i. e. there is no effect: 2.
