Week 4 - Quantitative Methods I PDF - PSY2041 Semester 2, 2023

PSY2041 Semester 2, 2023 Week 4: Quantitative methods I Daniel Bennett [email protected] image: detail from Evening (After Whistler) (1931) by Clarice Beckett  Lecture learning outcomes 1. Define what is meant by 'sample' and 'population' in the context of statistics,...

PSY2041 Semester 2, 2023 Week 4: Quantitative methods I Daniel Bennett [email protected] image: detail from Evening (After Whistler) (1931) by Clarice Beckett  Lecture learning outcomes 1. Define what is meant by 'sample' and 'population' in the context of statistics, and explain how the two concepts relate to each other. 2. Explain what is mean by a probability distribution, and interpret percentile norms in a normal distribution 3. Define the different descriptive statistics that measure the central tendency of a distribution: the mean, the median, and the mode. 4. Define the different descriptive statistics that measure the spread of a distribution: variance, standard deviation, range, and inter-quartile range. 5. Define the four different types of measurement scale (nominal, ordinal, interval, ratio) and identify the types of data that belong to each. Weekly reading Optional reading Shum et al., Chapter 3: pages 54-59 Navarro (2016). Learning Statistics with R. Chapters 2.2, 9.3, 9.4, 9.5 and 10.1 Shum et al., Chapter 6: pages 111-117 https://learningstatisticswithr.com/lsr-0.6.pdf PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Overview of this weekʼs videos Mini-lecture 1: Samples and populations Mini-lecture 2: Statistical distributions Mini-lecture 3: Descriptive statistics Mini-lecture 4: Measurement scales PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Mini-lecture 1 Samples and populations  Lecture learning outcomes 1. Define what is meant by 'sample' and 'population' in the context of statistics, and explain how the two concepts relate to each other. 2. Explain what is mean by a probability distribution, and interpret percentile norms in a normal distribution 3. Define the different descriptive statistics that measure the central tendency of a distribution: the mean, the median, and the mode. 4. Define the different descriptive statistics that measure the spread of a distribution: variance, standard deviation, range, and inter-quartile range. 5. Define the four different types of measurement scale (nominal, ordinal, interval, ratio) and identify the types of data that belong to each. PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Populations and samples Ø A population is the entire group of individuals, objects, or events that we are studying Ø The population of all living humans Ø The population of all humans, living or dead Ø The population of all household pets Ø The population of all PSY2041 students Ø The population of all land wars in Europe Ø A sample is a smaller group that has been drawn (or ʻsampledʼ) from the population Ø Thirty people chosen at random on Bourke Street at 3pm on a Monday Ø A telephone sample of people who agree to answer questions about their voting intention Ø All land wars in Europe in the 19th century Ø A common goal in using statistics is to use a sample to understand something about the population it is drawn from Ø Because we have access to samples, but we (usually) donʼt have access to populations PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  An illustration The population A sample from the population PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  An illustration The population of all border terriers A sample from the population (Ajax, age 8 months) PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Populations and samples Ø A common goal in using statistics is to use a sample to understand something about the population it is drawn from The population Ø In psychological testing and assessment, we might be interested in using a test to understand a population like all people diagnosed with schizophrenia Ø In this case, the participants with schizophrenia who we recruit to complete the test are a sample from the larger population of people with schizophrenia Ø Alternatively, we might be interested in a population like all possible questionnaire items that measure creativity Ø In this case, the items in a questionnaire are a sample from that larger population of items A sample from the population PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  An illustration The population of all PSY2041 students Average IQ in the general population = 100 Average IQ in a sample of 30 PSY2041 students = 115 Q: What is the average IQ of PSY2041 students? A: Probably around 115, but there is not enough information provided to know exactly Q: Do PSY2041 students in general have a higher average IQ than the general population? A: There is not enough information provided to know A sample from the population (30 students) PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Sampling methods Ø Where do samples come from? How are they drawn from populations? Ø In general, samples are most informative when they are drawn randomly from a population Ø Random = each individual from the population is equally likely to be chosen to be part of the sample Ø We can consider two kinds of random sampling: sampling with replacement and sampling without replacement PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett Sampling without replacement Navarro (2016): https://learningstatisticswithr.com/lsr-0.6.pdf, Chapter 10 Ø If samples are taken without replacement, then once a member of the population has been sampled, they cannot be sampled again Ø They are not ʻreplacedʼ in the population after having been sampled Sampling without replacement Navarro (2016): https://learningstatisticswithr.com/lsr-0.6.pdf, Chapter 10 Ø If samples are taken with replacement, then once a member of the population has been sampled, they can be sampled again Ø They are ʻreplacedʼ in the population after having been sampled  Sampling methods Ø Where do samples come from? How are they drawn from populations? Ø In general, samples are most informative when they are drawn randomly from a population Ø Random = each individual from the population is equally likely to be chosen to be part of the sample Ø We can consider two kinds of random sampling: sampling with replacement and sampling without replacement Ø In psychology, we usually do sampling without replacement, but most of our statistical methods actually assume that sampling is done with replacement Ø And actually, most of our samples are not random! PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett Non-random sampling methods Navarro (2016): https://learningstatisticswithr.com/lsr-0.6.pdf, Chapter 10 Ø Convenience sampling: samples are chosen in a way that is convenient to the researcher Ø e.g., undergraduate psychology students Ø Important to consider whether results from your sample are likely to generalise to other populations Ø Snowball sampling: one participant provides contact details for another participant Ø Useful for recruiting from hard-to-reach or ʻhiddenʼ populations (e.g., research with transgender participants) Ø Advantage: allows for sampling from populations that might be otherwise unreachable Ø Disadvantage: the resulting sample is highly non-random Ø It is important to consider the ethical considerations of snowball sampling carefully before using it Ø Stratified sampling: deliberately sampling more from some sub-populations (ʻstrataʼ) e.g., people with schizophrenia and people who donʼt have schizophrenia Ø if we sample equal numbers from each group, we have ʻoversampledʼ people with schizophrenia relative to the general population Ø the resulting sample is non-random, but may be well suited for asking other research questions (e.g., differences between groups)  Do we ever observe the entire population? Ø We do not usually observe the entire population, but it is possible Ø e.g., the population of all PSY2041 students Ø The census is an attempt to observe the entire population of people living in Australia Ø But even then, many people donʼt or canʼt respond ‒ so what is the population being measured, really? Ø Can be done by defining the population in unusual ways Ø “the population of all border terriers owned by a psychology lecturer at Monash University” Ø But this isnʼt a population that lends itself to many important research questions PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Mini-lecture 2 Statistical distributions  Lecture learning outcomes 1. Define what is meant by 'sample' and 'population' in the context of statistics, and explain how the two concepts relate to each other. 2. Explain what is mean by a probability distribution, and interpret percentile norms in a normal distribution 3. Define the different descriptive statistics that measure the central tendency of a distribution: the mean, the median, and the mode. 4. Define the different descriptive statistics that measure the spread of a distribution: variance, standard deviation, range, and inter-quartile range. 5. Define the four different types of measurement scale (nominal, ordinal, interval, ratio) and identify the types of data that belong to each. PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Places that Ajax likes to sleep On his On his On top of On the couch On the rug inside bed outside bed the speaker PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Places that Ajax likes to sleep Ø Having watched Ajax, I know that he likes sleeping in some of these places more than others Ø One way of capturing this knowledge about Ajax is in a probability distribution Ø Probability distributions represent the likelihood of different events with numbers between 0 and 1 Ø 0 = event has no chance of happening Ø 1 = event is certain to happen Ø 0.5 = event has a 50% chance of happening Ø The probabilities of all events together have to add up to 1 PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Probability and the ʻsurprisingnessʼ of events Ø The lower the probability of an event, the more surprised we should be when it happens Ø So I should be surprised if I walk into the room and Ajax is sleeping on the speaker... Ø...but not so surprised if I walk into the room and he is sleeping on the rug PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett Populations, samples and statistical inference Ø A distribution is a way of representing the possible values for a variable and how often each value occurs (or is likely to occur) Ø All probability distributions can all be interpreted this way Ø Some special/common distributions are given names The distribution of adult hand lengths The distribution of number of pets owned  A coin-tossing example Ø If we toss a fair coin, it has a 50% chance of coming up Binomial distribution for N = 1 heads and a 50% chance of coming up tails and Pr(heads) = 0.5 Ø Pr(Heads) = 0.5, Pr(Tails) = 0.5 PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  A coin-tossing example Ø An AFL team plays 23 games in a season. Before each Binomial distribution for N = 23 game, a coin is tossed to determine which team picks and Pr(correct) = 0.5 the end they are kicking to Ø How many coin tosses should we expect a team to win each season? Ø Assuming the captain predicts with 50% accuracy PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  A coin-tossing example Ø An AFL team plays 23 games in a season. Before each Binomial distribution for N = 23 game, a coin is tossed to determine which team picks and Pr(correct) = 0.9 the end they are kicking to Ø How many coin tosses should we expect a team to win each season? Ø Assuming the captain is clairvoyant and can predict with 90% accuracy which way the coin will come down PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  The normal distribution Ø The normal distribution (aka Gaussian distribution) is one of the most common in the real world Ø Human height and weight, IQ scores, many personality traits Ø It has a characteristic ʻbell shapeʼ mean standard deviation Ø Any normal distribution is completely described by its mean and standard deviation PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  The normal distribution The distribution of hand lengths (in the population of all adult humans) Mean = 18.5 cm Standard deviation = 1.4 cm PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett Different normal distributions Different mean, different standard Different mean, deviation same standard deviation Same mean, different standard deviation Norms Ø If scores are distributed normally, then we can interpret a single measurement with reference to the norms of the scale The weight distribution of border terriers (mean = 5.8, standard deviation = 1.2) Norms Ø If scores are distributed normally, then we can interpret a single measurement with reference to the norms of the scale The weight distribution of border terriers (mean = 5.8, standard deviation = 1.2) Ø 68.3% of observations fall within 1 SD of the mean Norms Ø If scores are distributed normally, then we can interpret a single measurement with reference to the norms of the scale The weight distribution of border terriers (mean = 5.8, standard deviation = 1.2) Ø 68.3% of observations fall within 1 SD of the mean Ø 95.4% of observations fall with 2 SDs of the mean Norms Ø If scores are distributed normally, then we can interpret a single measurement with reference to the norms of the scale The weight distribution of border terriers (mean = 5.8, standard deviation = 1.2) Ø 68.3% of observations fall within 1 SD of the mean Ø 95.4% of observations fall with 2 SDs of the mean Ø 15.9% of observations fall more than 1 SD below the mean Norms Ø If scores are distributed normally, then we can interpret a single measurement with reference to the norms of the scale The weight distribution of border terriers (mean = 5.8, standard deviation = 1.2) Ø 68.3% of observations fall within 1 SD of the mean Ø 95.4% of observations fall with 2 SDs of the mean Ø 15.9% of observations fall more than 1 SD below the mean Ø Ajax weighs 8kg. This puts him in the 97th percentile for border terriers Types of probability plots Ø We have shown mostly theoretical distributions in this video Ø Real-world sample distributions are often a bit messier, and are usually plotted with histograms rather than continuous ʻdensityʼ plots A density plot of hand lengths A histogram plot of hand lengths (in the population of all adult humans) (in 30 randomly sampled human adults)  Mini-lecture 3 Descriptive statistics  Lecture learning outcomes 1. Define what is meant by 'sample' and 'population' in the context of statistics, and explain how the two concepts relate to each other. 2. Explain what is mean by a probability distribution, and interpret percentile norms in a normal distribution 3. Define the different descriptive statistics that measure the central tendency of a distribution: the mean, the median, and the mode. 4. Define the different descriptive statistics that measure the spread of a distribution: variance, standard deviation, range, and inter-quartile range. 5. Define the four different types of measurement scale (nominal, ordinal, interval, ratio) and identify the types of data that belong to each. PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Different kinds of statistics Ø The two different kinds of statistics we work with in psychology are descriptive statistics and inferential statistics Ø Descriptive statistics are used to describe a population or a sample Ø e.g., “how much does an adult border terrier typically weigh?” Ø e.g., ”how much do different border terriers differ in how much they weigh?” PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Different kinds of statistics Ø The two different kinds of statistics we work with in psychology are descriptive statistics and inferential statistics A histogram plot of hand lengths Ø Descriptive statistics are used to describe a (in 30 randomly sampled human adults) population or a sample Ø e.g., “how much does an adult border terrier typically weigh?” Ø e.g., ”how much do different border terriers differ in how much they weigh?” Ø e.g., “what is the average hand length in my sample of 30 adults?” PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Different kinds of statistics Ø The two different kinds of statistics we work with in psychology are descriptive statistics and inferential statistics A histogram plot of hand lengths Ø Descriptive statistics are used to describe a (in 30 randomly sampled human adults) population or a sample Ø Inferential statistics are used when we want to use data from a sample to draw conclusions about a population Ø “How likely is it that my sample comes from the general population?” PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Different kinds of statistics Ø The two different kinds of statistics we work with in psychology are descriptive statistics and inferential statistics Ø Descriptive statistics are used to describe a population or a sample Ø Inferential statistics are used when we want to use data from a sample to draw conclusions about a population Ø “A football team wins 22 of 23 coin tosses. How likely is it that they are somehow cheating?” PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett Descriptive statistics Ø In PSY2041, there are two kinds of descriptive statistics that we will cover Ø (There are also other kinds of descriptive statistics, but they are beyond the scope of this unit) Ø Measures of central tendency: what is the centre or middle of the distribution? Ø Mean Ø Median Ø Mode Ø Measures of spread: how spread-out is the distribution? How similar/varied are the observed values? Ø Variance Ø Standard deviation Ø Range Ø Inter-quartile range  Measures of central tendency: the mean Ø The mean is the arithmetic average of a distribution Ø This is the most commonly used measure of central tendency Student Test score number out of 10 1 4 Ø To calculate the mean, we add all the observations together 2 5 and divide by the number of observations 3 5 AAAB/3icbVDJSgNBEO1xjXEbFbx4aQyCpzAjbhch6MWTRDALZIbQ0+lJmnT3DL2IYZyDv+LFgyJe/Q1v/o2d5aCJDwoe71VRVS9KGVXa876dufmFxaXlwkpxdW19Y9Pd2q6rxEhMajhhiWxGSBFGBalpqhlpppIgHjHSiPpXQ79xT6SiibjTg5SEHHUFjSlG2kptdzfgBl7AIJYIZ4EyHD7k2U3edkte2RsBzhJ/Qkpggmrb/Qo6CTacCI0ZUqrle6kOMyQ1xYzkxcAokiLcR13SslQgTlSYje7P4YFVOjBOpC2h4Uj9PZEhrtSAR7aTI91T095Q/M9rGR2fhxkVqdFE4PGi2DCoEzgMA3aoJFizgSUIS2pvhbiHbBTaRla0IfjTL8+S+lHZPy2f3B6XKpeTOApgD+yDQ+CDM1AB16AKagCDR/AMXsGb8+S8OO/Ox7h1zpnM7IA/cD5/AH6Qlcs= P 4 6 x 5 6 µ= 6 7 N 7 8 8 8 9 8 Mean = (4 + 5 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 10) / 10 10 10 = 67 / 10 = 6.7 PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Measures of central tendency: the mean Mean = 6.7 Student Test score number out of 10 1 4 2 5 3 5 4 6 5 6 6 7 7 8 8 8 9 8 10 10 PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Measures of central tendency: the median Ø The median is the point that 50% of observations fall above Student PSY2041 and 50% of the observations fall below number final mark 1 50 Ø When there is an odd number of 5 2 50 observations, the median will be observations 3 57 below equal to the ʻmiddleʼ observation 4 62 5 65 Median = 68 6 68 7 74 8 79 5 observations 9 80 above 10 81 11 87 PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Measures of central tendency: the median Ø The median is the point that 50% of observations fall above and 50% of the observations fall below Student Test score number out of 10 1 4 Ø When there is an odd number of 5 2 5 observations, the median will be observations 3 5 equal to the ʻmiddleʼ observation below 4 6 5 6 Ø When there is an even number of Median = 6.5 6 7 observations, the median is the 7 8 5 average of the middle two observations 8 8 observations above 9 8 10 10 PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Measures of central tendency: the mode Ø The mode is simply the value that occurs most commonly in the distribution Student PSY2041 Student Test score number final mark number out of 10 1 50 Mode = 50 1 4 2 50 2 5 3 57 3 5 4 62 4 6 5 65 5 6 6 68 6 7 7 74 7 8 8 79 Mode = 8 8 8 9 80 9 8 10 81 10 10 11 87 PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Measures of central tendency Q: When should you use the mean vs. median vs. mode? A: It depends on the shape of the underlying distribution Ø When data are normally distributed, all three should give the same answer Ø The median is typically preferred when data are skewed Ø When data are positively skewed, the mean will be higher than the median Ø When data are negatively skewed, the mean will be lower than the median PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Measures of central tendency Q: When should you use the mean vs. median vs. mode? A: It depends on the shape of the underlying distribution Ø The mode is most useful for categorical data Ø Though there are some cases where the mode makes sense even for non-categorical data Ø e.g., is it meaningful to say that people have a mean of 9.99 toes? PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett Measures of spread: standard deviation and variance Ø Distributions with large spread have values that fall further from the centre of the distribution Ø A natural way to quantify spread is therefore to calculate the average distance between observations from a distribution and the mean of the distribution Ø This is the idea underlying both variance and standard deviation Ø However, ʻaverage difference from meanʼ fails as a measure of spread Day Number of walks Ajax gets 1 1 2 5 Mean = 3 walks per day 3 1 4 5 Measures of spread: standard deviation and variance Ø Distributions with large spread have values that fall further from the centre of the distribution Ø A natural way to quantify spread is therefore to calculate the average distance between observations from a distribution and the mean of the distribution Ø This is the idea underlying both variance and standard deviation Ø However, ʻaverage difference from meanʼ fails as a measure of spread Day Number of Difference walks Ajax gets from mean 1 1 -2 2 5 +2 Average difference from mean = 0 3 1 -2 4 5 +2 Measures of spread: variance Ø Variance calculates the average squared difference of observations from the mean 2 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 2 ⌃ (X µ) = N Variance = (4 + 4 + 4 + 4) / 4 =4 Day Number of Difference Squared difference walks Ajax gets from mean from mean 1 1 -2 +4 2 5 +2 +4 3 1 -2 +4 4 5 +2 +4 Measures of spread: variance Ø The standard deviation is the square root of the variance Ø Taking the square root ʻundoesʼ the squaring of differences Ø The standard deviation is the average distance between observations and the mean 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 s 2 ⌃ (X µ) = N Variance = 4 SD = 2 Day Number of Difference Squared difference walks Ajax gets from mean from mean 1 1 -2 +4 2 5 +2 +4 3 1 -2 +4 4 5 +2 +4  Measures of spread: range and inter-quartile range Ø The range of a distribution is the difference between its highest and lowest values Ø e.g., if the oldest PSY2041 student is 42 and the youngest is 19, then the range of ages in PSY2041 students = (42 ‒ 19) = 23 Ø The inter-quartile range of a distribution is the difference between its first and third quartiles Ø First quartile (Q1): the value that has 25% of the distribution below it and 75% above it Ø First quartile (Q3): the value that has 75% of the distribution below it and 25% above it Ø IQR = Q3 - Q1 PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Mini-lecture 4 Measurement scales  Lecture learning outcomes 1. Define what is meant by 'sample' and 'population' in the context of statistics, and explain how the two concepts relate to each other. 2. Explain what is mean by a probability distribution, and interpret percentile norms in a normal distribution 3. Define the different descriptive statistics that measure the central tendency of a distribution: the mean, the median, and the mode. 4. Define the different descriptive statistics that measure the spread of a distribution: variance, standard deviation, range, and inter-quartile range. 5. Define the four different types of measurement scale (nominal, ordinal, interval, ratio) and identify the types of data that belong to each. PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Different kinds of data Ø Another common way of describing the different kinds of data is as nominal, ordinal, interval, or ratio Ø Nominal scale: data are assigned to different Mode of transport Number of people categories, and there is no systematic relationship Car 122 between the different category labels Public transport 61 Ø Also known as categorical data Bike 8 Ø e.g., responses to a survey asking students what mode Walk 20 Submarine 0 of transport they used to get to uni Helicopter 1 Ø It doesnʼt make any sense to say that any of these options is bigger or better than the others Ø It definitely doesnʼt make any sense to average them PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Different kinds of data Ø Another common way of describing the different kinds of data is as nominal, ordinal, interval, or ratio Ø Ordinal scale: data are assigned to different categories, and the different categories can be PSY2041 rating Number of people placed in a meaningful order Catastrophically bad 3 Bad 6 Ø e.g., responses to a survey asking students to rate Just OK 62 PSY2041 Good 84 Ø These categories can be placed in an order from worst Life changingly 1 to best wonderful Ø But we canʼt guarantee that the ʻdistanceʼ between the different categories is always equal Ø We can assign numbers to the different categories, but it still wouldnʼt make sense to average them PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Different kinds of data Ø Another common way of describing the different kinds of data is as nominal, ordinal, interval, or ratio Ø Interval scale: data have a meaningful numerical value and the intervals between different numbers First year of degree Number of people are equivalent 2019 2 2020 6 Ø but the scale does not have a 0 point that indicates an 2021 18 absence of the quantity measured 2022 128 Ø e.g., what year did you start your degree? 2023 1 Ø addition/subtraction of data makes sense, multiplication/division does not PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett  Different kinds of data Ø Another common way of describing the different kinds of data is as nominal, ordinal, interval, or ratio Ø Ratio scale: data have a meaningful numerical value, the intervals between different numbers are Number of Number of playmates at recess children equivalent, and the scale has a meaningful 0 point 0 3 Ø e.g., how many different children does an 8-year-old 1 8 child play with during their recess break? 2 13 Ø addition/subtraction/multiplication/division of data all 3 13 make sense 4 5 5 8 Ø Averaging makes sense 6 2 7 0 PSY2041 ‒ Quantitative Methods I ‒ Daniel Bennett Another way of conceptualising data Ø Continuous: observations can take on any value within the range of measurement Ø For any two values that you can think of, it is always logically possible to have another value in between Ø Discrete: there are only some values that observations can take (e.g., integers, categories) Ø It is sometimes the case that there is no ʻmiddleʼ value between two possible values The distribution of adult hand lengths The distribution of number of pets owned