Lecture 2 Basic maths check PDF

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Basic Maths check...

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Basic maths check Terminology    

Variables – the topics (height, gender etc.) Case – the ‘unit of observation’ (i.e. you!) Observation – specific answer for each person on a given variable Data – are a collection of observations – they whole data set

Uni, Bi and Multi 

Can analyse one, two or many variables at the same time o Univariate – dealing with one variable e.g. a univariate table having the number or percentage of people in prison in England and Wales in 2017 by ethnicities o Bivariate – two variables – a bivariate table displays the distribution of one variable across the categories of a second variable e.g. a table having prison population by ethnicity and sex, England and Wales  Cross-tabulation: a technique used to explore the relationship between two variables – make a table  Column variable: the variable whose categories comprise the columns of a bivariate table – column percentage – percentage within the column  Row variable: the variable whose categories comprise the rows of a bivariate table – row percentage – percentage within the row  Cell: the intersection of a row and a column in a bivariate table  Marginal: the row and column totals in a bivariate table o Multivariate – many variables

Populations vs Samples 

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The population is the whole group of people, or objects, or animals (a parameter) o All elements that are being studied o e.g. all Oscar nominated/winning films A sample is a subset of the population o Usually selected in order to be representative of the population – usually randomly (the statistics) o e.g. 1,100 British adults polled for the Ipsos MORI Political Monitor January 2019

Types of variables  

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We can think of different variables as having different ‘levels of measurement’ Continuous = infinite number of possible values – any value on a number line o Interval = a measurement where the difference between two values is meaningful i.e. temperature – when you do have zero but it’s an arbitrary (random) figure o Ratio = same as an interval variable but with a clear definition of zero as meaning ‘none of that thing’. i.e. height, weight – zero height means no height Categorical / Discrete= can be put into categories o Ordinal = Order of categories is meaningful i.e. low to high education levels o Nominal = No particular relevance of the order of categories i.e. eye colour

BODMAS/BIDMAS Brackets, Orders/Indices, Division, Multiplication, Addition, Subtraction Calculator Results    

Sometimes your calculator comes up with what looks like a strange result Say that you’re doing division: 0.24/60 On the calculator the answer may come up as 4-03x10 (Written as 4-03) This is not 4

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The -03X10 means that it is smaller than this– we put three zeros in front of it: 0.004

Standard Notation 

Formulas consist of letters in place of numbers, e.g.

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The little ‘i’ can stand for ‘individual’ – each person in each individual has a different X

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The

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So, in this formula you are taking the mean of X away from each individual score o This will give you a different result for each individual, not just one answer (as the Z has an ‘i’ too) Then will take divide this by standard deviation

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data set has a different value –

(or X-bar) means ‘the mean of X’ X bar is the mean of the data

When is pi not a pie?  

When we are talking about a proportion in the population (i.e. across everyone) we use the Greek letter π (pi) Do not use pi button on calculator

Proportions and Percentages   

π is a proportion o It is ALWAYS between 0 and 1 All proportions are between these limits A percentage is a proportion multiplied by 100

Guidelines for making tables       

Always have a clear title for a table which represents what is in there Always give tables a number (e.g. Table 1) Give appropriate and meaningful labels to rows and columns (e.g. ‘Male’ and ‘Female’ not ‘M’ & ‘F’) Take care with layout and format (be wary of defaults in Word, Excel) remove gridlines – vertical lines are distracting Refer to the source of the data Explicitly state the units of measurement (e.g. %, £, average) Tables should ‘stand-alone’

Things to avoid when making tables    

Too many decimal points If having percentages you do not need the numbers in each category o Just put the total number Cumulative percentages Clutter!

Different types of percentage   

Overall Row Column...