STATS - relationships and covariance

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what is cross tabulation? what does it show?
a statistical technique used to display breakdown of the data to understand the relationship between multiple variables, each cell shows the percentage falling in each combination of the categories.
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how does cross tabulation work if there are two continuous variables i.e too many levels to the data?
the data is divided into bands, i.e each column shows a range between values
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what are continuous variables?
variables that can take on any numeric value and can be divided into smaller sections
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what is a nominal variable?
variables with no numeric value, they are named i.e occupation or gender.
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how can the relationship between nominal variables be shown in diagrams?
compound or stacked bar charts
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what is a stacked bar chart?
shows sub-groups, but the sub-groups are stacked on the same bar. Each bar shows the total for sub-groups within each individual category
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what is a compound bar chart?
a graph which combines 2 or more types of info in one chart. Columns of each nominal variable are split into sections to show the breakdown of data and are coloured differently to show the different variables being compared.
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how can continuous and nominal variables be shown in a table?
the mean and other descriptives for the continuous variable can be shown in a table
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what diagrams can be used for continuous and nominal variables?
a bar chart to display the means of the score variable in each category
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what other diagram can be used only for continuous variables?
a scatter diagram, a graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present.
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what is a line of best fit?
The line of best fit (or trendline) is an educated guess using a line about where a linear equation might fall in a set of data plotted on a scatter plot.
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how does the line of best fit indicate a positive correlation?
If there is a positive relationship between your variables there will be a general trend from the bottom left to the top right
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how does the line of best fit indicate a negative correlation?
If there is a negative relationship between your variables there will be a general trend from the top left to the bottom right
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what is covariance?
a quantitative estimate of how two variables covary (i.e. change together), using a single number to illustrate this.
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what is the formula for covariance?
see document.
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how do you work out the formula for covariance?
Subtract mean of x scores from each individual x score. Subtract mean of y scores from each individual y scores. This will give you two separate numbers. Multiply these two numbers together. Divide this by number of pps.
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explain how covariance is applied to a graph?
see document.
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what does a positive correlation on a graph mean in terms of covariance?
A positive covariance means that as one score increases the other increases as well
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what does a negative correlation on a graph mean in terms of covariance?
A negative covariance means that as one score decreases the other decreases as well.
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what does it mean if there is a covariance of zero?
there is no relationship between the variables.
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why is standardisation a problem in covariance?
it doesn’t allow us to compare different data sets with different measurements as covariance values are not standardised.
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how do you standardise covariance? why?
correlation coefficient, by dividing the covariance values by the standard deviation, it essentially scales the value down to a limited range of -1 to +1 which is therefore standardised
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what are the two features of covariance?
magnitude and direction
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what is magnitude?
how big the covariance value is, the bigger it is the stronger the correlation.
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how can we tell the direction?
by whether the covariance is positive or negative.
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Other cards in this set

Card 2

Front

how does cross tabulation work if there are two continuous variables i.e too many levels to the data?

Back

the data is divided into bands, i.e each column shows a range between values

Card 3

Front

what are continuous variables?

Back

Preview of the front of card 3

Card 4

Front

what is a nominal variable?

Back

Preview of the front of card 4

Card 5

Front

how can the relationship between nominal variables be shown in diagrams?

Back

Preview of the front of card 5
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