Scottish election panel

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Scottish election panel

• Friday 2 March 10-12
• MacRobert 613
• Brian Adam (SNP)
• Alex Johnstone (Conservative)
• Robin Harper (Green)
• Mike Rumbles (LibDem)
• Richard Baker (Labour)

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Assignment Surgery

• In F35 Edward Wright
• Today (Thu) 10-12
• Tomorrow (Friday) 2-4
• Monday 9-12, 2-5

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Quantitative methods, lecture 7

• Scale levels
• Brief discussion on more advanced statistical
  techniques. Correlation, regression, factor
  analysis

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Scale levels

• Variables can be of different scale levels. The
  scale level of a variable determines how advanced
  statistical techniques we can use to analyse it
• There are four different scale levels
• Nominal scale
• Ordinal scale
• Interval scale
• Ratio scale

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Nominal scale variables

• are not numerical. Can therefore not be
  quantified
• Examples gender, nationality
• Possible mathematical operations ?
• We cannot rank or quantify nationality since it
  is not meaningful to give one nationality a
  higher value than another
• In a dataset, each nationality has a value on the
  variable. But these values mean nothing, they are
  only there to separate the different
  nationalities from each other
• The statistics software can do all sorts of
  things with nominal scale variables, such as
  calculating means and standard deviations. But it
  is meaningless
• Nominal scale variables are normally not possible
  to use for more than cross tabulations.

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Ordinal scale variables

• are possible to rank
• We know that one value is higher or lower than
  the other, but not by how much
• Possible mathematical operations ? gt lt
• But we do not know the distance between the
  values!!!
• How much higher than A levels or Highers is a
  university degree? We do not know
• Five response alternatives Agree entirely, agree
  on the whole, neither agree nor disagree,
  disagree on the whole and disagree entirely. They
  are not numerical
• so we do not know that two different persons who
  have answered 'agree on the whole' are located at
  the same place vis a vis the neutral standpoint
• Sometimes the researcher assumes that there is an
  equal distance between the different values. But
  such assumptions are always questionable

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Interval scale variables

• allow us not only to rank the values of a
  variable, but also determine the distance between
  them
• Possible mathematical operations ? gt lt -
• Interval scale variables have no natural zero
  point
• There may be a conventionally agreed zero point,
  but no absolute one. Thus interval scale
  variables are rare in social science
• Temperature. Celsius/ Centigrade and Fahrenheit
  scales have no natural zero point, but zero
  points set by agreed convention (Kelvin scale
  does have a zero point)
• Time. In the Western world, the birth of Jesus
  Christ is used as a conventional zero point. But
  we can hardly set an absolute zero point of time

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Ratio scale variables

• do have a natural zero point
• Possible mathematical operations ? gt lt -
  ?
• Age. The natural zero point is the time when the
  person was born
• Therefore we can measure the relationship between
  the values of the variable in question
• It is, for example, meaningful to state that a
  person is twice as old as another person

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Scale levels

• It is advantageous to have as high a scale level
  as possible.
• This can be affected with the questionnaire
• It is advantageous to make the responses to
  questions numerical, and to avoid open-ended
  questions
• One way of doing this is to let respondents
  answer in terms of scales
• For example like/dislike scales, where it is then
  assumed that you like something twice as much is
  you answer 10 (Really Like) as 5 (Neither like
  nor dislike)
• You can also set the scale so that zero is the
  mid point, surrounded by an equal number of
  positive and negative numbers.

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Scale levels

• Scales (0-10, -5 -- 5 etc) are based on the
  assumption that they reflect people's opinions,
  and that people interpret the scale in exactly
  the same way
• That it means exactly the same thing that persons
  A and B answer 2 on a like/dislike scale to a
  question on how much you like the prime minister
• With ordinal scale variables this is even more
  questionable
• An example is course evaluation forms, which have
  a five step agree/disagree scale
• Can it be assumed that there is an equal distance
  between the different response choices? And if
  the alternatives would have been numbered 2, 1,
  0, -1 and -2 instead, would that have meant that
  the 'interval scale assumption' is reasonable?
• This is of course a philosophical problem, and
  many would argue that any such quantification of
  what really is individual qualitative answers is
  misconceived
• As said in the first lecture, a lot of what we
  are doing in this module is based on assumptions,
  and these assumptions are by no means
  unquestionable

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Scale levels

• Variables at interval scale or higher can be used
  in two main statistical techniques correlation
  and regression
• Nominal and ordinal scale variables can also be
  transformed into ratio level variables
• by creating dummy variables
• A dummy variable has only two values, 1 and 0.
• For example, Nationality can be transformed into
  a great number of dummy variables is Finnish
  (1), is not Finnish (0), is Australian (1) is not
  Australian (0), and so on
• Virtually any variable can thus be transformed
  into ratio level variables
• However, the variable is then no longer
  nationality. It is instead a long series of
  separate variables 'Finnish', 'Australian' and
  so on

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Correlation

• Correlation analysis is a technique by which we
  can analyse the extent to which two variables are
  related to each other
• A correlation coefficient is a measure of the
  extent to which the value of variable X coincides
  with the value of variable Y
• A correlation can be positive (high values on
  variable X tend to coincide with high values on
  variable Y)
• or negative (high values on variable X tend to
  coincide with low values on variable Y)
• There are several types of correlation
  techniques. One of the most commonly used is
  Pearsons r
• which requires interval scale variables or higher

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Regression analysis

• In correlation, we cannot speak in terms of
  independent and dependent variables
• but this is possible in regression analysis
• A regression coefficient tells us how much a unit
  moves along the vertical scale if it moves one
  step along the horizontal scale
• In other words, the effect of the independent x
  variable on the dependent y variable.

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Correlation v regression 1

• Both correlation and the type of regression we
  are dealing with here assume and measure linear
  relationships
• We can calculate a straight line which reflects
  the relationship between the variables.
• This is done with the so-called Least-Squares
  method. I will not go into that, but it is a way
  of calculating the straight line which has the
  smallest sum of squared deviations from it.

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Correlation v regression 2

• Correlation tells us how closely concentrated all
  observations are to the line (see last point on
  previous slide)
• Correlation coefficients vary between 1 and 1,
  where 0 means no correlation at all
• A positive correlation means that high values on
  one variable tend to coincide with high values on
  the other, and vice versa (low values on one
  variable coincide with low values on the other)
• A negative correlation tells us that the
  relationship between the two variables is
  inverse, i.e. that high values on one variable
  coincide with low values on the other
• In a perfect correlation, i.e. 1 or 1, all
  observations would be the same as the line. In
  practice, we seldom we get higher correlation
  coefficients than 0.30.
• Regression tells us the slope of the line. This
  is done by using an equation y ? ?x
• (? intercept with y (vertical) axis. ? slope
  the change in y caused by one units change in x
  but do not worry about this!!!)

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Correlation v regression 3

• Thus, we may have a high correlation, but a low
  regression coefficient
• A mild slope, of an almost straight line, means
  that there is movement along one variable but not
  along the other
• Therefore there is little effect by the
  independent variable on the dependent variable,
  because the latter is not affected much by the
  former. Hence, a low regression coefficient
• But, at the same time, the observations are
  closely concentrated to that line. Hence, a high
  correlation coefficient
• We may also have a high regression coefficient
  and a low correlation coefficient at the same
  time. This when the slope is steep, but the
  observations are spread out far away from the
  line
• The above assumes a linear relationship. This is
  often a simplification of reality, and there are
  so-called curvilinear regression models which are
  open for more complex relationships

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Factor analysis

• Factor analysis is a technique which uses a long
  series of correlations among several variables,
  in order to find out whether they form patterns,
  or dimensions
• Factor analysis can for example determine that
  negative attitudes to inner city driving,
  willingness to raise the penalties for pollution,
  subsidies to organic food production and
  scepticism against economic growth constitute a
  factor
• This, simplistically put, means that they
  correlate more with each other, than with any
  other attitudes
• This can also be called an attitude dimension
• In this example, we can call it a green factor,
  or dimension