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Processing Uncertainties in Biology (SL IB Biology)

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Naomi H

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Naomi H

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Processing Uncertainties in Biology

What is uncertainty?

  • Scientific measurements are not perfect; there is always an associated level of uncertainty
  • Uncertainty is a quantitative indication of the quality of numerical results; it can be defined as:

The range of values around a measurement within which the true value is expected to lie

  • Uncertainties in measurements are recorded as a range (±) to an appropriate level of precision, e.g.
    • If a balance that measures mass shows scale graduations of 10 g, then mass is measured to the nearest 10 g (this is known as the margin of error)
      • The true value could be 5 g higher or lower than the measured value, so the uncertainty would be ±5 g
    • If a pipette shows scale graduations every 0.1 cm3, then volume is measured to the nearest 0.1 cm3
      • The true value could be 0.05 cm3 more or less than this, so the uncertainty would be ±0.05 cm3
  • Note that uncertainty is not the same as error
    • Error is the difference between a measured value and the true value for a measurement
    • Errors arise from equipment or practical techniques that cause a reading to be different from the true value

Error bars

  • The uncertainty in a measurement can be shown on a graph as an error bar
    • This bar is drawn above and below the point (or from side to side) and shows the uncertainty in that measurement
    • Usually, error bars will be in the vertical direction, for y-values, but can also be plotted horizontally, for x-values
  • Range, degree of precision, standard error and standard deviation can be expressed on a graph using error bars
    • Range = the difference between the lowest and highest value
    • Degree of precision = how close a set of data points are to each other
    • Standard error = an estimate of the reliability of the mean
    • Standard deviation = the spread of data around the mean
  • Note that it is important that you know what is represented by error bars on a graph, e.g. whether they represent standard deviation or standard error; in an exam this information would be provided in the question
    • Error bars that represent standard deviation can be used to assess whether or not two data sets are significantly different to each other
    • Overlapping error bars indicate that two sets of data are not significantly different
  • Error bars are used in the specification when measuring osmotic concentration

Error Bars

Error bars on a graph can be used to show uncertainty

Level of precision

  • Measurements and processed uncertainties must be expressed to an appropriate level of precision
    • E.g. number of decimal places
  • This may depend on the sensitivity of the apparatus used to collect data; the level of precision used to express the data should not exceed the level of precision at which the data is initially measured
  • Values in a raw data set should all be expressed to the same level of precision

The coefficient of determination, R2

  • The coefficient of determination is a measure of fit that can be applied to lines and curves on graphs
  • The coefficient of determination is written as R2 
  • It is used to evaluate the fit of a trend line / curve with its data set:
    • R= 0
      • The dependent variable cannot be predicted from the independent variable. 
      • R² is usually greater than or equal to zero
    • R2 between 0 and 1
      • The dependent variable can be predicted from the independent variable, although the degree of success depends on the value of R2 
      • The closer to 1, the better the fit of the trend line / curve
    • R= 1
      • The dependent variable can be predicted from the independent variable
      • The trend line / curve is a perfect fit  
      • Note: This does not guarantee that the trend line / curve is a good model for the relationship between the dependent and independent variables
  • Coefficient of determination is used in the specification when comparing the speed of nerve impulse transmission

Correlation

  • Correlation is an association, or relationship, between variables
    • Note that there is a clear distinction between correlation and causation: correlation does not necessarily indicate a causal relationship
    • Causation occurs when one variable has an influence or is influenced by another
  • Correlation can be positive or negative
    • Positive correlation: as variable A increases, variable B increases
    • Negative correlation: as variable A increases, variable B decreases
  • The correlation coefficient (r) can be calculated to determine whether a linear relationship exists between variables and how strong that relationship is
    • Perfect correlation occurs when all of the data points lie on a straight line; this will give a correlation coefficient of 1 or -1
      • +1 = a completely positive correlation
      • -1 = a completely negative correlation
    • A less-than perfect correlation will give a correlation coefficient between 1 and 0, or between 0 and -1
      • The closer to +1, or -1, the coefficient is, the stronger the correlation
    • If there is no correlation between variables the correlation coefficient will be 0
  • Correlation coefficients are used in the specification when evaluating data on coronary heart disease

2-4-1-correlation-diagram-1

A strong correlation will have a correlation coefficient close to 1, a weak correlation will have a correlation coefficient close to 0, while a lack of any correlation will give a correlation coefficient of 0

Statistical tests

  • Statistical tests are used to assess whether or not a data set supports a particular hypothesis. e.g.
    • A null hypothesis will state that there is no significant difference, or association, between two variables
    • An alternative hypothesis will state that there is a significant difference, or association, between two variables
  • Statistical analysis allows researchers to accept or reject the null hypothesis
  • If a statistical test shows that there is no significant difference, or association, between variables, then it is said that any visible difference is due to chance alone
  • Different statistical tests are used for different types of data set, e.g.
    • A t-test determines whether the means of two data sets differ significantly
    • A correlation test determines the presence and strength of a correlation
    • A chi-squared test determines whether the difference between observed and expected values is significant
  • You should be able to select and apply the correct statistical test
  • The chi-squared test is used in the specification as follows:

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Naomi H

Author: Naomi H

Expertise: Biology

Naomi graduated from the University of Oxford with a degree in Biological Sciences. She has 8 years of classroom experience teaching Key Stage 3 up to A-Level biology, and is currently a tutor and A-Level examiner. Naomi especially enjoys creating resources that enable students to build a solid understanding of subject content, while also connecting their knowledge with biology’s exciting, real-world applications.