Measurement plays a major role in scientific method.
Variation will always exist in a set of measurements.
Measurement error: discrepancy between our repeated measurements and the true value of the object.
Sources of error must be eliminated as much as possible.
Precision: variation in repeated measurements.
Little variation = high precision
Great variation = low precision
Accuracy: how close the measured value is to the true value.
Single measurement consists of:
Scale factor: relative magnitude of value
Sig figs are dependent on accuracy of the measuring instrument.
Sig figs should reflect the number that are known to be correct.
Also expressed using scientific notation.
Sample: Subset of a population (“N”), usually a small proportion of the individuals.
Sampling units must represent the range and frequency of values in the population.
Sample size (“n”) is always reported
Sample size can’t be increased by repeating measurements on the same sampling unit.
More units measured increase sample size.
Part B: Organizing Data
Data is grouped according to qualitative or quantitative nature.
Qualitative attributes have a definite number of possibilities
Ex: Sex, hair colour, presence of a disease.
Discrete: Only whole units are measured/counted.
Ex: Number of trees in a forest.
Continuous: Fractional units can be measured.
Ex: measurement of hemoglobin in blood.
Common methods of representing data:
Should summarize data
Figures consisting of graphs, diagrams etc.
Should be self explanatory if used effectively.
Line graph: shows relationship between values using x-axis and y-axis
Dependent variable (y-axis): changes in accordance to the independent.
Independent variable (x-axis): not affected in the experiment.
Line of best fit is used to show a consistent relationship between variables.
Interpolation: Using the line of best fit to predict values not plotted on the graph.
Extrapolation: Extending the line of best fit beyond known data but still maintaining the trend shown my interpolation.
Bar graph: Used for discrete variables, which may be similar but don’t have to be related.
Gaps between bars
Histogram: Used for showing continuous data
No gaps as data is continuous and data is partitioned into groups/classes
Part C: Analyzing Data – Descriptive Statistics
Observational studies are dependent on statistical tests.
Statistics of location: Describes position of sample along a given dimension
Measurements of central tendency:
Mean: Average value used to describe a sample.
Median: Middle value in an ordered set of values.
Mode: Most common/frequent value of a set of values.
Doesn’t describe distribution of observation, rather this is done by the statistic of dispersion.
Statistic of dispersion:
Most common is Range: difference between largest and smallest values in a sample
Gives a rough estimate of the dispersion
Variance: How much scatter there is around the mean.
Standard deviation (“s”): average size of the deviation from the mean.
Standard error: Measure of how reliable the sample mean is to the approximation to the population mean.
Size is important in determining how reliable the estimate of the mean is
Part D: Analyzing Data – Tests of significance
Evaluates the probability of rejecting the null hypothesis when it is actually true.
Tests depend on type of data.
Student’s t-test: William S. Gosset