Statistics

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Worksheet 1 - Basic Concepts
1. What is Inferential statistics?
Inferential statistics uses observations of past occurrences or available data i.e. descriptive statistics to make decisions about future possibilities and/or the nature of the entire body of data. Inferential statistics draws conclusions or makes interpretations, predictions and inferences about a population based upon an analysis of a sample. 2. Give 2 different techniques which are used in descriptive statistics to represent the data. Tables or graphs (histograms, boxplots, etc) or numerical summaries 3. Define each of the following terms:

a) Variable
The topics/issues under investigation in statistical analysis. The variable is a characteristic or property of the members of the population which may vary e.g. height, weight, perception etc. b) Population

The total group about which information is being sought. If information is sought about voting intentions, the population is all those people eligible to vote in an electorate, or a state or the nation. c) Sample

A sample is a group taken from the population. Most statistical situations do not allow an entire population to be used for analysis (usually because it is too large, the geographical dispersion of subjects, logistical issues, funding, time restraints etc) so a sample must be used. The sample chosen should be representative of and reflect all of the characteristics of the population. 4. What is the difference between a sample and a random sample? A sample is any subset of individuals taken from a population, and there are many types of sampling strategies (to be covered in the next few weeks). A random sample is the objective of all good research studies; to design a sampling strategy with the objective of reducing and/or eliminating bias. 5. What are the four levels of measurement and give an example of each? Qualitative Nominal – Gender, Qualitative Ordinal – Star rating on a hotel, Quantitative Interval – Celcius temperature scale, and Quantitative Ratio – Mass (in kg). Quantitative measurements may also be measured on a continuous or discrete scale.

6. You are conducting research into whether the results obtained at secondary school influence the quality of the results that students obtain in the TPP. a) What is the population applicable to the research?

The population is all students who have attended the TPP course who have been to secondary school. b) Describe one possible sample you could select to obtain data which would assist in the research. The current TPP cohort would be a sample of all TPP students. You could also select a smaller sample from within the current TPP cohort, but it would need to be characteristic of the entire population; i.e. representative. c) Is the sample you have chosen a random sample? Justify you answer. The current cohort would be a reasonably random sample provided the characteristics of the current cohort were similar to ALL the TPP students who have attended TPP, and there was no inherent bias in their selection. d) What are the variables which are being examined in this research? The variables would be secondary school results and TPP results. e) Are the variables qualitative or quantitative?

OP Scores and percentages are quantitative however grades such as Pass/Fail are qualitative. f) Are the variables discrete or continuous?
The values would be discrete. OP scores can only be the numbers 1 to 25. You can’t get a 1.5. Even percentages are discrete as they are rounded to the nearest whole number in this instance. g) Identify which variable is the independent (explanatory) variable and justify your selection. The explanatory, or independent variable would be the school results, while the TPP results would be the response (or dependent) variable. In other words, the school results explain (to some extent at least) the relative response in the TPP result . h) What level of measurement are each variable...
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