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Teacher Statistical Literacy

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Steps In Running A Survey



Show details for Step 1: Planning a surveyStep 1: Planning a survey
Hide details for Step 2: Collecting dataStep 2: Collecting data

Once you have decided on your question, how many people will be in your sample, and randomly selected them, you will need to consider how to collect the data. Will it be through an interview or will you collect written responses? The data you collect will also need to be in a form that is easily organised in order to analyse it. For example, you need consistency in units and fractional answers so request that the data be recorded to the nearest centimetre or half centimetre.

Interview
In an interview, a participant can ask questions if they haven’t understood something.

Written response
Written responses can be completed by many participants at the same time and are quicker than interviews.

Variables
A variable is any measurable characteristic or attribute that can have different values for different subjects – for example, eye colour, distance from school etc.
Characteristic is another way of saying variable. For example, height, age or country of birth are all characteristics or variables of people.




Hide details for Step 3: Organising dataStep 3: Organising data

After you have collected the data, it needs to be organised so that it is useful and ready to display.

Frequency tables
A useful way to record raw data is a tally table or frequency table.
A frequency table counts the number of times – or frequency – a value occurs in the data. For example, twenty people are asked "How many TVs do you have in your household?" If 2 households have 1 TV, the frequency of households with 1 TV is 2.

Frequency tables with class intervals
When a variable has a large spread, the values can be grouped together to make the data easier to manage and present.
For example, if you asked students how much time it takes them to get to school each day, their responses may vary considerably. In this case, you can group the responses together in 5 minute intervals. These intervals are called class intervals. All class intervals should have an equal range. Class intervals are usually in groups of 5, 10, 20, 50 etc.


NUMBER OF TVsTALLYFREQUENCY (f)
0l l l l4
1l l2
2l l l l l6
3l l l l l l l8
Figure 1: Frequency table of number of TVs per household

TIME TAKEN TO GET TO SCHOOL (min)TALLYFREQUENCY (f)
1 - 5l l l l l l7
6 - 10l l l l l l l l9
11 - 15l l l l l l l l9
16 - 2011
Figure 2: Example of a frequency table showing five minute class intervals


Show details for Step 4: Displaying informationStep 4: Displaying information
Hide details for Step 5: Analysing the dataStep 5: Analysing the data

You need to decide what statistics you will use and what summary information will enable you to answer your survey question.
For example:
  • Will you find the mean or median or both?
  • Will you exclude extreme values?
When describing a distribution, statisticians usually comment on its centre, spread and shape.

a) Measures of centre
The centre of a set of data is important. Often you want to know which value occurs most commonly or the average of a set of values.

Numerical data
Mean: The arithmetic mean is calculated by finding the sum of all values in the data set and then dividing it by the number of values in the set. The mean is often called the average.
Median: The median is the middle value of a dataset when all the values are arranged from smallest to largest number. If a dataset contains an even number of values, the median is taken as the mean of the middle two. The median is the preferred measure of centre when the data is not symmetric or contains outliers.

Numerical and categorical data – Figure 14
Mode: The mode is the value that occurs most often in a data set.

b) Measures of Spread
The spread of a data set, when combined with its centre, will give a more complete picture.

Range
The range is the distance from the minimum value to the maximum value in the data set.
Range = maximum – minimum

Interquartile range – Figure 15
Quartiles: As the name suggests, quartiles divide data into four equal sets.
When observations are placed in ascending order according to their value, the first or lower quartile is the value of the observation at or below which one-quarter (25%) of observations lie. The second quartile is the median at or below which half (50%) of observations lie. The third or upper quartile is the value of the observation at or below which three-quarters (75%) of the observations lie.
Another way to think about this is: the median divides the data into two equal sets: the lower quartile is the value of the middle of the lower half, and the upper quartile is the value of the middle of the upper half. The difference between upper and lower quartiles (Q3 - Q1) also indicates the spread of a data set. This is called the interquartile range (IQR).

Interquartile Range = Upper quartile - Lower quartile
The interquartile range spans 50% of a data set, and eliminates the influence of outliers because, in effect, the highest and lowest quartiles are removed.
Calculating the IQR will help you to identify potential outliers in the data. Any data above Q3 +1.5 x IQR (upper fence) and below Q1 – 1.5 x IQR (lower fence) should be investigated to decide whether or not these observations need to be excluded from the data before it is analysed further.

Outliers
A potential outlier might be a mistake or an extreme value so you need to check the original data to determine if it is to be discarded or retained. However, cleaning data by discarding extreme values might give you a false view of variations that can be found in datasets. In turn, this could result in inaccurate modelling based on the data and false conclusions.

The standard deviation – Figure 16
The standard deviation measures the average distance each value in a data set is from the mean. A data set with a higher standard deviation will be more spread out than one with a lower standard deviation. Compare the following two data sets:

c) Shape
The standard distribution – Figure 17
Data which has a standard distribution is characterised by a symmetric, single curve. Also known as the normal or bell shaped distribution.
You would expect data such as the height of Year 9 students or the length of cane toads to show a standard distribution. A standard distribution results from most of the data clustering around the mean and less data occurring further away from the mean.

Bi modal – Figure 18
Bi modal data usually comes from two distinct populations. The bar chart of Year 5 girls' and Year 10 boys' heights shows two distinct modal groups.

Skew – Figure 19
Some non-symmetric data distributions can be described as skewed.
Data which is positively skewed typically has a cluster of lower end values and a taper of higher end values. Data which is negatively skewed typically has a cluster of higher end values and a taper of lower end values.
You could expect data such as the amount of total weekly income to show a negative skew. The number of people on a higher weekly income is fewer than those on low or medium incomes. Data you could expect to show a positive skew might be the amount of hours spent on Facebook by age. It's likely that the amount of time spent on Facebook will peak in the late teens to twenties and then taper off as a person's age increases.


Figure 14: Mean median and mode of a data set

Figure 15: Calculating 5 figure summary statistics



Figure 16: Box and Whisker plot with upper and lower fences


Figure 17: Comparing the standard deviation of two data sets


Figure 18: Standard distribution based on 2011 C@S random sample


Figure 19: Bi modal graph of distribution of height


Figure 20: Positive skew, distribution of age of Indigenous males



Hide details for Step 6: Drawing conclusionsStep 6: Drawing conclusions

Communicating the results of your investigation is a critical part of the survey process. Ensuring the accuracy of any interpretations and avoiding misinterpretations are crucial. Keeping in mind the purpose of the investigation and your audience will help to keep your conclusions on track and avoid including unnecessary information.

Accuracy of Data
All your calculations need to be accurate, verifiable from the data and clearly communicated using simple language.

Misinterpretation
To effectively communicate your results, you will need to be aware of avoiding any misinterpretation of the data such as using the mean when the median is more appropriate or not taking seasonal variation into account.

Stating your conclusions
With statistics, there is always a risk that the results you have do not tell the whole story. You can use the following checklist to help judge the reliability of your statistical information.

  • Do your conclusions communicate the message told by the data?
  • Are your conclusions based on results rather than on your opinions?
  • Have you considered alternative explanations for the same results?
  • Is your report set out logically including using an organisational framework such as headings and sub headings?
  • Have you included the source of any information you have used or referred to?
  • Have you included relevant tables and graphs?
  • Are your findings clear, related to your aim and only contain necessary information?

Audience
  • Have you considered your audience and used appropriate language?
  • Have you anticipated questions your reader might have? For example, have you explained unusual or unexpected results? Have you justified your choice of analysis, indicated your sampling process etc?
  • Can your reader check your conclusions by viewing your analysis?

Sampling Error
Finally, if you intend for your results to be applicable in other contexts, it is important to understand the limits that might apply.
The difference between an estimate based on a sample survey and the true value that would result if a census of the whole population was taken is called the sampling error. Sampling error can be measured mathematically and is influenced by the size of the sample. In general, the larger the sample size the smaller the sampling error.
The way a sample is drawn is also important. In general, a random sample will result in data that is more able to be generalised to the population.



Commonwealth of Australia 2008

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