Quantitative Data Analysis.pdf

# Variance the average of the squared deviations for

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Variance – the average of the squared deviations for the individual values from the mean. Standard deviation – the square root of the variance. Standard error – the standard deviation of the mean score. These measures do not mean much on their own unless they are compared with some expected measures or those of other variables . Charts and diagrams SPSS provides a choice of display options to illustrate the measures listed above. The most basic is a summary table of descriptive statistics that gives figures for all of the

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University of Western Sydney Copyright ©2014 SAGE Research Methods Page 10 of 26 Social Research Methods: Quantitative Data Analysis measures. More graphical options, which make comparisons between variables simpler, are: Bar graph – this shows the distribution of nominal and ordinal variables. The categories of the variables are along the horizontal axis (x axis) and the values are on the vertical axis (y axis). The bars should not touch each other. Histogram – a bar graph with the bars touching to produce a shape that reflects the distribution of a variable. Frequency polygon (or frequency curve) – a line that connects the tops of the bars of a histogram to provide a pure shape illustrating distribution. Pie chart – this shows the values of a variable as a section of the total cases (like slices of a pie). The percentages are also usually given. Standard deviation error bar – this shows the mean value as a point and a bar above and below that indicates the extent of one standard deviation. Confidence interval error bar – this shows the mean value as a point and a bar above and below that indicates the range in which we can be (probabilistically) sure that the mean value of the population from which the sample is drawn lies. The level of confidence can be varied, but it is commonly set at 95 per cent. Box and whisker plot – this gives more detail of the values that lie within the various percentiles (10th, 25th, 50th, 75th and 90th). Individual values that are outside this range can be pinpointed manually if they are judged to be important. [p. 116 ] Charts and diagrams are far easier to understand quickly by the non-expert than are | results presented as numbers . Normal and skewed distributions Normal distribution is when the mean, median and mode are located at the same value. This produces a symmetrical curve. Skewedness occurs when the mean is pushed to
University of Western Sydney Copyright ©2014 SAGE Research Methods Page 11 of 26 Social Research Methods: Quantitative Data Analysis one side of the median. When it is to the left, it is known as negatively skewed, and to the right, positively skewed. The curve is lopsided in these cases. If there are two modes to each side of the mean and median points, then it is a bimodal distribution. The curve will have two peaks and a valley inbetween.
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• Two '18
• ECA
• Statistics, Level of measurement, University of Western Sydney

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