Data Handling & Analysis

DATA HANDLING AND ANALYSIS

Display of Quantitative Data

- Tables and graphs must have a title and clear labels.

- Tables may contain measures of central tendency and dispersion.

Bar chart - height of bar represents frequency, data on x-axis may not be continuous.

Histogram - represents frequency of continuous data, true zero and bars next to each other.

Line graph - frequency represented by a line rather than bars.

Scattergram - shows correlation between co-variables.

Data Distributions

Normal distribution - symmetrical bell-shaped curve; mean, median and mode at mid-point with about 68% of people are 1 standard deviation above and below the mid point, 95% within 2 standard deviations from mid-point.

Positive skew - tail to right, occurs when test is too hard.

Negative skew - tail to left, occurs when test is too easy.

Mathematical Skills

Fractions - numerator and denominator, can be reduced to simplest form by dividing both by the lowest common denominator. Percentage is out of 100, can be converted to a fraction by writing 'number'/100 and reducing to simplest form. Can convert a fraction to a percentage by dividing denominator by numerator and move decimal 2 places to the right (x100).

Ratios - can be part-to-part (e.g. 4:1) or part-to-whole (e.g. 4:5), can reduce to simplest form or change to fraction.

Estimate results - round your numbers up or down to produce a sum you can do in your head, then add the zeros.

Significant figures - refers to the number of important digits used to represent a number.

Order of magnitude - show number by giving 1 or 2 significant figures and powers of 10.

Mathematical symbols: =, :, <, <<, >>, >, ~

Introduction to Statistical Testing

When to use the test? the sign test is used with paired or related data.

How to do the test? represent each pair of data with plus or minus, calculated value of S - least frequent sign.

- Look up critical value of S. Need to know N and whether one-tailed (directional hypothesis) or two-tailed (non-directional hypothesis).

- Conclusion if calculated value is less than or equal to critical value, the difference is significant.

- Probability level of 5% is commonly used.

Measures of Central Tendency & Dispersion

Mean - add up all numbers and divide by N (number of numbers). Ratio and interval data only.

Median - order all numbers and select mid-point. Ratio, interval and ordinal data.

Mode - most common value or group. May be bi-modal and can be used with all levels of measurement.

Range - subtract lowest from highest and add a correction of 1.

Standard deviation - average distance between each number and the mean.

Evaluation

Mean - most sensitive because uses exact distance, distorted by extreme values, but not appropriate for ordinal data or discrete values.

Median - useful for extreme values, but not as sensitive as the mean.

Mode - useful for nominal data but not good where there are many modal groups.

Range - easy to calculate, but effected by extreme numbers and doesn't reflect data distribution.

Standard deviation - takes exact values into account, but may be affected by extreme values.

Types of Data

Quantitative data- numerical (e.g. measuring a dependent variable or answers to closed questions).

Qualitative data - can't be directly counted, non-numerical (e.g. answers to open questions).

Primary data - collected by the researcher for current study, involves design of study to collect data.

Secondary data - using data collected for a previous study (e.g. government statistics).

Evaluation

Quantitative data - easy to analyse, but may not represent reality.

Qualitative data - detailed and possibly unexpected information, but more difficult to draw conclusions.

Primary data - suits the needs of the study but time consuming and expensive.

Secondary data -​​​​​​ saves time and money but may not fit exact needs of study.