Practical – Cognitive
| (a) Devise and conduct one practical, which must be an experiment, to gather data relevant to a topic covered in the Cognitive Approach for this course.
This experiment must be designed and conducted according to ethical principles. Suitable examples: (b) Comment on the research design decisions. (c) Collect, present and comment on data gathered including using measures of central tendency (mean, median, mode), measures of dispersion (at least range), bar graph, histogram, frequency graph as relevant. |
Descriptive Statistics
Experiments produce quantitative data which can be analysed statistically. Statistics are a method of summarising and analysing data for the purpose of drawing conclusions about the data.
We can make a distinction between descriptive and inferential statistics. Descriptive statistics simply offer us a way to describe a summary of our data.
Inferential statistics go a step further and allow us to make a conclusion related to our hypothesis.
Descriptive statistics give us a way to summarise and describe our data but do not allow us to make a conclusion related to our hypothesis.
When carrying out an experiment there are two main ways of summarising the data using descriptive statistics. The first way is to carry out of measure of central tendency (mean, median or mode) for each of the two conditions.
The mean is the arithmetic average that indicates the typical score in a data
set and is calculated by adding all the scores together in each condition and then dividing by the number of scores. This is a useful statistic as it takes all of the scores into account but can be misleading if there are extreme values. For example if the scores on a memory test were 2, 4, 5, 6, 7, 42, the mean would be 10 which is not typical or representative of the data. The mean can not be used with nominal data. Nominal data are data in the form of separate categories such as grouping people according to their favourite type of cheese.
The median is calculated by finding the mid point in on ordered list. The median is calculated by placing all the values of one condition in order and finding the mid- point. This is a more useful measure than the mean when there are extreme values. For example, six scores on a test out of 100 are 70, 74, 75, 77, 78, 100. The mean is 79 but this is misleading in the sense that only one of the six participants has scored this high. The median score of 76 is a better description of the data. The disadvantage of the median is though that not all of the scores are taken into account. The median can also not be used when data are nominal.
The mode is the most common value in a set of values. This measure is often used when we have nominal data such as number of people who prefer Mozzarella. When looking at a set of scores the mode is the score that applies to the greatest number of participants. For example, with scores of 30, 30, 30, 50, 96, 100 the mean is 61 which is misleading in the sense that no-one scored anywhere near this; the median is 40, which again does not approximate to anyone’s score and the mode is 30, which at least lets us know that more people obtained this score than any other score. The mode is useful in certain instances where other measures of central tendency are rather meaningless. For instance, if you are a buyer for a shop whose target population consists of 50% of people who wear size 12 clothes and the remaining 50% are size 16 then it is no use you ordering size 14 clothes just because this is the average size. Nevertheless, modes are used less often than other measures of central tendency. They do not tell us anything about other scores in the distribution; they often are not very ‘central’ and they tend to fluctuate from one random sample of a population to another more often than either the median or the mean.
The second way of summarising and describing data is to calculate a measure of dispersion or variability. This simply shows us the spread of a set of data.
The range: A crude way of describing the variability of scores is simply to give the range of the scores – the highest score minus the lowest. The range is usually used when we have used the median as the measure of central tendency.
The standard deviation: A much more sensitive description is provided by what is called the standard deviation, often abbreviated to SD. The standard deviation is usually used when we have used the mean as the measure of central tendency. The range only takes account of the highest and lowest scores but the SD takes every score into account. Loosely speaking, it gives us an idea of how much, on average, scores in a distribution differ from the mean. If the standard deviation of a group of scores is large, this means that the scores are widely distributed with many scores occurring a long way from the mean. If the standard deviation is small, most scores occur very close to the mean.
Suppose two classes took an exam and both classes had a mean score of 65 out of a possible 90. From the means alone, we could conclude that the two classes were very similar in ability. But if the SD of one class was 10 while that of the other class was 5 then they would need to be treated very differently and this would need to be considered in the planning of teaching materials.
Standard deviation can be defined as a statistical device for describing the variability of measurements.
Graphs
We can very easily create a graphical display of descriptive statistics. For example, bar charts can show at a glance the measures of central tendency of two conditions in an experiment. When drawing a bar chart ensure that it has a title and the axis are labelled. You can even colour the bars in.
Types of data (levels of measurement)
The type of descriptive and inferential statistic we employ is partly determined by the type of data we have obtained from our study. This section describes the three main types of data and includes a table indicating which measure of central tendency and dispersion should be used depending on the type of data you have collected
Nominal Data (counting)
Nominal data are data in separate categories such as number of runners that finished a marathon. If you simply count the number of participants that did one thing or another, or fall into this category or that, you are using nominal data (sometimes called frequency data). When a nominal scale is used, each participant is put into one category or another, there is no overlap, or in other words, categories are mutually exclusive.
Ordinal Data (ordering)
Ordinal data are data that are ordered such as the order of runners that finished the marathon – first, second, third and so on. However ordinal data do not tell you how much difference there is between the runners, simply the order in which they finished.
Interval and Ratio Data (measuring)
Interval data are data that are measured using a public unit of measurement. For example this could be the times in which the runners finished the marathon. Public units of information, such as seconds, minutes, pounds, ounces, kilograms, degrees Celsius and so on are called public because each unit has an agreed value. Because each unit has an agreed value then the difference between 4 and 5 seconds is exactly the same as that between 10 and 11 seconds. Interval and ratio data therefore give more than just order; they also show how much difference there is between the first and second, the second and third and so on.
If data describes each value in terms of the exact number of minutes, seconds, metres, words remembered or any other public information, it is interval or ratio data.
When comparing the levels of measurement, interval data contain most information and nominal contains least. This means that interval level data can be converted into ordinal level (by ranking the scores) or into nominal level data. Ordinal level data can be converted into nominal level data. Although every time we convert from interval to ordinal and from ordinal to nominal, we lose information.
The level of data will partly determine the choice of descriptive statistics.
Note that any measure which can be used at a lower level of measurement can also be used at a higher level of measurement. The mode and the median, for example, could be used at the interval scale level, but the mean cannot be used at either of the lower levels of measurement.