Descriptive and Inferential Statistics: Lectures summary24th Dec 2022
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Course
STAT MISC
Institution
Open Universiteit (OU)
When analyzing data, such as the marks achieved by 100 students for a piece of coursework, it is possible
to use both descriptive and inferential statistics in your analysis of their marks. Typically, in most research
conducted on groups of people, you will use both descriptive and inferential st...
When analysing data, such as the marks achieved by 100 students for a piece of coursework, it is possible
to use both descriptive and inferential statistics in your analysis of their marks. Typically, in most research
conducted on groups of people, you will use both descriptive and inferential statistics to analyse your results
and draw conclusions. So what are descriptive and inferential statistics? And what are their differences?
Descriptive Statistics
Descriptive statistics is the term given to the analysis of data that helps describe, show or summarize data
in a meaningful way such that, for example, patterns might emerge from the data. Descriptive statistics do
not, however, allow us to make conclusions beyond the data we have analysed or reach conclusions
regarding any hypotheses we might have made. They are simply a way to describe our data.
Descriptive statistics are very important because if we simply presented our raw data it would be hard to
visulize what the data was showing, especially if there was a lot of it. Descriptive statistics therefore enables
us to present the data in a more meaningful way, which allows simpler interpretation of the data. For
example, if we had the results of 100 pieces of students' coursework, we may be interested in the overall
performance of those students. We would also be interested in the distribution or spread of the marks.
Descriptive statistics allow us to do this. How to properly describe data through statistics and graphs is an
important topic and discussed in other Laerd Statistics guides. Typically, there are two general types of
statistic that are used to describe data:
o Measures of central tendency: these are ways of describing the central position of a frequency
distribution for a group of data. In this case, the frequency distribution is simply the distribution
and pattern of marks scored by the 100 students from the lowest to the highest. We can describe
this central position using a number of statistics, including the mode, median, and mean.
o Measures of spread: these are ways of summarizing a group of data by describing how spread
out the scores are. For example, the mean score of our 100 students may be 65 out of 100.
However, not all students will have scored 65 marks. Rather, their scores will be spread out.
Some will be lower and others higher. Measures of spread help us to summarize how spread out
these scores are. To describe this spread, a number of statistics are available to us, including the
range, quartiles, absolute deviation, variance and standard deviation.
When we use descriptive statistics it is useful to summarize our group of data using a combination of
tabulated description (i.e., tables), graphical description (i.e., graphs and charts) and statistical commentary
(i.e., a discussion of the results).
Inferential Statistics
We have seen that descriptive statistics provide information about our immediate group of data. For
example, we could calculate the mean and standard deviation of the exam marks for the 100 students and
this could provide valuable information about this group of 100 students. Any group of data like this, which
includes all the data you are interested in, is called a population. A population can be small or large, as
long as it includes all the data you are interested in. For example, if you were only interested in the exam
marks of 100 students, the 100 students would represent your population. Descriptive statistics are applied
, Often, however, you do not have access to the whole population you are interested in investigating, but only
a limited number of data instead. For example, you might be interested in the exam marks of all students in
the UK. It is not feasible to measure all exam marks of all students in the whole of the UK so you have to
measure a smaller sample of students (e.g., 100 students), which are used to represent the larger
population of all UK students. Properties of samples, such as the mean or standard deviation, are not called
parameters, but statistics. Inferential statistics are techniques that allow us to use these samples to make
generalizations about the populations from which the samples were drawn. It is, therefore, important that
the sample accurately represents the population. The process of achieving this is called sampling (sampling
strategies are discussed in detail here on our sister site). Inferential statistics arise out of the fact that
sampling naturally incurs sampling error and thus a sample is not expected to perfectly represent the
population. The methods of inferential statistics are (1) the estimation of parameter(s) and (2) testing of
statistical hypotheses.
Hypothesis Testing
When you conduct a piece of quantitative research, you are inevitably attempting to answer a research
question or hypothesis that you have set. One method of evaluating this research question is via a process
called hypothesis testing, which is sometimes also referred to assignificance testing. Since there are
many facets to hypothesis testing, we start with the example we refer to throughout this guide.
An example of a lecturer's dilemma
Two statistics lecturers, Sarah and Mike, think that they use the best method to teach their students. Each
lecturer has 50 statistics students who are studying a graduate degree in management. In Sarah's class,
students have to attend one lecture and one seminar class every week, whilst in Mike's class students only
have to attend one lecture. Sarah thinks that seminars, in addition to lectures, are an important teaching
method in statistics, whilst Mike believes that lectures are sufficient by themselves and thinks that students
are better off solving problems by themselves in their own time. This is the first year that Sarah has given
seminars, but since they take up a lot of her time, she wants to make sure that she is not wasting her time
and that seminars improve her students' performance.
The research hypothesis
The first step in hypothesis testing is to set a research hypothesis. In Sarah and Mike's study, the aim is to
examine the effect that two different teaching methods – providing both lectures and seminar classes
(Sarah), and providing lectures by themselves (Mike) – had on the performance of Sarah's 50 students and
Mike's 50 students. More specifically, they want to determine whether performance is different between the
two different teaching methods. Whilst Mike is skeptical about the effectiveness of seminars, Sarah clearly
believes that giving seminars in addition to lectures helps her students do better than those in Mike's class.
This leads to the following research hypothesis:
Research Hypothesis: When students attend seminar classes, in addition to lectures, their
performance increases.
Before moving onto the second step of the hypothesis testing process, we need to take you on a brief
detour to explain why you need to run hypothesis testing at all. This is explained next.
Sample to population
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