As the last few videos have shown, psychologists collect a large amount of data in their investigations,
in fact, with lots of participants the amount of data collected, known as raw data, can
be overwhelming, and it can be hard to tell a clear story about exactly what was found
in a study.
That’s where descriptive statistics come in, these are simply the statistics that summarise,
meaning they describe certain features of a quantitative data set, like what the average
score is or what the spread of the scores in a data set is.
INTRO The term descriptive statistics sounds a little
scary, but in reality, you likely know what they are, descriptive statistics include both
measures of central tendency and measures of dispersion.
Measures of central tendency include the mean, median and mode, so the measures of central
tendency are averages.
Measures of dispersion refer to how spread out the individual scores are, so this includes
both the range and standard deviation.
But be prepared, if a question ever asks about descriptive statistics, measures of central
tendency or measures of dispersion you need to remember what calculations those terms
are referring to.
Measures of Central Tendency To understand the differences with measures
of central tendency, let’s imagine your going for a job at a small company, and they
ask if you have any questions.
And reasonably you asking what the average wage of the people who at that company is.
The CEO is interviewing you and he has a list of all the salaries of the company employees.
Let's say this is the set of data.
10,000, 15,000, 15,000, 15,000, 20,000, 24,000, 24,000, 26,000, 36,000, 195,000
Mode Let's start calculating measures of central
tendency with the simplest, the mode.
The mode is the most frequent score in a quantitative data set.
So you can see in this data set the mode is 15 thousand.
There can in some sets of data more than one mode, if there are two modes we could call
that data bi-modal, and if there are more than two, multimodal.
Positives of the mode are, it isn't affected by outliers, meaning it's particularly useful
for discrete numbers, for example, it can make more sense to say the average family
has two children than 1.89 children and if the data is in categories, like average pet
choice, giving the modal group is the only way of giving an average.
However a criticism of the mode, is in small data sets there are likely to be multiple
modes, or even no mode if every score is different, so not giving a clear average value.
Also it doesn't include all of the values in its calculation so it’s not as sensitive
as the mean.
Median The median value is calculated by ordering
the values from lowest to highest and using the number in the middle as the average.
If there are an even number of data points then take the two middle scores and it’s
halfway between the two.
So in this case the median value would be 22,000
Positives of the median are, it's also not affected by extreme outline scores, and like
the mode and its very easy to calculate.
However, criticisms of the median are not all the raw scores are used in its calculation
so we would say that it's not as sensitive as the mean.
Mean So to work out the Mean we add the scores
together which gives us £380,000 and divide by the number of scores, in this case 10,
so in this data set our mean average salary at this company would be thirty eight thousand
pounds.
Positives of the mean are we have used and represented all of the raw data in its calculation,
so we would say it is sensitive.
However the main criticism of the mean is because of its sensitivity it is easily shifted
towards extreme values.
Now going back to our scenario the CEO would be perfectly accurate in giving any of these
figures as the average wage of the company's employees, and may be tempted to state the
mean to show his company in the best light to get you to join his company.
And you have probably noticed this careful selection of descriptive statistics is often
used by politicians and companies to spin and misrepresent their policies.
So because of their contrating strengths and weaknesses the correct measure of central
tendency should be used for the right situations.
Measures of Dispersion Range
As measures of dispersion are about the spread of a set of data the range may be the first
you think of.
It’s easy to calculate you just take the smallest value from the largest to get the
range.
Using our example 195,000 - 10,000 gives a range of 185,000.
Some of you may have been told to add a 1 when working out the range, thats fine its
also an acceptable way of stating the range.
Well a positive of the range is it's clearly very easy to calculate.
However, the main criticism of the range is extreme scores easily distort its value, and
the range does not show if the scores are more spread out or are clustered around the
mean.
Standard deviation The standard deviation is a much more complex
calculation and gives a value that shows how spread or clustered the scores are around
the mean value are.
Now while calculating the standard deviation is outside of you need to know for your course,
we do need to understand how to interpret the value of the standard deviation.
The main thing to keep in mind is the bigger the standard deviation the more spread out
the scores are.
So let's say we have two classes of 10 students taking part in a study and at the end they
take part in the same 50 question quiz.These are the scores for each student.
And these are the standard deviations for both groups.
From these standard variations I would expect you to be able to tell me that group 1 has
scores that are more consistent than group 2, or put another way, group 2’s scores
are more variable than group 1’s scores.
Positives of the standard deviation are it includes all values in its calculation unlike
the range However, the standard deviation is still distorted
by extreme values and is more difficult to calculate than the range
Percentages Percentages are also a way of describing data,
and we can be asked in the exam how to calculate percentages.
You may already know how to calculate percentages in that case keep in mind that when you see
a percentage question in your exam you may need to explain what that percentage means
rather than just stating what the percentage is.
But you can skip this next bit if you know how to work out a percentage.
Grab your calculator, you are allowed one in your A level psychology exam, don't forget
it.
What follows is how I calculate percentages, there are a few ways and you may have been
shown a different way that makes more sense to you and thats fine.
Firstly Lets cover how to calculate the percentage of any number we are given.
In this example the psychologist is conducting a stratified sample for a questionnaire.
Her target population is all the students at a large further education college.
She knows the full population of the college is 2480 students, 595 (24%) students are studying
for A-levels, and 1389 (56%) students are studying for Btec qualifications.
288 (12%) students are only attending to retake GCSE. and 208 (8%) students are adults taking
access to university courses.
So what is the percentage of each subgroup and how many of each group should she include
in her sample of 250 students?
You may know percentages can also be expressed as a fraction or decimal, in this case we
have both the parts of the fracton we need, because for our percentage we want to know
595 out of 2480, so lets write our fraction as 595 over 2480.
We can convert this fraction into a decimal by dividing 2480 by 595.
Here is my calculation.
Now we have the fraction as a decimal, to turn this decimal into a percentage we times
by 100, or more simply we just move the decimal place over to the right twice.
I’m going to round this up, and we get 24%.
Pause the video and try the same calcuatlons with the other groups
[PAUSE] Okay here are the percentages, and how many
participants should be in the sample, to find that out I just multiplied
Secondly, lets see what we need to do if we need to find the percent of a number, you
know now the sample in this study is 250, and we need strata that are 24%, 56%, 12%
and 8% of this number Well the easiest way to work it out is to
turn each of the percentages given into a decimal, then times the decimal by the number
of participants.
So we can work out 24% of 250, by multiplying 0.24 by 250, giving 60 participants, who are
in our a level strata.
By the way We can use this same method to check our original working out of the percentages
of the starta, if im saying 24% of 2480 is 595 I can times 2480 by 0.24 and I get 595.2.
Or we can work out one percent of 250 by dividing 250 by 100, then timesing that figure by the
percentage we want.
Try to complete the other strata of in this stratified sample using either of these methods.
[PAUSE] And here are the answers
I may want to talk about the percentage difference between two numbers.
Lets say the next year the questionnaire is repeated at the college, and the number of
alevel students at the college grew to 724.
What is the percentage change in the number of A-level students from one year to the next?
Well to work out the percentage change between two numbers subtract the old number from the
new number, so 724 minus 595 and then divide this by the old number, then times this by
100.
That gives an increase of 21.7% Lets say the number of btec students reduced
from 1389 to 974 using the same calculation we get minus 29.9%, of course the minus means
there is a decrease in the number of Btec students.
Okay I hoped that helped with calculating percentages.
correlations Correlations are also descriptive statistics,
but of course, we covered positive, negative and zero correlations as well as the correlation
co-efficient in the correlation videos, if you would like a reminder of what they are
and evaluations of the use of correlation, jump back to that video.
Outro I have 8 tutorial videos covering the AS and
A-level research methods sections from 2017 to 2020, these videos have worked examples
to every question and are full of exam tips.
Patrons at the neuron level and above can access these, and many, many more hours of
exam tutorial videos, as well as over a hundred printable resources from across the A-level
over on psych boost .com I do want to thank all the students and teachers
who have supported psych boost over on patreon during the development of the research methods
unit.
It's their support that allows me to teach part time so I can make psych boost on youtube
for everyone.
So thanks to them, and I will see you all in the next research methods video