Quantitative Methods: Measurement Levels, Statistics & Interpretation

This assignment provides a comprehensive overview of quantitative research methods for social scientists. It begins by identifying and explaining the four levels of measurement: nominal, ordinal, interval, and ratio scales, detailing their characteristics and applications. The assignment then discusses measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation), highlighting their importance in data analysis. Furthermore, it differentiates between descriptive and inferential statistics, outlining their respective roles in summarizing data and drawing conclusions about populations. Key statistical terms such as hypothesis, null hypothesis, independent and dependent variables, and extraneous variables are explained. Finally, the assignment includes an interpretation of statistical outputs generated by SPSS, focusing on frequency distributions, cross-tabulation, Chi-square results, and Phi/Cramer's V, providing insights into data relationships and statistical significance. Desklib offers a wealth of similar solved assignments and study resources for students.

Quantitative Research
Methods for Social Scientist

Table of Contents
1. Identification and explanation of four level of measurement:.................................................3
2. Measure of central tendency and dispersion............................................................................3
3. Difference between Descriptive statistics and inferential statistics:........................................4
4. Explanation of terms................................................................................................................5
5. Interpretation as per SPSS.......................................................................................................5
REFERENCES................................................................................................................................1

1. Identification and explanation of four level of measurement:
There are four levels to measurement such as:
Nominal scale: nominal scale measurement falls under the easiest category of measurement and
one of the most used tool. For example there are five colours which can be arranged as per the
number or number can be a representative of particular colour. YES/NO also can be used in
various survey done by the brands.
Ordinal scale: this measurement tool is most commonly used for market research to find out the
satisfaction level of the customer (Maranell, 2017). For example if the brand sell the product and
often conduct a questionnaire where they got the data of satisfaction level in a systematic
manner.
Interval scale: interval means the distance or the difference between two units, this is mainly
help researcher to find out the variable difference. For example 80 degree will remain high as
compared to 50 degree, but the difference can be noted between two of these interval. Calendar
and time are the best example of interval scale.
Ratio scale: ratio measurement is the most used tool, this provide detailed and accurate
information of the data. Without ratio measurement, the mean, median and modes are useless, as
they need ratio to calculate the data. For example, what is the height of a person and that height
can be in ratio of 5 feet or more than 5 feet.
2. Measure of central tendency and dispersion
Measure of Central Tendency:
Central tendency is one of the statistical measures which represent the value of the given
dataset that exist just in the middle of same data base. This is also known as centre of the data
distribution. In order to measure the central tendency, the three important measures available are
Mean, Mode and Median (Rayat, 2018). Mean basically represent the average value of the
dataset, median represent the middle value of the given data base and mode on the same side
represent the value which occur frequently or maximum time in the data set. It provides
summary of the dataset.
Measure of Dispersion:

The measure of dispersion also known as statistical dispersion states the extent to which a
particular numerical data is vary or away from its average or mean value. This is one of the best
measures which is of two types i.e., absolute and relative dispersion. It helps in identifying and
understanding the distribution of data (Gries, 2019). In other word, the measure of dispersion
helps in interpretating the variability of data i.e., homogeneous and heterogeneous of the data.
Range, variance, standard deviation, quartile and quartile deviation, mean and mean deviation
are type of absolute deviation. The coefficient of all absolute measure is type of relative measure.
3. Difference between Descriptive statistics and inferential statistics:
Descriptive statistics Inferential statistics
It is used for the summarization of the
characteristics of the data set.
It allows the testing of hypothesis or enable
that the data is generalizable to broader
population or not.
It is used for the describing of population
under study.
It is focussed towards drawing of conclusion
about the population on the basis of
observation and sample analysis.
It is used for organizing, analysing and
presentation of data in a meaningful manner.
It is used for comparing, testing and predicting
the data.
It present the result in the form of graph,
charts, and tables (Amrhein, Trafimow and
Greenland, 2019).
Here probability would be emerged as a result
It is used for describing the situation It is used for the explanation of the chances of
occurrence of event (Surbhi, 2019).
Under this statistics the explanation of data
would be performed that is already known.
Under this statistics the data is studied and
evaluated which is beyond the available data.
It is used for definitive measurement It is used for the determination of margin of
error that the is performed and occurred during
the research.
It is used for drawing conclusion regarding the
data set that is obtained by sampling.
It generally summarize the information that is
revealed in the data set

4. Explanation of terms
Hypothesis and null hypothesis:
It refers to the proposed explanation of the phenomenon (Harms and Lakens, 2018). There are
two types of hypothesis:
Alternative hypothesis: There is a significant relationship between the variables.
Null hypothesis: There is no significant relationship between the variables (Gigerenzer, 2018).
Independent and dependent variables:
Independent variables are those variables under which there is nonexistence of
dependency. This means that they are non-dependent on any variable (Guetterman, 2019).
Dependent variables are those variables in which the outcome and results are dependent
upon the variables (Mood, Morrow and McQueen, 2019). This means that the result of these
variables are depended upon other variables.
In other terms it can be considered that independent variables are the cause while the
dependent variable is the effect. This means that the independent variable would affect the result
of the dependent variables (Priyadarshan, 2019).
Extraneous variables:
These are all the variables which is not independent variable but they affect the result of
the experiments. It can be considered as a manipulation of independent variables that would
affect the dependent variables (Young, 2018). This can be understood with an example that if the
participant are taking a chilly test, the temperature of the room would be considered as an
extraneous variable. Under this some participants would be affected by the temperature but the
other may not.
5. Interpretation as per SPSS
Frequency:
Frequency refers to the largest number of people and the response towards a specified
problem and response (Xu and et.al., 2020). As per the frequency of Noisy neighbours it can be
interpreted that the frequency of not at all common is highest which means that majority of
neighbours are not noisy and loud. This frequency table also shows that the least response have
got towards the fairy common which means that very low proportion said that the neighbours are
loud.

Cross tabulation:
Cross tabulation enable the information that is related with the determination of
information about the variables (Momeni, Pincus and Libien, 2018). as per the cross-tab it can be
interpreted that Adults are that proportion of population that is loudest among all i.e. young adult
and elderly. The cross tab also interpret that the young adults are those population which is
lowest among loudest people.
Chi-square results:
It is used for the comparison of observed results with the expected one (Zhai and et.al.,
2018). As per the table of observation it can be clarified that the p value is 0.00 which is less than
0.05 that means alternative hypothesis is accepted and null is rejected. This shows that the age of
population is depended upon the loudness of voice.
Phi/Cramer:
As per the observed table it can be interpreted that the value as the value of Phi/crammer is
0.17 and 0.12 then it can be analysed that there is an existence of weak relationship. This means
that the relationship of age with the loudness of voice is not related with each other.

REFERENCES
Books and journals
Amrhein, V., Trafimow, D. and Greenland, S., 2019. Inferential statistics as descriptive statistics:
There is no replication crisis if we don’t expect replication. The American
Statistician. 73(sup1). pp.262-270.
Gigerenzer, G., 2018. Statistical rituals: The replication delusion and how we got
there. Advances in Methods and Practices in Psychological Science. 1(2). pp.198-
218.
Gries, S. T., 2019. Analyzing dispersion. Practical handbook of corpus linguistics. New York,
NY: Springer.
Guetterman, T.C., 2019. Basics of statistics for primary care research. Family medicine and
community health. 7(2).
Harms, C. and Lakens, D., 2018. Making'null effects' informative: statistical techniques and
inferential frameworks. Journal of Clinical and Translational Research. 3(Suppl 2).
p.382.
Maranell, G. ed., 2017. Scaling: A sourcebook for behavioral scientists. Routledge.
Momeni, A., Pincus, M. and Libien, J., 2018. Cross Tabulation and Categorical Data Analysis.
In Introduction to Statistical Methods in Pathology (pp. 93-120). Springer, Cham.
Mood, D.P., Morrow, J.R. and McQueen, M.B., 2019. Advanced Statistics. In Introduction to
Statistics in Human Performance (pp. 311-330). Routledge.
Priyadarshan, P.M., 2019. Basic Statistics. In PLANT BREEDING: Classical to Modern (pp.
131-169). Springer, Singapore.
Rayat, C. S., 2018. Measures of Central Tendency. In Statistical Methods in Medical
Research (pp. 33-46). Springer, Singapore.
Xu, and et.al., 2020. Learning in the frequency domain. In Proceedings of the IEEE/CVF
Conference on Computer Vision and Pattern Recognition (pp. 1740-1749).
Young, M.E., 2018. A place for statistics in behavior analysis. Behavior Analysis: Research and
Practice. 18(2). p.193.
Zhai, and et.al., 2018, November. A chi-square statistics based feature selection method in text
classification. In 2018 IEEE 9th International Conference on Software Engineering
and Service Science (ICSESS) (pp. 160-163). IEEE.
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Online references
Surbhi. S., 2019. Difference Between Descriptive and Inferential Statistics. [Online]. Available
through <https://keydifferences.com/difference-between-descriptive-and-inferential-
statistics.html>
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