This document provides an overview of quantitative data analysis techniques for research. It describes the different levels of measurement (nominal, ordinal, interval, ratio) and key descriptive statistics like measures of central tendency, frequency distributions, and measures of dispersion. It also discusses inferential statistics and common tests like t-tests, ANOVA, correlation, and chi-squared tests. The purpose of statistical analysis is to summarize and make inferences about data to either support or reject research hypotheses.

1. Quantitative Research-Part 3
Data Analysis
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BSN312 Research Methodology
AY 2022/23 Semester 3
Week 00

2. Expected Learning Outcomes
• Describe the major characteristics of measurement
• Identify and interpret various descriptive & Inferential statistics
• Discuss hypothesis testing procedures and interpret p values
• Specify the appropriate application for t-tests, correlation
coefficients, analysis of variance, Chi-squared tests and
interpret the meaning of the calculated statistics
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3. Measurements
Measurement: involves the assignment of numbers to objects to
represent the amount of an attribute, using a specified set of rules.
Types:
1. Nominal
2. Ordinal
3. Interval
4. Ratio
• Levels of measurement are ranked from lowest to highest
• As a measurement becomes more precise (higher level), data
analysis is more sophisticated and powerful
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6. I. Nominal Measurement
• Is the lowest of the four categories
• Used when data can be organized into categories
• For example, ethnicity, married, age, disease…
• The categories differ in quality, not quantity
• Data such as gender marital status and diagnosis are examples of nominal data
• Example:
• Please indicate which of the following symptoms you experience by ticking the
appropriate boxes
• Persistent cough
• Poor circulation to feet, legs, and/or hands
• High blood pressure
• Sleep problems
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7. II. Ordinal Measurement
• Ranked data: first to last
• Refers to variables that are not able to be measured precisely but can be
compared to one another to rank them
• First, second, third…
• Highest rate of …
• Example:
• Please rank in order (from 1-7) the importance of the following concerns you have for your own
health:
• Diet
• Weight
• Cigarette smoking
• Alcohol
• Exercise and activity
• Sleep
• Stress
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8. III. Interval Measurement
• Data is obtained as distinct units or whole numbers, with equal
intervals between the numbers (the rank of objects and the distance
between them).
• For example, when we measure temperature (in Fahrenheit), the
distance from 30-40 is the same as distance from 70-80.
• The interval between values is interpretable. Because of this, it
makes sense to compute an average of an interval variable
• Also obtained in response to ‘How many’? Questions. Like the
number of cigarettes per day, admissions per week…
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9. IV. Ratio Measurement
• Is the highest level of measurement
•
• Continuous data that can be measured on a scale from zero to
infinity
• Ratio measures have a real zero, not like temperature, for
example.
• Decimal places
• Weight, length, time, blood chemistry…
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11. Statistical Analysis of Quantitative Data
• Statistical procedures are numerical summary descriptions of
information gathered through observation or measurement
• Statistical procedures enable the researchers to organize,
interpret, and communicate numerical information.
• There are 2 types of statistics:
1. Descriptive
2. Inferential
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12. Descriptive Statistics
• Descriptive statistics are used to synthesize and describe data
• They are summary indicators of larger groups of data
• Averages and percentages are examples of descriptive statistics
• These conventional statistical procedures are also called parametric
tests.
• Types
1. Frequency Distribution
2. Central Tendency
3. Measure of Dispersion
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13. 1. Frequency Distribution
• Is a systematic arrangement of numerical values from the
lowest to the highest, together with a count (or percentage) of
the numbers of times each value was obtained.
• On graphs, data distribution can be described by their shapes
using frequency polygon
• Symmetrical distribution or skewed distribution
• Positive
• Negative
• A normal distribution (called a bell-shaped curve) is
symmetrical, unimodal, and not very peaked
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20. 3. Measure of Dispersion - Range
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21. 3. Measure of Dispersion –Standard
Deviation
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22. Standard Deviation
• In normal distribution there are around 3 standard deviations
above and below the mean
• For example, if the mean is 50 and the SD is 10 a fixed
percentage of cases fall within certain distances from the mean
• Of all cases 68% fall within 1SD above and below the mean.
• In a normal distribution 95% of these scores fall within 2 SDs
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24. Inferential Statistics
• Statistical procedures that allow researchers to make inferences
about the population
• Inferential statistics are used to:
• Help the researcher decide if the result of an experiment
supports the hypothesis that there is a difference between the
experimental and the control group. In other words, to test
Hypotheses.
• Inferences: Draw conclusions and implications
• Enables conclusion to be made from data based upon probability
theory
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25. Inferential Statistics
• There are two types of inferential statistics: Parametric and
non-parametric
• Parametric tests relate to the existence of real differences
between the experimental and control groups. They are used
when the data meet certain criteria :
• Data must be interval/ratio level
• Subjects should have been randomly selected.
• Data should be normally distributed
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26. Inferential Statistics
• For each parametric test, there is a non-parametric test.
• Nonparametric tests are used when:
• Data measured on a nominal or ordinal scale
• Data distribution is markedly skewed or
• The sample size is too small to be confident about the distribution
• Parametric tests are more powerful than nonparametric tests
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27. Hypothesis Testing
• Statistical hypothesis testing provides objective criteria for deciding whether the
research hypothesis should be accepted as true or rejected as false
• The research hypothesis states that there is a relationship between the
independent and dependent variable
• The null hypothesis states that there is no relationship between the independent
and dependent variables.
• When the null hypothesis shows that it has a high probability of being
incorrect (rejected), this is considered evidence to support (accept) the
research hypothesis.
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28. Example- Hypothesis Testing
• Suppose we hypothesized that maternity patients exposed to a
teaching film on breastfeeding would breastfeed longer than mothers
who did not see the film.
• We find that the mean number of days of breastfeeding is 131 for the
experimental subjects and 125 for the control subjects
• Two explanations for the observed outcome are possible:
• The film is truly effective in encouraging breastfeeding (the research hypothesis)
• or the difference in this sample was due to chance factors (the null hypothesis)
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29. Hypothesis Testing- Type I and II Errors
• Type I error
• Reject the null hypothesis when it is true
• say the treatment has had an effect when in reality, it has not
• Type II error
• Fail to reject (accept) the null hypothesis when it is false
• say there is no treatment effect when in reality, there is
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30. Type I and II Errors
• The actual situation is that the null hypothesis is:
• True False
• The researcher’s True
• calculate (Accept)
• statistics
• and decides
• That the null False
• Hypothesis (Reject)
• is:
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Correct Decision Type II error
Type I Error Correct Decision

31. Level of Significance
• Researcher controls the risk of making a type I error by
establishing a level of significance or alpha levels
• It is expressed as a probability (p) or Alpha level
• E.g. a p-value of 0.05 means a 5% probability of a type I error. i.e.
There is only a 5% probability that the result achieved is due to chance
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32. Level of Significance
• P < .05 Significant
• P < .01 Highly significant
• P < .001 Very highly significant
• P = 0.05 we are 95% confident that the difference found is
actually true (5% chance we are wrong)
• P = 0.01 we are 99% confident that the difference found is
actually true (1% chance we are wrong)
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33. Common Inferential Statistical Tests
• Correlation
• t-test
• ANOVA
• Chi-squared test
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34. 1. Correlation
• Examine relationships between the characteristics of people
between groups variables
Studying hours and grades or watching TV and grades.
• Pearson correlation coefficient ‘r ’ : Most commonly used measure to
indicate the degree of the linear relationship between two variables
• Range +1 to –1 (+1 indicating a perfect, positive, linear relationship) -
1.00 indicating a perfect, negative, linear relationship)
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35. Correlation Tests
• Pearson’s r : is a correlation coefficient designating the
magnitude of relationship between two interval – or ratio level
variables (parametric test)
• The Spearman rank order correlation coefficient test is the
nonparametric test used when data collected in ordinal level
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36. 2. t-tests (Dependent and Independent t-
tests) - parametric test
Dependent t-test: used on interval and ratio data. It is used to
measure two means in the same group using before and after/
pretest- post-test design (within subjects)
• BP pretest and then post-test for the same group
Independent t-test: used on interval and ratio data. It is used to
compare the means of two separate groups (between subjects)
• Mean Bp of the control group compared with the mean Bp of the
experimental group
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37. Analysis of Variance (ANOVA)
• Analysis of variance (ANOVA) is a statistical procedure for
testing mean differences among three or more groups by
comparing variability between groups to variability within groups
• For example, an ANOVA would be appropriate for the following
hypothesis:
"There will be a difference between grades 1, 2, and 3 scores on
the elementary mathematics achievement test”.
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38. Chi-Squared test (ꭓ²)
• Chi –squared test ꭓ² is a statistical test used to assess group
differences in proportion. It is a non-parametric test uses
nominal data. It looks at whether the difference between the two
groups was as expected.
• Are the groups the same or different?
• Applies to nominal or ordinal data.
• E.g. Sex (male, female) and dropping out of school (dropout,
stay-in)
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39. Statistical Analysis Software Program
• SPSS (Statistical Package for Social Sciences) is one of the
mostly used computer programs for statistical analysis.
• Statistics included in this software:
• Descriptive statistics (means, SD, frequencies,….)
• Inferential statistics (parametric tests such as ANOVA, Correlation, t-
test, and nonparametric tests such as chi-square)
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40. References
• Polit, D.F. & Beck, C.T. (2017). Essentials of nursing research:
Appraising evidence for nursing practice (9th ed.). Philadelphia:
Lippincott.
• Burns, N., & Grove, S.K. (2020). The practice of nursing
research: Appraisal, synthesis, and generation of evidence (8th
ed.). St. Louis, Mo: Saunders
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