INTBUS 6 Lecture Notes - Lecture 9: Central Tendency, Frequency Distribution, Categorical Variable
23 Oct 2020
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Chapter 11: Basic Data Analysis for Quantitative Research
11.1: Value of Statistical Analysis
- Once data have been collected and prepared for analysis, several statistical procedures can
help to better understand the responses.
11.1.1. Measures of Central Tendency
Central tendency: central or typical value for a normal distribution
- Frequency distributions can be useful for examining the different values for a variable.
- Frequency distribution tables are easy to read and provide a great deal of basic
information.
- The mean, median, and mode are measures of central tendency.
- These measures locate the center of the distribution.
- For this reason, the mean, median, and mode are sometimes also called measures of
location
Exhibit 11.1.
Mean: the arithmetic average of the sample
- all values of a distribution of responses are summed and divided by the number of valid
responses.
- The mean can be calculated when the data scale is either interval or ratio.
- generally, the data will show some degree of central tendency, with most of the responses
distributed close to the mean
- It is a very robust measure of central tendency.
- It is fairly insensitive to data values being added or deleted.
- It can be subject to distortion, if extreme values are included in the distribution.
- be carefull when interpreting the mean, take into account the underlying distribution
(coffee, male/female example)
Median: the middle value of a rank-ordered distribution; exactly half of the responses are
above the median value.
- number above and below median is the same
- If the number of data observations is even, the median is generally considered to be the
average of the two middle values.
- If there is an odd number of observations, the median is the middle value.
Chapter 11: Basic Data Analysis for Quantitative Research
- The median is especially useful as a measure of central tendency for ordinal data and for
data that are skewed.
Mode: the most common value in the set of responses to a question; the response most
often given to a question.
- it’s the value that represents the highest peak in the distributions’ graph
- The mode is especially useful as a measure for data that have been somehow grouped into
categories.
→ For nominal data, the mode is the best measure.
→ For ordinal data, the median is generally the best.
→For interval or ratio data, the mean is appropriate, except when there are extreme values
within the data, which are referred to as outliers.
11.1.2. SPSS application
book page 276
11.1.3. Measures of Dispersion
- Measures of central tendency often do not tell the whole story about a distribution of
responses.
- Measures of dispersion describe how close to the mean or other measure of central
tendency the rest of the values in the distribution fall.
→ Two measures of dispersion that describe the variability in a distribution of numbers are
the range and the standard deviation:
• Range: the distance between the smallest and largest values in a set of responses.
- e.g. the difference between the response category “Very frequently” (largest value
coded 5) and the response category “Very infrequently” (smallest value coded 1)
- The range is more often used to describe the variability of open-ended questions.
- It is calculated as (highest point – lowest point) = range.
• Standard deviation: the average distance of the distribution values from the mean.
- The difference between a particular response and the distribution mean is called a
deviation.
- If we subtracted each value in a distribution from the mean and added them up, the
result would be close to zero.
- To calculate the estimated SD, we use the formula:
Chapter 11: Basic Data Analysis for Quantitative Research
- Once the sum of the squared deviations is determined, it is divided by the number
respondents minus 1.
- The number 1 is subtracted from the number of respondents to help produce an unbiased
estimate of the SD.
- Sometimes the average squared deviation is also used as a measure of dispersion for a
distribution.
- The average squared deviation is called the variance
→ estimated SD is the square root of the average squared deviation (variance) → represents
the average distance of the values in a distribution from a mean
- If the estimated SD is large, the responses in a distribution of numbers do not fall very close
to the mean of the distribution, and vice versa.
- size of SD tells you something about the level of agreement among respondents when they
answered a particular question
• Together with the measures of central tendency, these descriptive statistics can
reveal a lot about the distribution of a set of numbers representing the answers to an
item on a questionnaire.
11.1.4. SPSS application
page 278
11.1.5. Preparation of Charts
- Many types of charts and graphics can be prepared easily using the SPSS software.
- Chart and other visual communication approaches should be used whenever practical.
- They help information users to quickly grasp the essence of the results developed in data
analysis, and also can be an effective visual aid to enhance the communication process and
add clarity and impact to research reports and presentations.
Bar chart: shows tabulated data in form of bars that may be horizontally or vertically
orientated
- they are excellent tools to depict both absolute and relative magnitudes, differences and
change
- be cautious when using charts and figures
11.2. How to Develop Hypotheses
- Researchers often have preliminary ideas regarding data relationships based on the
research objectives.
- These ideas are derived from previous research, theory, and/or the current business
situation, and typically are called hypotheses.
- Hypotheses are developed prior to data collection, generally as a part of the research plan
- When we test hypotheses that compare two or more groups, if the groups are different
subsets of the same sample then the two groups must be considered related samples for
