Summary Management Research Methods 1 (MRM1) Grade: 8,5

Week 1: Data types, describing and exploring your data
The type of statistical analysis depends on the type of variable

QUALITATIVE variable: outcomes are categories
 4. Nominal: unordered categories (Male/Female)
 3. Categorical: ordered categories (Likert scale, Job skill)

QUANTITATIVE variables: outcomes are numbers
 2. Discrete: series of isolated numbers (numbers of cars sold, change in
employees)
 1. Continuous: interval of possible values (BNP, temperature)

A variable can always be treated as a lower type.

For QUALITATIVE data we use:
 Pie chart (suited for ordinal data)
 Bar chart (suited for ordinal data)
 Frequency table  Note: cumulative 50% is the Median.

 Median (the middle outcome only for ordinal data) 
 Mode (the most frequent number)

For QUANTITATIVE data we use:
 Histogram (the highest bar in the graph is the Mode)
 Mode, Range
 Percentiles, including Median and Quartiles
 Boxplot
 Mean, Standard deviation, Kurtosis, Skewness
 Z-scores

Likert variable cannot be treated as quantitative (then one would
assume that the differences between the scales are similar,
which is not).
Binary variable is a categorical variable consisting of 2 categories (k=2) can always be
treated as nominal, categorical and discrete (Male / Female)

A histogram provides information about the distribution of the values:

1. Location (Central tendency, Median, Mode, Mean) 2 distributions with
different locations.

2. Spread (Variability)  2 distributions with different spreads.

3. Skewness (lack of symmetry)

4. Kurtosis (thick and long tails)

5. Outliers (remote (afgezonderde) values)

, 6. Special features (e.g. gaps in the data)




Percentiles
80th percentile = score with 80% cumulative percentage (80% below and 20%
of the scores above it).

Quartiles:
The 1st and 3rd quartile are called Turkey’s Hinges. The 2nd quartile is called the
Median.
Q1: first quartile: 25th percentile  if n is odd use the lower half including the median.
Q2: second quartile: 50th percentile  if n is even the Median is the midway between the 2 values.
Q3: third quartile: 75th percentile  if n is odd use the upper half including the median.

Reading a Box plot:
1 - Location (central tendency) - median, Q2
2 - Spread (variability) - length of box (IQR)= Q3 –
Q1
3 - Skewness (no symmetry) - compare
whiskers & outliers
4 - Length of tails - difficult to judge
5 - Outliers - indicated individually

Measure of central tendency, or sample mean (or
average) – similar to population mean:




Range = Maximum score – Minimum score

Measure the spread of observations around the
central tendency.
Variance average of the squared differences between each
observation and the mean: 

Standard Deviation: Square root of the variance:
 The useful distance of the observation to the sample mean. So it
measures the spread of the observations.
 A larger variances makes it harder to predict an individual
value of the variable

Skewness: the measure of asymmetry of a distribution (is one tail longer than the other?): 
Values outside -1, 1 indicate serious skew
 Positive skewness: Sample Mean > Median
 Negative skewness: Sample Mean < Median

Efficient statistics (actually use all statistics): Mean, Standard
Deviation, Skewness
Inefficient statistics: Median, mode, IQR, Range
(Sensitive to
outliers)
Z-score: The amount of standard deviations a score is above/below the sample
mean: 
 Z-score ouside (-2,5; 2,5) indicates an outlier.

,  If the lowest score lies less than 1 SD from the mean it indicates positive skewness and vice
versa.

If the distribution is bell-shaped, then approximately:
 5% of the observations has zi < -1.645 and 5% has zi > 1.645
 2.5% of the observations has zi< -1.96 and 2.5% has zi > 1.96
 0.5% of the observations has zi< -2.576 and 0.5% has zi > 2.576




The sample statistics provide information about the distribution of the values:
1 Location (central tendency) → mean, median, mode
2 Spread (variability) → standard deviation, IQR, range
3 Skewness (lack of symmetry) → skewness
4 Kurtosis (thick and long tails) → not covered in this course
5 Outliers → see z-scores

Requirements for the variables:
 Bell-shaped (strong requirement)
 Symmetrical distribution (weak requirement)

Lessons learned
Homework exercises:
 If there is asked to give Q2 of a variable and the n= even (e.g. 68). Q2 = (x34+
x35)/2.
o For Q1 and Q3 if n = even (68) take the middle of the first/last half including
Q2. So in this case35/2 is (x17 + x18)/2 = Q1.
 After calculating the variance DON’T FORGET to Root the variance to calculate SD!
 If the Mean > Median  positive skew and vice versa.
 Skewness is not a valid statistic for Ordinal data.
 Mode and median are valid statistics for Ordinal data.
o Mode IS and Median IS NOT a valid statistic for nominal data.
 In case one is asking to interpret the spread  it is calculated with the IQR.
 High/positive kurtosis is presence if both whiskers are relatively long (longer than
the box).
 The distribution is positively skewed if the upper whisker is longer than the other
(Boxplot).
 The distribution is positively skewed if the bars left in the histogram are higher than
right.

Additional exercises:
 2b. If they ask relative frequency  number/total  don’t give percentages just
give e.g. 0.16.
 2b. You would use a histogram instead of a bar chart because the spaces between
the bars (with a bar chart) would suggest the value between the bars are not
possible.