Management Research Methods 1: an overview of calculations
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Course
Management Research Methods 1
Institution
Universiteit Van Amsterdam (UvA)
This course reviews and explains the basic statistical concepts and techniques that are used in the area of Management and Business Administration and MSc theses, and emphasizes the practical application of the various techniques using SPSS software.
Σ = “sigma”, add everything up xi = values
n = sample size s2 = variance
ε = error π = “pi”, multiply everything
p = probability s = standard deviation (sample)
x̄ = “mean” (average, sample) = “mean” (average, sample) σ = standard deviation (population)
Mode:
1) Arrange all the numbers from low to high in a vertical table
2) Find the “middle number” (if an odd number) = mode
3) If there is no “middle number” (if even number of data points) = no mode
Mean (average):
1) Add up all the scores
2) Divide by the “n” (number of scores)
Range (spread of scores):
1) Start with the largest value on the baseline of the graph
2) Subtract the smallest value from that
Sample Standard Deviation:
When you have one set of data points, sd shows how far each score falls from the mean
(average) within each group: “sample”
Standard Deviation is the square root of Variance
1) Calculate the mean (average) of scores (x̅ or “x bar”) or “x bar”)
a. 5 scores
b. 2, 3, 4, 7, 9
c. x̅ or “x bar”) = 5
2) Subtract the mean from each data point (x - x̅ or “x bar”))
a. x - x̅ or “x bar”) = -3, -2, -1, 2, 4
b. CHECK: adding up this column should always =0
3) Square each of these values (squaring two negatives = positive)
a. x - x̅ or “x bar”)2 = 9, 4, 1, 4, 16
4) Divide this sum by (n-1)
a. 6.8 (this is your variance)
5) Take the square root
a. 2.6
6) This number (2.6) is your standard deviation
x x̅ or “x bar”) x - x̅ or “x bar”) x - x̅2 x̅ or “x bar”)/n-1 σ
2 - -3 9 - -
3 - -2 4 - -
4 - -1 1 - -
7 - 2 4 - -
9 5 4 16 6.8 2.6
, -2 σ = -5.2 -1 σ = -2.6 1 σ = 2.6 2 σ = 5.2
Sample Variance
The average of the squared differences from the mean.
1) Calculate the mean (average) of scores (x̅ or “x bar”) or “x bar”)
2) Subtract the mean from each data point (x - x̅ or “x bar”))
a. CHECK: adding up this column should always =0
3) Square each of these values (two negatives2 = positive)
4) Add them all up (Σ)
5) Find your n-1 value (n = 5, n - 1 = 4)
6) Divide the sum by the (n-1)
7) The result of this is standard deviation.
8) Square this to get variance.
Deviance
1) Subtract a data point from the average (xi - x̅ or “x bar”))
a. Data point = 5, average = 6
b. Deviance = -1
Total deviance
1) Add up all deviances for every data point
Interquartile range
Interquartile range: IQR = Q3 – Q1
1) Put the numbers in order: 1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27
2) Find the median: place parentheses around the numbers above and below the
median so Q1 and Q3 are easier to spot:(1, 2, 5, 6, 7), 9, (12, 15, 18, 19, 27)
3) Find Q1 (Lower Quartile) and Q3 (Upper Quartile)
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