This document provides an introduction to descriptive statistics and statistical methods. It discusses the aims of exploring data through descriptive statistics like measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation). It also covers testing assumptions like normal distribution through histograms and statistical tests. Examples are provided to demonstrate calculating and interpreting these descriptive statistics in SPSS. Practices are included to have the reader conduct descriptive analyses and normality tests on sample data sets in SPSS.

1. Introduction to applied statistics &
applied statistical methods
Prof. Dr. Chang Zhu1

2. Aims
• Exploring data (descriptive statistics)
central tendency
data distribution (spread/dispersion)
• Testing assumption
normal distribution

3. population vs. sample
• In reality, we can just collect a small
subset of the population.

4. descriptive vs. inferential
• Inferential statistics: draw conclusions
based on a data set (sample) to the entire
population.
• Descriptive statistics: summarize a data
set

5. descriptive statistics
• Measures of central tendency
(mean, median, mode)
• Measures of spread or dispersion
(range, variance, standard deviation)

6. measures of central tendency
• A researcher is interested in the degree to
which a person spends time on Facebook
(in hours per week) and the amount of
time spent socialising with friends (number
of social encounters per month).
• He comes up with the following data set.
(adapted from
http://wps.pearsoned.co.uk/ema_uk_he_dancey_statsmath
_4/84/21626/5536329.cw/index.html)

7. measures of central tendency
P_ID Facebook use Social encounters
1 10 1
2 11 2
3 11 3
4 12 3
5 14 4
6 15 9
7 16 10

8. measures of central tendency
10 11 11 12 14 15 16
Facebook use (hours per week)
• How many hours do the participants spend on
average? (sum = 89)
• What is the score that occurs with the most
frequency?
• What is the score that divides the data into 2
equal halves?

9. measures of central tendency
10 11 11 12 14 15 16
Facebook use (hours per week)
• Mean: on average = 12.7
• Mode: the most frequency = 11
• Medium: divides the data into 2 equal halves = 12

10. measures of central tendency
10 11 11 12 14 15 16
Facebook use (hours per week)
• mean = 12.7
• mode = 11
• median = 12

11. measures of central tendency
– Mean: For normally distributed data, measured as
interval and ratio (scales), the appropriate
measure of central tendency is the mean.
– Median: The median is most appropriate for data
measured as ordinal (but can still be used for
continuous data)
– Mode: is the appropriate measure of central
tendency for nominal data.

12. measures of spread
observed deviance from
mean (M = 12.7)
squared
deviances
10 -2.7 7.29
11 -1.7 2.89
11 -1.7 2.89
12 -0.7 0.49
14 1.3 1.69
15 2.3 5.29
16 3.3 10.89

13. measures of spread
How representative is the mean?
• add up all the squared deviances: sum of
squared errors
affected by sample size
• divide by the number of participants minus 1:
variance
• square root the variance: standard deviation

14. measures of spread
• Range: the difference between the highest
(maximum) and lowest (minimum) scores.
e.g. range = 16-10 = 6
not quite objective, depending on the
length of the data set.

15. In SPSS
Analyse > Descriptive Statistics > Frequencies
> Statistics

16. SPSS output
M = 12.7
SD = 2.28

17. Check it!
Are the standard deviations correct for gender
and modes of learning (full-time/part-time)
variables?

18. visualize the distribution
with histogram
Analyse > Descriptive Statistics >
Frequencies > Charts

19. normal curve
visualize the distribution
with histogram

20. a histogram with normal
distribution (bell-shaped)
• unimodal (one peak)
• symmetrical
• centered around the mean

21. skewed distribution
mode<median<meanmode>median>mean
skewness: measure of symmetry

22. kurtosis
kurtosis: measure the shape of the “bell”

23. testing assumption
quantifying normal distribution:
• the Kolmogorov-Smirnov (K-S) test and the
Shapiro-Wilk test: compare the scores of our
data set with a normally distributed set of
scores with the same mean and standard
deviation)
• p>.05: non-significant
not different: normally distributed
• p<.05: significant
different : non-normal

24. normality assumption
• not normally distributed
• outliers: a score which is very different
from the others
• How to identify outliers?
Boxplot

25. In SPSS
Graphs > Chart Builder > Boxplot

26. In SPSS
Graphs > Chart Builder > Boxplot

27. Questions?
• Descriptive statistics (mean, median,
mode, range, variance, standard
deviation)
• Skewness/Kurtosis
• Histogram to visualize the distribution
In SPSS: Analyse > Descriptive Statistics
> Frequencies > Statistics/Charts
• Test of normal distribution (the K-S test)
In SPSS: Analyse > Descriptive Statistics
> Explore > Plots> Normality plots with tests

28. PRACTICE

29. Practice 1
• using the date file sample data 1.sav
• conduct the descriptive statistics to explore (the
variable named Intrinsic_Motivation_learn)
mean, mode, median
range, variance, standard deviation
draw a histogram to see the frequency of
scores

30. In SPSS
Analyse > Descriptive Statistics > Frequencies

31. Frequencies: Statistics dialogue box

32. Frequencies: Charts dialogue box

33. Descriptive Statistics: results

34. Descriptive Statistics: Histogram

35. Practice 2
• using the date file sample data 1.sav
• conduct the Kolmogorov-Smirnov (K-S) test
and the Shapiro-Wilk test
• Are the scores of the variable
Intrinsic_Motivation_learn normally
distributed?

36. In SPSS
Analyse > Descriptive Statistics > Explore

37. Explore: Plots dialogue box

38. Test of normality: results
According to the result, the Kolmogorov-Smirnov test and the
Shapiro-Wilk test are highly significant, indicating that the distribution
of scores for the variable Intrinsic_Motivation_learn is significantly
different from a normal distribution. In other words, the distribution is
not normal.

39. Practice 3
• using the date file SPSSexam.sav
• conduct the Kolmogorov-Smirnov (K-S) test
and the Shapiro-Wilk test for the variable
exam
1. Are the scores of the variable exam
normally distributed?
2. Redo the K-S test, this time organize the
data by university (Hint: move the variable uni
to the Factor List)