A training workshop that assists researchers in dealing with statistics throughout the research. It is the science of dealing with numbers. It is used for collection, summarization, presentation & analysis of data.

1. STATISTIC IN RESEARCH
Dr. Dalia El-Shafei
Assoc. prof., Community Medicine Department, Zagazig University
http://www.slideshare.net/daliaelshafei

3. STATISTICS
It is the science of dealing with numbers.
It is used for collection, summarization, presentation & analysis of data.
Collection Summarization Presentation Analysis

4. USES OF MEDICAL STATISTICS
Epidemiological research studies.
Planning, monitoring & evaluating community health care programs.
Diagnosis of community health problems.
Comparison of health status & diseases in different countries and in
one country over years.
Form standards for the different biological measurements as weight,
height.

5. STATISTIC IN RESEARCH
A training workshop that assists researchers in dealing with
statistics throughout the research.
Protocol
Thesis
Manuscript
Presentation

6. STATISTIC IN THE PROTOCOL

7. Sample size
Statistical
design
Hypothesis

8. SAMPLE SIZE
The sample size was calculated through Open Epi-Info
(Epidemiological information package) software version
6.1, according to the prevalence of “LBP among workers in
O&G industry” in a previous study which was 51.0% (Jensen
& Laursen, 2014) and at a confidence interval of 95%, power
of the study 80%, the estimated sample size was calculated to
be 80 workers. They were selected using simple random
sampling technique after preparing a list of workers who met
the inclusion criteria.

9. STATISTICAL DESIGN (DATA MANAGEMENT)
 The collected data will be presented by tables and graphs , and
analyzed by computer using a data base software program (Epi-info
statistical package version 6.04) and Statistical Package of Social
Services version 19 (SPSS).
 The results will be considered statistically significant when the
significant probability is less than or equal to 5 % (p ≤ 0.05).

10. NULL & ALTERNATIVE HYPOTHESES
 A specific hypothesis is formulated & data is collected to
accept or to reject it.
 Null hypotheses: H0: x1=x2 “No difference between x1 &
x2”.
 If we reject the null hypothesis, i.e there is a difference
between the 2 readings, it is either H1: x1 < x2 or H2: x1>
x2
 Null hypothesis is rejected because x1 is different from x2.

13. STATISTIC IN THE THESIS

20. Same format for all tables
• Use subheadings to separate the results of different
experiments.
• Should be presented in a logical order & in order of
importance.
• Use the past tense to describe your results; however, refer
to figures & tables in the present tense.

22. The results of this study are presented in eight sections:
Section I: Socio-demographic characteristics of the study subject (Psychiatric
nurses).
Section II: Patient Safety Incidents (Adverse Patients' Events) Assessment
• Assessment questionnaire
• Hospital records.
Section III: Educational needs assessment
Section IV: Knowledge Test (pre / post-test)
Section V: Psychiatric nurses’Attitude towards patient safety and its measures
Section VI: Assessment of psychiatric nurses’ performance
Section VII: Assessment of Physical environment in mental health settings.
Section VIII: Evaluation of the program outcome from nursing staff 'point of
views.

23. STATISTICAL ANALYSIS
The collected data were computerized and statistically
analyzed using SPSS program (Statistical Package for Social
Science) version 16.0. Qualitative data were represented as
frequencies and percentages. Quantitative data were
compared using Student’s t test. The test results were
considered significant when p value < 0.05.

24. STATISTICS IN THE MANUSCRIPT

26. Same format for all tables
• Use subheadings to separate the results of different
experiments.
• Should be presented in a logical order & in order of
importance.
• Do not duplicate data among figures, tables, and text.
Follow the journal’s instructions

27. STATISTICS IN THE PRESENTATION

30. TYPES OF DATA

31. Data
Quantitative
Discrete (no
decimal)
Continuous
(decimals
allowed)
Qualitative
Categorical Ordinal

33. DATA COLLECTION

34. 1ry sources
2ry sources

36. DATA PRESENTATION

37. Tabular
Graphical
Textual

38. Eighty-nine construction workers were included in the study.
About half of them(59.6%) were ≤ 30 years old with a mean age
of 33.9 ± 9.7.

39. TABULATION
Basic form of presentation
• Table must be self-explanatory.
• Title: written at the top of table to define precisely the content,
the place & the time.
• Clear heading of the columns & rows
• Units of measurements should be indicated.
• The size of the table depends on the number of classes “2 -10
rows or classes”.

43. Assume we have a group of 20 individuals whose blood groups were as
followed: A, AB, AB, O, B, A, A, B, B, AB, O, AB, AB, A, B, B, B, A,
O, A. we want to present these data by table.
Distribution of the studied individuals according to blood group:

44. These are blood pressure measurements of 30 patients with hypertension.
Present these data in frequency table: 150, 155, 160, 154, 162, 170, 165,
155, 190, 186, 180, 178, 195, 200, 180,156, 173, 188, 173, 189, 190, 177,
186, 177, 174, 155, 164, 163, 172, 160.
Blood pressure “mmHg” Frequency %
150 –
160 –
170 –
180 –
190 -
200 -
6
6
8
6
3
1
20
20
26.7
20
10
3.3
Total 30 100
Frequency distribution of blood pressure measurements among studied
patients:

47. Eighty-nine construction workers were included in the study.
About half of them (59.6%) were ≤ 30 years old with a mean
age of 33.9 ± 9.7 with basic education (50.6%). Most of them
were married (71.9%) and living in rural areas (69.7%).
Unskilled workers represented near two thirds of the sample
(67.4%). As regarding occupational history, more than half of
participants (60.7%) had worked in the construction industry
for more than 10 years with a mean of 12.6 ± 6.9 with average
49.2 (Table 1).

48. GRAPHICAL PRESENTATION
Simple “easy to
understand”
Save a lot of words Self explanatory
Has a clear title
indicating its content
“written under the
graph”
Fully labeled
The y axis (vertical)
is usually used for
frequency

49. Graphs
Bar chart
Pie diagram
Histogram
Scatter diagram
Line graph
Frequency polygon

53. BAR CHART
 Used for presenting discrete or qualitative data.
 A graphical presentation of magnitude (value or %) by
rectangles of constant width & lengths proportional to the
frequency & separated by gaps

55. Simple Multiple Component

56. PIE DIAGRAM
 Consist of a circle whose area represents the total frequency
(100%) which is divided into segments.
 Each segment represents a proportional composition of the
total frequency.

57. HISTOGRAM
• It is very similar to bar chart with the difference that the
rectangles or bars are adherent (without gaps).
• It is used for presenting class frequency table (continuous
data).
• Each bar represents a class & its height represents the
frequency (No. of cases), its width represent the class
interval.

60. SCATTER DIAGRAM
It is useful to represent the relationship between 2 numeric
measurements, each observation being represented by a
point corresponding to its value on each axis.

62. LINE GRAPH
It is diagram showing the relationship between two numeric
variables (as the scatter) but the points are joined together to
form a line (either broken line or smooth curve)

65. FREQUENCY POLYGON
 Derived from a histogram by connecting the mid points of the tops of
the rectangles in the histogram.
 The line connecting the centers of histogram rectangles is called
frequency polygon. We can draw polygon without rectangles so we will
get simpler form of line graph.
 A special type of frequency polygon is “the Normal Distribution
Curve”.

67. NORMAL DISTRIBUTION CURVE
The NDC is the frequency polygon of a quantitative continuous
variable measured in large number.
It is a form of presentation of frequency distribution of biologic
variables “weights, heights, hemoglobin level and blood pressure”.

69. CHARACTERISTICS OF THE CURVE
Bell shaped, continuous curve
Symmetrical i.e. can be divided into 2 equal halves
vertically
Tails never touch the base line but extended to infinity
in either direction
Mean, Median and Mode values coincide
2 parameters: Mean (X) “center of the curve” &
Standard deviation (SD) “scatter around the mean”

70. AREAS UNDER THE NORMAL CURVE
X ± 1 SD = 68% of the area on each side of the mean.
X ± 2 SD = 95% of area on each side of the mean.
X ± 3 SD = 99% of area on each side of the mean.

71. SKEWED DATA
If we represent a collected data by a frequency polygon & the resulted
curve does not simulate the NDC (with all its characteristics):
“Not normally distributed”
“Curve may be skewed to the Rt. or to the Lt. side”

73. CAUSES OF SKEWED CURVE
The data collected are from
So; the results obtained from these data can not be applied or
generalized on the whole population.
Heterogeneous group Diseased or abnormal population

74. Example:
If we have NDC for Hb levels for a population of normal adult males
with mean±SD = 11±1.5
If we obtain a Hb reading for an individual = 8.1 & we want to know if
he/she is normal or anemic.
If this reading lies within the area under the curve at 95% of normal
(i.e. mean±2 SD)he /she will be considered normal. If his reading is
less then he is anemic.
NDC can be used in distinguishing between normal from abnormal
measurements.

75. • Normal range for Hb in this example will be:
Higher Hb level: 11+2 (1.5) =14.
Lower Hb level: 11–2 (1.5) = 8.
i.e the normal Hb range of adult males is from 8 to 14.
Our sample (8.1) lies within the 95% of his population.
So; this individual is normal because his reading lies within the
95% of his population.

76. DATA SUMMARIZATION

77. Datasummarization Measures of
Central tendency
Mean
Mode
Median
Measures of
Dispersion
Range
Variance
Standard
deviation
Coefficient of
variation

79. Datasummarization
Measures of
Central tendency
Mean
Mode
Median
Measures of
Dispersion
Range
Variance
Standard
deviation
Coefficient of
variation

80. ARITHMETIC MEAN
Sum of observation divided by the number of observations.
x = mean
∑ denotes the (sum of)
x the values of observation
n the number of observation

81. MEDIAN
The middle observation in a series of observation after
arranging them in an ascending or descending manner

84. MODE
The most frequent occurring value in the data.

86. ADVANTAGES & DISADVANTAGES OF THE
MEASURES OF CENTRAL TENDENCY:
Mean
• Usually preferred since it takes into account each
individual observation
• BUT affected by the value of extreme observations.
Median
• Useful descriptive measure if there are one or
two extremely high or low values.
Mode
• Seldom used.

88. Datasummarization Measures of
Central tendency
Mean
Mode
Median
Measures of
Dispersion
Range
Variance
Standard
deviation
Coefficient of
variation

89. MEASURES OF DISPERSION
Describes the degree of variations or scatter or
dispersion of the data around its central values
(dispersion = variation = spread = scatter).

90. RANGE
The difference between the largest & smallest values.
The simplest measure of variation
It can be expressed as an interval such as 4-10, where 4 is the
smallest value & 10 is highest.
But often, it is expressed as interval width. For example, the
range of 4-10 can also be expressed as a range of 6.

91. Disadvantages:

92.  To get the average of differences between the mean & each
observation in the data; we have to reduce each value from the mean &
then sum these differences and divide it by the number of observation.
V = ∑ (mean - x) / n
 The value of this equation will be equal to zero, because the differences
between each value & the mean will have negative and positive signs that
will equalize zero on algebraic summation.
 To overcome this zero we square the difference between the mean &
each value so the sign will be always positive. Thus we get:
V = ∑ (mean - x)2 / n-1
VARIANCE

94. STANDARD DEVIATION “SD”
The main disadvantage of the variance is that it is the square of
the units used.
So, it is more convenient to express the variation in the original
units by taking the square root of the variance.
This is called the standard deviation (SD).
Therefore SD = √ V
SD = √ ∑ (mean – x)2 / n - 1

96. COEFFICIENT OF VARIATION “COV”
 C.V expresses the SD as a % of the mean.
 C.V is useful when, we are interested in the relative
size of the variability in the data.

98. • Example:
If we have observations 5, 7, 10, 12 and 16.
Their mean will be 50/5=10.
SD = √ (25+9 +0 + 4 + 36 ) / (5-1) = √ 74 / 4 = 4.3
C.V. = 4.3 / 10 x 100 = 43%
Another observations are 2, 2, 5, 10, and 11.
Their mean = 30 / 5 = 6
SD = √ (16 + 16 + 1 + 16 + 25)/(5 –1) = √ 74 / 4 = 4.3
C.V = 4.3 /6 x 100 = 71.6 %
Both observations have the same SD but they are different in
C.V. because data in the 1st group is homogenous (so C.V. is
not high), while data in the 2nd observations is heterogeneous
(so C.V. is high).

100. INFERENTIAL STATISTICS

101. INFERENCE
Inference involves making a generalization about a larger
group of individuals on the basis of a subset or sample.

103. HYPOTHESIS TESTING
To find out whether the observed variation among sampling is
explained by sampling variations, chance or is really a
difference between groups.
The method of assessing the hypotheses testing is known as
“significance test”.
Significance testing is a method for assessing whether a
result is likely to be due to chance or due to a real effect.

104.  If the data are not consistent with the null hypotheses, the
difference is said to be “statistically significant”.
 If the data are consistent with the null hypotheses it is said that
we accept it i.e. statistically insignificant.
 In medicine, we usually consider that differences are
significant if the probability is <0.05.
 This means that if the null hypothesis is true, we shall make
a wrong decision <5 in a 100 times.

106. Quantitative
Not paired data
Normal
distributed
2 groups
Independent t-test
> 2 groups
ANOVA
Not Normal
distributed
2 groups
Mann Whitney
> 2 groups
Kruskal Wallis
Paired data
Normal
distributed
2 groups
Paired t-test
> 2 groups
Repeated ANOVA
Not Normal
distributed
2 Groups
Wilicoxon
> 2 groups
Friedman

107. Qualitative Not paired data
Chi square test
Z test
Paired data
McNemmar
Wilicoxon
Fridman

110. CORRELATION & REGRESSION

111. CORRELATION & REGRESSION
Correlation measures the closeness of the association
between 2 continuous variables, while Linear
regression gives the equation of the straight line that
best describes & enables the prediction of one
variable from the other.

112. CORRELATION IS NOT CAUSATION!!!

113. CORRELATION

115. t-test for correlation is used to test the significance
of the association.

118. LINEAR REGRESSION
Same as correlation
•Determine the relation &
prediction of the change in a
variable due to changes in
other variable.
•t-test is also used for the
assessment of the level of
significance.
Differ from correlation
•The independent factor has to be
specified from the dependent
variable.
•The dependent variable in linear
regression must be a continuous
one.
•Allows the prediction of
dependent variable for a particular
independent variable “But, should
not be used outside the range of
original data”.

119. SCATTERPLOTS
An X-Y graph with symbols that represent the
values of 2 variables
Regression
line

120. MULTIPLE REGRESSION
 The dependency of a dependent variable on several
independent variables, not just one.
 Test of significance used is the ANOVA. (F test).

121. For example: if neonatal birth weight depends on these factors:
gestational age, length of baby and head circumference. Each
factor correlates significantly with baby birth weight (i.e. has
+ve linear correlation). We can do multiple regression analysis
to obtain a mathematical equation by which we can predict the
birth weight of any neonate if we know the values of these
factors.