6/9/2020
Basic Concepts for Biostatistics
SlideShare Explore Search You
Upload
Login
Signup
Search
Submit Search
Home
Explore
Presentation Courses
PowerPoint Courses
by LinkedIn Learning
Search
Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad
preferences anytime.
1 of 98
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
1/92
6/9/2020
Basic Concepts for Biostatistics
Basic Concepts for Biostatistics
8,061 views
Share
Like
...
Dr Medical, General Dentist at Private Practice and Clinical Practice
Follow
Published on Feb 9, 2019
https://userupload.net/j72hszhboqcp
Biostatistics can be defined as
...
Published in: Health & Medicine
1 Comment
68 Likes
Statistics
Notes
Full Name
Comment goes here.
12 hours ago Delete Reply Block
Are you sure you want to Yes No
Your message goes here
Share your thoughts…
Post
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
2/92
6/9/2020
Basic Concepts for Biostatistics
Belinda Norman
Got a new Iphone 6 in just 7 days completing surveys and offers! Now I'm just a few days away from completing and
receiving my samsung tablet! Highly recommended! Definitely the best survey site out there!
http://ishbv.com/goldops777/pdf
5 months ago Reply
Are you sure you want to Yes No
Your message goes here
2 “when you can measure what you are speaking about and express it in numbers, you know something about it but when
Yogamaya Pradhan
23 hours ago
PriyankaChavda9
1 day ago
Tina Rawat , Software Engineer at T-Mobile at Software Engineer
1 day ago
JitenderYadav66
6 days ago
RitikaShrivastav
6 days ago
Show More
No Downloads
Views
you
Totalca...
views
8,061
On SlideShare
0
From Embeds
0
Number of Embeds
3
Actions
Shares
0
Downloads
0
Comments
1
Likes
68
Embeds 0
No embeds
No notes for slide
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
3/92
6/9/2020
Basic Concepts for Biostatistics
What went well?
connect the data types, data collection, and design to their projects/help individuals problem solving as a class/clarify their
design
2. The ERIC site is not that helpful, showing it briefly.
3. China’s big Mac attack—went very well, but the question can be more clear. (Finding a better way to present it, don’t
mention the cultural piece yet).
4. SD:
Distributing Barlo’s article and show that chart on the screen
Mention normal distribution->The world is balanced, the Chinese Yin-Yang theory.
->SD What’s the variable for 250-Million Americans—a variable that will possibly generate a normal distribution?
Eye color? Ethnicity? Income! Yes, let’s pretend that income will.
generate a mean income, SD=5K, so 68% people’s income will fall within this range.
BiostatisticsBiostatistics
Collectingpersonality
Data, Understanding
Dataand
andshow
Numbers
Thetest
word
5. 3Concept
and construct->use
as an example
the visual
on is
the“Statistics”
website. not “Sadistics”
6. Level of significance->confidence level->use a real experimental example to illustrate.
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
4/92
6/9/2020
Basic Concepts for Biostatistics
4 At the end of this session you will be able to: What is statistics? Use of statistics Sampling & sample designs
Percentage for each item:
6 issues as unresolved (40% or more)
6 issues as resolved (40% or more)
Not an issue (24% or more)
Percentage for each item:
6 issues as unresolved (40% or more)
6 issues as resolved (40% or more)
Not an issue (24% or more)
Dr Blahblah: The statistical procedures that you apply are determined by:
the specific evaluation questions you are attempting to answer.
The evaluation design you have planned, and
By the types of data that you collect, for example nominal, ordinal, interval or ratio.
Numerical information or data can be classified into one of two basic ways, as either categorical or quantitative.
Categorical data is just that, data that can be categorized into specific areas. They simply indicate the total number of objects,
Data... or events found in a particular category. The votes for Bush or Gore are categorical data. Categorical data is
individuals
usually portrayed as frequency of the item. The frequency is sometimes shown as a percentage.
Next slide.
Basic Concepts for Biostatistics
1. 1. BIOSTATISTICSBIOSTATISTICS 1 Check out ppt download link in description Or Download link :
https://userupload.net/j72hszhboqcp
2. 2. 2 “when you can measure what you are speaking about and express it in numbers, you know something about it but
when you cannot measure, when you cannot express it in numbers, your knowledge is of meagre and unsatisfactory
kind.” ....Lord Kelvin
3. 3. 3 BiostatisticsBiostatistics Collecting Data, Understanding Data and Numbers The word is “Statistics” not
“Sadistics”
4. 4. 4 At the end of this session you will be able to: What is statistics? Use of statistics Sampling & sample designs
Data Presentation of data Measures of central tendency Measures of variability Normal distribution & curve
Probability Tests of significance Correlation & regression
5. 5. CLICK HERE TO DOWNLOAD THIS PPT https://userupload.net/j72hszhboqcp
6. 6. 6 Statistics The science of collecting, monitoring, analyzing, summarizing, and interpreting data. This includes
design issues as well. Statistics are tools Statistics – singular means figures plural - body of knowledge German
statastik political state Italian statista statesman
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
5/92
6/9/2020
Basic Concepts for Biostatistics
7. 7. 7 What is Biostatistics ? tool of statistics are applied to the data that is derived from biological sciences John
Graunt (1620-1674) : father of health statistics Statistics applied to biological (life) problems, including: Public
health Medicine Ecological and environmental Much more statistics than biology, however biostatisticians must
learn the biology also.
8. 8. 8 Statistical Analyses Descriptive Statistics Describe the sample Science of collecting, summarizing,
presenting, Inference Make inferences about the population using what is observed in the sample Primarily
performed in two ways: Hypothesis testing Estimation
9. 9. 9 What Do Biostatisticians Do? Identify and develop treatments for disease and estimate their effects. Identify risk
factors for diseases. Design, monitor, analyze, interpret, and report results of clinical studies. Develop statistical
methodologies to address questions arising from medical/public health data. Locate , define & measure extent of
disease Ultimate objective improve the health of individual & community
10. 10. CLICK HERE TO DOWNLOAD THIS PPT https://userupload.net/j72hszhboqcp
11. 11. 11 Use of statistics in dental sciences Assess the state of oral health in community Indicate basic factors
CLICK
HERE state
TO DOWNLOAD
PPT https://userupload.net/j72hszhboqcp
underlying
of oral health THIS
Determine
success or failure of specific oral health care programmes or to evaluate the
programme action Promote health legislation and in creating administrative standards for oral health
12. 12. 12 Populations and Parameters Population – a group of individuals that we would like to know something about
Parameter - a characteristic of the population in which we have a particular interest Examples: The proportion of
the population that would respond to a certain drug The association between a risk factor and a disease in a
population
13. 13. 13 Samples and Statistics Sample – a subset of a population (hopefully representative) Statistic – a
characteristic of the sample Examples: The observed proportion of the sample that responds to treatment The
observed association between a risk factor and a disease in this sample
14. 14. 14 Populations and Samples Studying populations is too expensive and time-consuming, and thus impractical
If a sample is representative of the population, then by observing the sample we can learn something about the
population And thus by looking at the characteristics of the sample (statistics), we may learn something about the
characteristics of the population (parameters).
15. 15. CLICK HERE TO DOWNLOAD THIS PPT https://userupload.net/j72hszhboqcp
16. 16. 16
17. 17. 17 Sample size Extent to which sample population represents general population Type of study i.e. descriptive,
experimental etc. Variability of population (expressed as S.D.) No. of variables Level of precision Sensitivity
of measurement tools Sampling method employed Data analysis techniques A sample will be representative if all
members of the population have an equal chance of being picked.
18. 18. 18
19. 19. 19 Random :chance of population unit being selected in sample Probability sampling Selection of unit by
chance only Applicable when – small population , homogenous , readily available To ensure randomness – lottery
method Table of random numbers Simple random sampling
20. 20. 20 Simple Random Sampling A simple random sample of 20 cases 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123
124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150
151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177
178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
21. 21. 21
22. 22. 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
23. 23. 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
24. 24. 24 Systematic random sampling Used in cases where a complete list of population available Applied to field
studies K = sample interval K = total population/ sample size desired Adv – simple Less time & labor Results
fairly accurate
25. 25. 25 Systematic Random sample of 20 cases 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129
130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156
157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183
184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
26. 26. 26 Stratified sampling Target population divided into homogenous groups or classes called strata Strata – age ,
sex , classes , geographical area More representative sample Greater accuracy Covers wide area
27. 27. 27 Stratified Random Sampling
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
6/92
6/9/2020
Basic Concepts for Biostatistics
28. 28. 28 Cluster sampling Cluster is a randomly selected group Units of population in natural groups or clusters
Simple method , less time and cost Higher error
29. 29. 29 Example: Imagine that you wanted to conduct in-person interviews with neighborhood organizations. There are
9 cities scattered around the country with the relevant types of organizations, and 16 organizations within each of the 9
cities (or 144 total organizations). You need to interview 12 organizations. A simple random sample would likely
require interviews in (and this travel to) these 9 distant cities:
30. 30. 30 If you used multi-stage clustered sampling, you would first randomly select a certain number of cities (here
three), and then randomly select four organizations within each of the three cities. This saves travel time, and also
makes it easier to assemble a sampling frame (a list of the ultimate sampling elements).
31. 31. 31 Cluster sampling used where (1) no sampling frame directly available, and/or (2) simple random sampling
would be expensive, complex, time-consuming and/or logistically difficult.
for each level (sampling unit), take a
random sample of each, and then a random sample within that larger "cluster", etc. (Since this process involves more
than one stage or step of sampling, it is often called "Multistage Cluster Sampling".
632.Statistics
The in
science
of collecting,
monitoring,
analyzing,
summarizing,
and interpreting
This
includes
32. 32 Errors
sampling
Sampling
errors faulty
sample design
small sample
size Nondata.
sampling
errors
coverage
error observational error processing error
33. 33. 33 What is data? Pieces of information Fraenkel & Wallen (2000) the term “data” refers to the kinds of
information researchers obtain on the subjects of their research. The vast majority of errors in research arise from a
poor planning (e.g., data collection) Fancy statistical methods cannot rescue garbage data. Collect exact values
whenever possible.
34. 34. 34 Where do you get your data? Collective recording of observations is data Main sources experiments,
surveys , records [ census , public reports] Demographic data- details of population D a t a Q u a n t it a t iv e Q u a
lit a t iv e D is c r e t e C o n t in u o u s
35. 35. 35 Level of Measurement Nominal - categorical gender, race, hypertensive Ordinal - categories that can be
ranked none, light, moderate, heavy smoker Interval - continuous blood pressure, age, days in the hospital
Discrete – fixed values
36. 36. 36 Horse race example Nominal Did this horse come in first place? 0=no, 1=yes Ordinal In what position
did this horse finish? 1=first, 2=second, 3=third, etc. Interval (scale) How long did it take for this horse to finish?
60 seconds, etc.
37. 37. 37 Presentation of data Data collected & compiled from experimental work , surveys , records –raw data Needs
to be sorted & classified To make it simple ,concise ,meaningful , interesting & helpful 2 methods tabulation
diagrams / drawings
38. 38. 38 Visual Data Summaries Quantitative/ continuous / measured data Histogram Frequency polygon
Frequency curve Line chart/ graph Cumulative frequency diagram Scatter / dot diagram Qualitative/ discrete /
counted data Bar diagram Pie/sector diagram Pictogram Map diagram / spot diagram
39. 39. 39 Tabulation Tables – devices …presentation of data 1st step ….. Before analysis/interpretation Rules for
frequency distribution table Each table shld contain title n no-Table1,Table2…. Headings …rows & columns clear
n concise No. of class interval b/w 5-25 Class interval of equal width Units of measurements specified Source
of data mentioned Groups tabulated in order
40. 40. 40 Classes (standard) No. of students 1st 68 2nd 65 3rd 63 4th 62 5th 60 Table1 students in a primary school Table
design...
2
41. 41. 41 Bar diagram Represent only one variable Represent qualitative data Compare qualitative data with respect
to single variable
42. 42. 42 Proportional bar diagram Comparison of data Populations or groups compared with respect to single variable
Compare only the proportion of subgroups
43. 43. 43 Line diagram / graph Simplest mean to represent data Useful in representing trends over time X –axis
represent time Y –axis , value of any variable under study
44. 44. 44 Histogram Depict quantitative data of continuous type
45. 45. 45 Frequency polygon Represents frequency distributions Comparative analysis Area diagram developed over
a histogram Point marked over mid point of class interval
46. 46. 46 Cartograms or spot maps Used to show geographical distribution of frequency
47. 47. 47 Pictogram or picture diagram To impress the frequency of occurrence of health related events
48. 48. 48 Pie diagram / Sector diagram Show percentage breakdown Degrees of angle denote frequency and area of
sector Angle = class frequency/total observation x 360
49. 49. 49 Summary Measures Central Tendency Mean Median Mode Summary Measures Variation Variance Standard
Deviation Range
50. 50. 50 Describing-Central tendency refers to the Middle of the Distribution Value or parameter which serves as single
estimate of a series of data Mental picture of central value Enables comparison One central value around which all
other observations are dispersed
51. 51. 51 Mean (Arithmetic Mean) The most common measure of central tendency Affected by extreme values
(outliers) 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Mean = 5 Mean = 6
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
7/92
6/9/2020
Basic Concepts for Biostatistics
52. 52. 52 Median Robust measure of central tendency Not affected by extreme values In an ordered array, the
median is the “middle” number If n or N is odd, the median is the middle number If n or N is even, the median is
the average of the two middle numbers 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Median = 5 Median = 5
53. 53. 53 Mode Value that occurs most often Not affected by extreme values Used for either numerical or categorical
data There may may be no mode There may be several modes 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mode = 9 0 1 2 3 4
5 6 No Mode
54. 54. 54 mean .
55. 55. 55 median
56. 56. 56 mode
57. 57. 57 Dr A = 2,4,3,4,6,6,2,5 Dr B = 4,5,4,3,4,5,3,4 Dr C = 3,3,8,3,3,3,4,5 Mean x¯Dr A = 32/8 = 4 days
Mean x¯Dr B = 32/8 = 4 days Mean x¯Dr C = 32/8 = 4 days Range of the days varies Dr A = 2-6 days Dr B =
3-5 days Dr C = 3-8 days This ranges r known as Measures of dispersion
58. 58. 58 Measures of Variation Variation VarianceStandard Deviation Population Variance Sample Variance Population
7 What
is Biostatistics
tool of
statistics
are applied
to the
data that isRange
derived from biological sciences John Gra...
Standard
Deviation?Sample
Standard
Deviation
Range
Interquartile
59. 59. 59 The Range Measure of variation Difference between the largest and the smallest observations: Ignores
the way in which data are distributed Largest SmallestRange X X= − 7 8 9 10 11 12 Range = 12 - 7 = 5 7 8 9 10 11 12
Range = 12 - 7 = 5
60. 60. 60 ( ) 2 2 1 N i i X N µ σ = − = ∑ Shows variation about the mean (x-x¯) Dr A = -2,0,-1,0, 2,2,-2,1 = 0 Dr b
= 0,1,0,-1,0,1,-1,0 = 0 Dr c = -1, -1, 4,-1,-1,-1,-1,0 = 0 (x-x¯)2 Dr A = 18, Dr B = 4 , Dr C = 22 Thus, Dr A =18/8
= 2.25 Dr B = 4/8 = 0.5 Dr C = 22/8 = 2.75 ( ) 2 2 1 1 n i i X X S n = − = − ∑ Variance Population variance: Sample
variance:
61. 61. 61 Standard Deviation Most important measure of variation Shows variation about the mean Root Mean
Square Deviation So for Dr A = 1.5 Dr B = 0.7 Dr C = 1.66 Has the same units as the original data Sample
standard deviation: Population standard deviation: ( ) 2 1 1 n i i X X S n = − = − ∑ ( ) 2 1 N i i X N µ σ = − = ∑
62. 62. 62 Comparing Standard Deviations Mean = 15.5 s = 3.338 11 12 13 14 15 16 17 18 19 20 21 11 12 13 14 15 16 17
18 19 20 21 Data B Data A Mean = 15.5 s = .9258 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 4.57 Data C
63. 63. 63 Shape of a Distribution Describes how data is distributed Measures of shape Symmetric or skewed Mean
= Median =ModeMean < Median < Mode Mode < Median < Mean Right-SkewedLeft-Skewed Symmetric
64. 64. 64 Frequency distribution--Normal Curve Many statistics assume the normal, bell-shaped curve distribution for
scores. A distribution with this nature is normal distribution / Gaussian distribution 50% > mean; 50% < mean
Normal curve for population (height, weight) Mean=median=mode Mean + 1SD/34.13% of the score Mean –
1SD/34.13% of the score Mean +/- 3SD = more than 99% of the score
65. 65. 65 Skewed Distribution Non-symmetrical distribution Mean, median, mode not the same Negatively skewed
extreme scores at the lower end Mean < median <mode most did well, a few poorly Positively skewed at the
higher end Mean >median >mode Most did poorly, a few well The further apart the mean and median, the more
the distribution is skewed.
66. 66. 66 Examples of Normal and Skewed 44-DAYS IN ICU 70.0 65.0 60.0 55.0 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0
10.0 5.0 0.0 44-DAYS IN ICU Frequency 1000 800 600 400 200 0 Std. Dev = 3.99 Mean = .9 N = 933.00 35SYSTOLIC BLOOD PRESSURE FIRST ER 250.0 240.0 230.0 220.0 210.0 200.0 190.0 180.0 170.0 160.0 150.0
140.0 130.0 120.0 110.0 100.0 90.0 80.0 70.0 60.0 35-SYSTOLIC BLOOD PRESSURE FIRST ER Frequency 160 140
120 100 80 60 40 20 0 Std. Dev = 27.74 Mean = 146.9 N = 925.00
67. 67. 67 Hypothesis Tests Hypothesis testing is always a five- step procedure: Formulation of the null and the
alternative hypotheses Specification of the level of significance Calculation of the test statistic Definition of the
region of rejection Selection of the appropriate hypothesis
68. 68. 68 The simplest case for a decision is the 'yes-or- no' question. For any parameter to be tested two hypothesis
are made Null hypothesis or hypothesis of no difference Asserts that there is no real difference in sample & general
population The difference found is accidental & arises out of sampling variations Alternative hypothesis of
significant difference States that sample result is different than the hypothetical value of population To minimize
errors the sampling distribution or area under normal curve is divided into two regions or zones Zone of acceptance :
mean +-1.96 SE Zone of rejection
69. 69. 69
70. 70. 70 Types of Error
71. 71. 71 Degree of freedom Defined as number of independent numbers in sample X +Y + Z /3 = 5 When there are
10 values , 9 choices or degrees of freedom
72. 72. 72 Standard Error Standard deviation of a statistic like mean , proportion etc Diff samples from same population
have diff mean Variability of such mean’s is assessed Standard error of mean = SD of means of several sample from
same population SE = SD of obser in the sample No of obser in the sample Variation in biological observation
73. 73. 73 Probability or chance Defined as relative frequency or probable chances of occurrence with which an event is
expected to occur on an average Denoted relative frequency or odds Expressed as ‘p’ Range zero (0) – one (1)
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
8/92
6/9/2020
Basic Concepts for Biostatistics
when p= 0 no chance of event happening When p=1 , 100% p = no of events occurring / total no of trials q = negative
probability
74. 74. 74 What does Not Significant really mean? An impossible even has probability 0 An event which must occur
has probability 1 P < 0.001 very highly significant P < 0.01 Highly significant P < 0.05 Significant Measure on a
scale 0 10.5 0.750.25 Event Impossible Event Unlikely happen Event = like happen Event certain
75. 75. 75 Tests of Significance Whenever 2 sets of observation have been compared, it becomes essential to find whether
the diff observation b/w the 2 groups is bcos of sampling variation/ any other factor Method – Tests of Significance
76. 76. 76 How to know what to use There are many theoretical distributions, both continuous and discrete. We use 4 of
these a lot: z (unit normal), t, chi-square, and F. Z and t are closely related to the sampling distribution of means; chisquare and F / ANOVA are closely related to the sampling distribution of variances.
77. 77. 77 Objective of using tests of significance To compare – sample mean with population Means of two samples
Sample proportion with population Proportion of two samples Association b/w two attributes
78. 78. 78 One-Sided vs. Two-Sided Tests One-sided tests have one rejection region, i.e. you check whether the
8 Statistical
Analyses
Describe
sample
Science
of collecting,
summarizing,
presenting,for
parameter
of interest Descriptive
is larger (orStatistics
smaller) than
a giventhe
value.
Two-sided
tests
are used when
we test a parameter
equivalence to a certain value. Deviations from that value in both directions are rejected.
79. 79. 79 Z test large samples Large samples ( > 30) Difference observed b/w sample estimate and that of population is
expressed in terms of SE Score of value of ratio b/w the observed difference & SE is called ‘Z’ Z = diff in means /
SE of mean
80. 80. 80 What is a t Test? Commonly Used Definition: Comparing two means to see if they are significantly different
from each other Technical Definition: Any statistical test that uses the t family of distributions
81. 81. 81 t-Test Small Samples Designed by W.S Gossett Used in case of small samples Ratio of observed
difference b/w means of two small samples to the SE of difference in same When each individual gives a pair of
observations , to test for difference in pair of values , paired ‘t’ test utilized.
82. 82. 82 Student’s t-test Used to compare the average (mean) in one group with the average in another group.
Univariate, Unmatched, Interval, Normal, 2 groups. Eg 6 boys on diet A- 4,3,5,2,3,1 9 boys on diet B6,3,8,9,5,3,4,2,5 x=6 y= 9 SD – 2.04 Test the significance of diff in diet A n B with regards to their effect on inc in
weight ?
83. 83. 83 Paired t-test Used to compare the average for measurements made twice within the same person - before vs.
after. For example, Did the systolic blood pressure change significantly from the scene of the injury to admission?
Univariate, Matched, Interval, Normal, 2 groups.
84. 84. 84
85. 85. 85 Chi square test ( χ² test ) The most commonly used statistical test. Developed by Karl Pearson Used for
qualitative data To test whether the difference in distribution of attributes in different groups is due to sampling
variation or otherwise. For example, suppose that in a study of 933 patients with a hip fracture, 10% of the men
(22/219) of the men develop pneumonia compared with 5% of the women (36/714). What is the probability that this
could happen by chance alone?
86. 86. 86 Calculation of χ² value χ² = (observed f – expected f )²ΣΣ Expected f Expected f = row total x column total /
grand total Group No Of cavities new total 0-1 2-3 4-5 Who rec instr 30 15 5 50 Who did not rec inst 20 15 15 50 Total
50 30 20 100
... 87. 87. 87 Group No Of cavities new total 0-1 2-3 4-5 Who rec instr 50x50/ 100= 25 30x50 / 100= 15 20x50/ 100= 10 50
Who did not rec inst 50x50/ 100= 25 30x50/ 100= 15 20x50/ 100= 10 50 Total 50 30 20 100 1+0+2.5=1=0+2.5=7² =χ
Df = (2-1) x (3-1) = 2
88. 88. 88
89. 89. 89 Two-Sample F-Test to compare two methods, it is often important to know whether the variabilities for both
methods are the same. In order to compare two variances v1, and v2…calculate the ratio of the two variances. This
ratio is called the F-statistic F = v1/v2
90. 90. 90
91. 91. 91 Analysis of variance (ANOVA) Compare more than two samples Compares variation between the classes as
well as within the classes For such comparisons there is high chance of error using t or Z test One-way used to
compare more than 3 means from independent groups. “Is the age different between White, Black, Hispanic patients?”
Two-way used to compare 2 or more means by 2 or more factors. “Is the age different between Males and Females,
With and Without Pnuemonia?”
92. 92. 92 Coefficient of Correlation Measures the strength of the linear relationship between two quantitative variables
Denoted by letter ‘r’ Ranges between –1 and 1 The closer to –1, the stronger the negative linear relationship
The closer to 1, the stronger the positive linear relationship The closer to 0, the weaker any positive linear
relationship
93. 93. 93 Scatter Plots of Data with Various Correlation Coefficients Y X Y X Y X Y X Y X r = -1 r = -.6 r = 0 r = .6 r = 1
94. 94. 94 Calculation of correlation coefficient Pearson’s correlation coefficient r = Σ (X – x) (Y-y) √ Σ (X –x)² Σ (Yy)² Does not prove whether one variable alone cause the change in other
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
9/92
6/9/2020
Basic Concepts for Biostatistics
95. 95. 95 Overview of Biostatistics Research question Continuous Discrete 1. Describe 1 sample Mean , SD , SE Counts,
% , proportion 2. Compare 2 groups a. Non paired Student’s t- test Chi2 test b. Paired Paired t test Confidence interval
b/w 2 proportion 3. Compare 2 or more groups ANOVA F- test 4.Correlate 2 variables in 1 grp Pearson correlation r
5.Correlate > 2 variables in 1 grp Multiple correlation coefficient R
96. 96. 96 ….ConclusionKnow thyself Why does he keep saying this all the time?
97. 97. 97 “He who accepts statistics indiscriminately, will often be duped unnecessarily. But he who distrusts statistics,
indiscriminately will often be ignorant, unnecessarily.”
98. 98. 98 List of References Primer of biostatistics – Stanton A Glantz; 4th edi Park’s Textbook of Preventive and Social
medicine; 17th edi Methods in Biostatistics – BK Mahajan; 6th edi An introduction to Biostatistics – PSS Sundar Rao;
3rd edi Essentials of Preventive and Community dentistry – Soben Peter; 2nd edi Jong’s Community Dental Health –
George M Gluck; 5th edi
Recommended
9 What Do Biostatisticians Do? Identify and develop treatments for disease and estimate their effects. Identify risk facto...
Bleeding Disorders: Causes, Types, and Diagnosis
Dr Medical
Bite mark management and analysis
Dr Medical
Health care delivery system in india
Dr Medical
CLICK HERE TO DOWNLOAD THIS PPT https://userupload.net/j72hszhboqcp
Normal growth and development
Dr Medical
Gingival diseases in children
Dr Medical
Tissue Engineering and Regenerative Medicine
Dr Medical
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
10/92
6/9/2020
Basic Concepts for Biostatistics
Clinical genetics: a guide to a career
Dr Medical
English
Español
Português
Français
Deutsch
11 Use of statistics in dental sciences Assess the state of oral health in community Indicate basic factors underlying s...
About
Dev & API
Blog
Terms
Privacy
Copyright
Support
LinkedIn Corporation © 2020
×
Share Clipboard
×
Facebook
Twitter
LinkedIn
Link
Public clipboards featuring this slide
×
No public clipboards found for this slide
Select another clipboard
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
11/92
6/9/2020
Basic Concepts for Biostatistics
×
Looks like you’ve clipped this slide to already.
12 Populations
and
Search
for a clipboard
Parameters
Population – a group of individuals that we would like to know something about
Create a clipboard
You just clipped your first slide!
Clipping is a handy way to collect important slides you want to go back to later. Now customize the name of a clipboard to
store your clips.
Name* Best of Slides
Description Add a brief description so
Visibility
Others can see my Clipboard
Cancel
Save
Save this presentation
Parameter...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
12/92
6/9/2020
13 Samples and Statistics
Basic Concepts for Biostatistics
Sample – a subset of a population (hopefully representative)
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
Statistic – a characteristic of...
13/92
6/9/2020
14 Populations and Samples
Basic Concepts for Biostatistics
Studying populations is too expensive and time-consuming, and thus impractical
If a
sample ...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
14/92
6/9/2020
Basic Concepts for Biostatistics
CLICK HERE TO DOWNLOAD THIS PPT https://userupload.net/j72hszhboqcp
16
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
15/92
6/9/2020
Basic Concepts for Biostatistics
17 Sample size Extent to which sample population represents general population
Type of study i.e. descriptive,
experime...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
16/92
6/9/2020
Basic Concepts for Biostatistics
18
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
17/92
6/9/2020
Basic Concepts for Biostatistics
19 Random :chance of population unit being selected in sample Probability sampling Selection of unit by chance only
Ap...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
18/92
6/9/2020
Basic Concepts for Biostatistics
20 Simple Random Sampling A simple random sample of 20 cases 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 2...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
19/92
6/9/2020
Basic Concepts for Biostatistics
21
22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
20/92
6/9/2020
Basic Concepts for Biostatistics
23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
21/92
6/9/2020
Basic Concepts for Biostatistics
24 Systematic random sampling Used in cases where a complete list of population available Applied to field studies K
= ...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
22/92
6/9/2020
Basic Concepts for Biostatistics
25 Systematic Random sample of 20 cases 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
30 3...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
23/92
6/9/2020
Basic Concepts for Biostatistics
26 Stratified sampling Target population divided into homogenous groups or classes called strata Strata – age , sex , cl...
27 Stratified Random Sampling
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
24/92
6/9/2020
Basic Concepts for Biostatistics
28 Cluster sampling Cluster is a randomly selected group Units of population in natural groups or clusters Simple
metho...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
25/92
6/9/2020
Basic Concepts for Biostatistics
29 Example: Imagine that you wanted to conduct in-person interviews with neighborhood organizations. There are 9 cities
s...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
26/92
6/9/2020
30
Basic Concepts for Biostatistics
If you used multi-stage clustered sampling, you would first randomly select a certain number of cities (here three), ...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
27/92
6/9/2020
31 Cluster sampling
Basic Concepts for Biostatistics
used where (1) no sampling frame directly available, and/or (2) simple random sampling would be
expe...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
28/92
6/9/2020
Basic Concepts for Biostatistics
32 Errors in sampling Sampling errors faulty sample design small sample size Non sampling errors coverage error
observat...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
29/92
6/9/2020
33 What is data?
Basic Concepts for Biostatistics
Pieces of information
Fraenkel & Wallen (2000)
the term “data” refers to the kinds of information
r...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
30/92
6/9/2020
34 Where do you get your data?
Basic Concepts for Biostatistics
Collective recording of observations is data
Main sources
experiments, surveys ,
reco...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
31/92
6/9/2020
35 Level of Measurement Nominal - categorical
Basic Concepts for Biostatistics
gender, race, hypertensive Ordinal - categories that can be ranked
non...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
32/92
6/9/2020
36 Horse race example Nominal
Basic Concepts for Biostatistics
Did this horse come in first place?
0=no, 1=yes Ordinal
In what position did
this ho...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
33/92
6/9/2020
Basic Concepts for Biostatistics
37 Presentation of data Data collected & compiled from experimental work , surveys , records –raw data Needs to be
sorte...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
34/92
6/9/2020
Basic Concepts for Biostatistics
38 Visual Data Summaries Quantitative/ continuous / measured data
curve
Histogram
Frequency polygon
Frequency
Line...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
35/92
6/9/2020
Basic Concepts for Biostatistics
39 Tabulation Tables – devices …presentation of data 1st step ….. Before analysis/interpretation Rules for frequency
di...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
36/92
6/9/2020
Basic Concepts for Biostatistics
40 Classes (standard) No. of students 1st 68 2nd 65 3rd 63 4th 62 5th 60 Table1 students in a primary school Table 2
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
37/92
6/9/2020
Basic Concepts for Biostatistics
41 Bar diagram Represent only one variable Represent qualitative data Compare qualitative data with respect to
single v...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
38/92
6/9/2020
Basic Concepts for Biostatistics
42 Proportional bar diagram Comparison of data Populations or groups compared with respect to single variable
Compare o...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
39/92
6/9/2020
Basic Concepts for Biostatistics
43 Line diagram / graph Simplest mean to represent data Useful in representing trends over time X –axis represent
time ...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
40/92
6/9/2020
Basic Concepts for Biostatistics
44 Histogram Depict quantitative data of continuous type
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
41/92
6/9/2020
Basic Concepts for Biostatistics
45 Frequency polygon Represents frequency distributions Comparative analysis Area diagram developed over a
histogram P...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
42/92
6/9/2020
Basic Concepts for Biostatistics
46 Cartograms or spot maps Used to show geographical distribution of frequency
47 Pictogram or picture diagram To impress the frequency of occurrence of health related events
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
43/92
6/9/2020
Basic Concepts for Biostatistics
48 Pie diagram / Sector diagram Show percentage breakdown Degrees of angle denote frequency and area of sector
Angle = ...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
44/92
6/9/2020
Basic Concepts for Biostatistics
49 Summary Measures Central Tendency Mean Median Mode Summary Measures Variation Variance Standard Deviation
Range
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
45/92
6/9/2020
Basic Concepts for Biostatistics
50 Describing-Central tendency refers to the Middle of the Distribution Value or parameter which serves as single
estimat...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
46/92
6/9/2020
Basic Concepts for Biostatistics
51 Mean (Arithmetic Mean) The most common measure of central tendency Affected by extreme values (outliers) 0 1 2
3 4 5 ...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
47/92
6/9/2020
Basic Concepts for Biostatistics
52 Median Robust measure of central tendency Not affected by extreme values In an ordered array, the median is the
“mid...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
48/92
6/9/2020
Basic Concepts for Biostatistics
53 Mode Value that occurs most often Not affected by extreme values Used for either numerical or categorical data
Ther...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
49/92
6/9/2020
Basic Concepts for Biostatistics
54 mean .
55 median
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
50/92
6/9/2020
Basic Concepts for Biostatistics
56 mode
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
51/92
6/9/2020
57
Basic Concepts for Biostatistics
Dr A = 2,4,3,4,6,6,2,5
Dr B = 4,5,4,3,4,5,3,4
Dr C = 3,3,8,3,3,3,4,5
Mean x¯Dr A = 32/8 = 4 days
Mean
x¯Dr B ...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
52/92
6/9/2020
Basic Concepts for Biostatistics
58 Measures of Variation Variation VarianceStandard Deviation Population Variance Sample Variance Population Standard
Devi...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
53/92
6/9/2020
59 The Range
Basic Concepts for Biostatistics
Measure of variation
Difference between the largest and the smallest observations:
Ignores the way in
w...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
54/92
6/9/2020
Basic Concepts for Biostatistics
60 ( ) 2 2 1 N i i X N µ σ = − = ∑ Shows variation about the mean (x-x¯)
Dr A = -2,0,-1,0, 2,2,-2,1 = 0
Dr b =
0,1,0...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
55/92
6/9/2020
61 Standard Deviation
Basic Concepts for Biostatistics
Most important measure of variation
Shows variation about the mean
Root Mean Square
Deviation ...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
56/92
6/9/2020
Basic Concepts for Biostatistics
62 Comparing Standard Deviations Mean = 15.5 s = 3.338 11 12 13 14 15 16 17 18 19 20 21 11 12 13 14 15 16 17 18 19
20 21 D...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
57/92
6/9/2020
63 Shape of a Distribution
Basic Concepts for Biostatistics
Describes how data is distributed
Measures of shape
Symmetric or skewed Mean =
Median =Mo...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
58/92
6/9/2020
64 Frequency distribution--Normal Curve
Basic Concepts for Biostatistics
Many statistics assume the normal, bell-shaped curve distribution for scores.
...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
59/92
6/9/2020
65 Skewed Distribution
Basic Concepts for Biostatistics
Non-symmetrical distribution
Mean, median, mode not the same
Negatively skewed
extreme scores...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
60/92
6/9/2020
Basic Concepts for Biostatistics
66 Examples of Normal and Skewed 44-DAYS IN ICU 70.0 65.0 60.0 55.0 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 10.0
5.0 0.0 4...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
61/92
6/9/2020
Basic Concepts for Biostatistics
67 Hypothesis Tests Hypothesis testing is always a five- step procedure:
Formulation of the null and the alternative
hy...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
62/92
6/9/2020
Basic Concepts for Biostatistics
68 The simplest case for a decision is the 'yes-or- no' question. For any parameter to be tested two hypothesis are
made...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
63/92
6/9/2020
Basic Concepts for Biostatistics
69
70 Types of Error
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
64/92
6/9/2020
Basic Concepts for Biostatistics
71 Degree of freedom Defined as number of independent numbers in sample X +Y + Z /3 = 5 When there are 10
values , 9 ch...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
65/92
6/9/2020
Basic Concepts for Biostatistics
72 Standard Error Standard deviation of a statistic like mean , proportion etc Diff samples from same population have
di...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
66/92
6/9/2020
Basic Concepts for Biostatistics
73 Probability or chance Defined as relative frequency or probable chances of occurrence with which an event is
expected ...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
67/92
6/9/2020
Basic Concepts for Biostatistics
74 What does Not Significant really mean? An impossible even has probability 0 An event which must occur has
probability...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
68/92
6/9/2020
Basic Concepts for Biostatistics
75 Tests of Significance Whenever 2 sets of observation have been compared, it becomes essential to find whether the
diff...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
69/92
6/9/2020
Basic Concepts for Biostatistics
76 How to know what to use There are many theoretical distributions, both continuous and discrete. We use 4 of these a
l...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
70/92
6/9/2020
Basic Concepts for Biostatistics
77 Objective of using tests of significance To compare – sample mean with population Means of two samples Sample
propor...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
71/92
6/9/2020
Basic Concepts for Biostatistics
78 One-Sided vs. Two-Sided Tests One-sided tests have one rejection region, i.e. you check whether the parameter of
inter...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
72/92
6/9/2020
Basic Concepts for Biostatistics
79 Z test large samples Large samples ( > 30) Difference observed b/w sample estimate and that of population is
expresse...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
73/92
6/9/2020
Basic Concepts for Biostatistics
80 What is a t Test? Commonly Used Definition: Comparing two means to see if they are significantly different from
each o...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
74/92
6/9/2020
81 t-Test Small Samples
Basic Concepts for Biostatistics
Designed by W.S Gossett
Used in case of small samples
Ratio of observed difference b/w
means...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
75/92
6/9/2020
Basic Concepts for Biostatistics
82 Student’s t-test Used to compare the average (mean) in one group with the average in another group. Univariate,
Unmat...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
76/92
6/9/2020
Basic Concepts for Biostatistics
83 Paired t-test Used to compare the average for measurements made twice within the same person - before vs. after.
For ...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
77/92
6/9/2020
Basic Concepts for Biostatistics
84
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
78/92
6/9/2020
85 Chi square test ( χ² test )
Basic Concepts for Biostatistics
The most commonly used statistical test.
Developed by Karl Pearson
Used for
qualitati...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
79/92
6/9/2020
Basic Concepts for Biostatistics
86 Calculation of χ² value χ² = (observed f – expected f )²ΣΣ Expected f Expected f = row total x column total / grand
to...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
80/92
6/9/2020
Basic Concepts for Biostatistics
87 Group No Of cavities new total 0-1 2-3 4-5 Who rec instr 50x50/ 100= 25 30x50 / 100= 15 20x50/ 100= 10 50 Who did
not r...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
81/92
6/9/2020
Basic Concepts for Biostatistics
88
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
82/92
6/9/2020
Basic Concepts for Biostatistics
89 Two-Sample F-Test to compare two methods, it is often important to know whether the variabilities for both methods
are...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
83/92
6/9/2020
Basic Concepts for Biostatistics
90
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
84/92
6/9/2020
91 Analysis of variance (ANOVA)
Basic Concepts for Biostatistics
Compare more than two samples
Compares variation between the classes as well as
within...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
85/92
6/9/2020
92 Coefficient of Correlation
Basic Concepts for Biostatistics
Measures the strength of the linear relationship between two quantitative variables
Deno...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
86/92
6/9/2020
Basic Concepts for Biostatistics
93 Scatter Plots of Data with Various Correlation Coefficients Y X Y X Y X Y X Y X r = -1 r = -.6 r = 0 r = .6 r = 1
94 Calculation of correlation coefficient Pearson’s correlation coefficient
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
r = Σ (X – x) (Y-y) √ Σ (X –x)² Σ (Y- y)² ...
87/92
6/9/2020
Basic Concepts for Biostatistics
95 Overview of Biostatistics Research question Continuous Discrete 1. Describe 1 sample Mean , SD , SE Counts, % ,
proport...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
88/92
6/9/2020
Basic Concepts for Biostatistics
96 ….ConclusionKnow thyself Why does he keep saying this all the time?
97 “He who accepts statistics indiscriminately, will often be duped unnecessarily. But he who distrusts statistics, indisc...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
89/92
6/9/2020
Basic Concepts for Biostatistics
98 List of References Primer of biostatistics – Stanton A Glantz; 4th edi Park’s Textbook of Preventive and Social
medicin...
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
90/92
6/9/2020
Basic Concepts for Biostatistics
Upcoming SlideShare
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
91/92
6/9/2020
Basic Concepts for Biostatistics
Loading in …5
×
https://www.slideshare.net/DrMedical2/basic-concepts-for-biostatistics
92/92