1. Average Arithmetic and Average Quadratic Deviation

2. Average Arithmetic and Average Quadratic Deviation
The average values, which give the generalized quantitative description of certain characteristic in statistical totality at the certain terms of place and time, are the most widespread form of statistical indices. They represent the typical lines of variation characteristic of the explored phenomena.

3. Average Arithmetic and Average Quadratic Deviation
Because of that quantitative description of characteristic is related to its high-quality side, it follows to examine average values only in light of terms of high-quality analysis. Except of summarizing estimation of certain characteristic the necessity of determination of changeable quantitative average values for the totality arises up also, when two groups which high-quality differ one from other are compared.

5. The use of averages in health protection
for description of work organization of health protection establishments (middle employment of bed, term of stay in permanent establishment, amount of visits on one habitant and other);

8. The use of averages in health protection
for description of indices of physical development (length, mass of body, circumference of head of new-born and other);

10. Introduction
The purpose of HYPOTHESIS TESTING is to aid the clinician, researcher, or administrator in reaching a conclusion concerning a POPULATION by examining a SAMPLE from that population.
population
sample
sample
inference

11. statistics
sample
inference
parameter

12. Hypothesis is…. A statement about one or more populations. e.g.
The average length of stay of patients admitted to the hospital is 5 days;
A certain drug will be effective in 90 percent of the cases for which it is used.

13. Estimation: approximate a characteristic
of the population with a statistic computed
from the sample x m = of
estimate
our is
mean
sample
population

15. Types of hypotheses Research hypothesis
The research hypothesis is the conjecture or supposition that motivates the research.
Statistical hypothesis
Statistical hypotheses are hypotheses that are stated in such a way that they be evaluated by appropriate statistical techniques.

16. Example
Twenty patients with a certain disease were randomly selected. The mean of enythrocyte sedimentation (ES) is 9.15 with standard deviation of However, references reported mean of ES of this type of patients is
Question: Does the mean of ES of this sample differ from 10.50?

18. Types of errors True False Condition of null hypothesis P>0.05
Fail to
reject H0
Correct action
Type II error β
P<0.05
Reject H0
Type I error α
Possible action

19. Type I and II error (one tailed)
H0:μ=0 α
1-α μ
H1:μ=μ0>0 β
1-β μ Uα
(critical value)
μ+δ

20. Decision making α/2=0.025 α/2=0.025 α/2=0.025 Rejection region
-1.96
Non rejection region
1.96

21. Chi-square distribution
3.84

22. Distribution rule
To reject the H0 if the value of the test statistic that we compute from our sample is one of the values in the rejection region ;
To not reject the H0 if the computed value of the test statistic is one of the values in the non-rejection region.

23. Significance level
The decision as to which values go into the rejection region and which ones go into the non-rejection region is made on the basis of the desired level of significance, designated by α;
The test statistic that falls in the rejection region is said to be significant.

24. Hypothesis testing steps
Data ----the nature of data ---test methods
Assumption ---e.g. normality of population distribution, equality of variance, and independence of samples-makes it possible to use certain mathematic models to reach an estimation of the sample.
Statistical Hypothesis and αlevel
Statistic computation
Decision making

25. Hypothesis
The NULL HYPOTHESIS (H0) is the hypothesis to be tested----hypothesis of no difference between mean of sample and mean of population
The ALTERNATIVE HYPOTHESIS (H1) is a statement of what we will believe is true if our sample data cause us to reject the null hypothesis.

26. Way of thinking
First, we hypothesize that the mean of ES from our sample is equal to 10.50(H0). And we also have a alternative hypothesis H1.
According to the distribution of statistic of the sample, we judge that whether the sample information support the H0 or not.

27. Rules for Stating Statistical Hypotheses
What you hope or expect to be able to conclude as a result of the test usually should be placed in the H1;
An indication of equality (either =, ≥ or ≤) must appear in the H0;
The H0 is the hypothesis that is tested;
The H0 and H1 are complementary. That is, the 2 together exhaust all possibilities regarding the value that the hypothesized parameter can assume.

28. A Precaution
When we fail to reject a null hypothesis, we do not say that it is true, but that it may be true.
Neither hypothesis testing nor statistical inference, leads to the proof of a hypothesis, it merely indicates whether the hypothesis is supported or is not supported by the available data.

29. Test statistic Decision maker (reject or not to reject the H0)
Computed from the data of the sample.
Compare the computed statistics from our sample to the corresponding CRITICAL VALUE, make decision

30. General Formula for Test Statistic

31. Distribution of test statistic
Sample distribution is the key to statistical inference. t distribution or standard normal distribution
For example; t=
Follows the standard normal distribution if the hypothesis is true and the assumptions are met. S

32. t distribution and u distribution

33. Distribution rule
All possible values that the test statistic can assume are point on the horizontal axis of the graph of the distribution of the test statistic and are divide into two group,
Rejection region & non-rejection region

34. Decision making α/2=0.025 α/2=0.025 α/2=0.025 Rejection region
-1.96
Non rejection region
1.96

35. Chi-square distribution
3.84

36. Distribution rule
To reject the H0 if the value of the test statistic that we compute from our sample is one of the values in the rejection region ;
To not reject the H0 if the computed value of the test statistic is one of the values in the non-rejection region.

37. Significance level
The decision as to which values go into the rejection region and which ones go into the non-rejection region is made on the basis of the desired level of significance, designated by α;
The test statistic that falls in the rejection region is said to be significant.

38. α level
The level of significance α is a probability and, in fact, is the probability of rejection a true null hypothesis.
Small αmakes the probability of rejection a true null hypothesis small.
The more frequently encountered values of α are:0.01; 0.05 and 0.10

39. Types of errors A true H0 is rejected ----type I error ;
A false H0 is not rejected----type II error;
The probability of committing a type II error is designated as β.
When H1 is true, and we get P<0.05, the probability of that we get right conclusion is 1- β, which is called the power of the test.

40. Types of errors True False Condition of null hypothesis P>0.05
Fail to
reject H0
Correct action
Type II error β
P<0.05
Reject H0
Type I error α
Possible action

41. Type I and II error (one tailed)
H0:μ=0 α
1-α μ
H1:μ=μ0>0 β
1-β μ Uα
(critical value)
μ+δ

42. Calculation of test statistic
We computed the test statistic of the sample and compare it with the critical value of rejection and non-rejection regions that have already been specified.

43. Conclusion If H0 is rejected, we conclude that H1 is true.
If H0 is not rejected, we conclude that H0 may be true.

44. P values
The p value is a number that tells us how UNUSUAL our sample results are, given that the null hypothesis is true (the probability of observing equal or more extreme value of test statistic, when H0 is true).
A p value indicating that the provide justification for doubting the truth of the null hypothesis.
The p value is the probability of obtaining, when H0 is true, a value of the test statistic as extreme as or more extreme then the one actually computed.
P value is the probability of type I error when H1 is true.

45. The use of averages in health protection
for determination of medical-physiology indices of organism (frequency of pulse, breathing, level of arterial pressure and other);

46. The use of averages in health protection
for estimation of these medical-social and sanitary-hygienic researches (middle number of laboratory researches, middle norms of food ration, level of radiation contamination and others).

47. Averages
Averages are widely used for comparison in time, that allows to characterize the major conformities to the law of development of the phenomenon. So, for example, conformity to the law of growth increase of certain age children finds the expression in the generalized indices of physical development. Conformities to the law of dynamics (increase or diminishment) of pulse rate, breathing, clinical parameters at the certain diseases find the display in statistical indices which represent the physiology parameters of organism and other.

48. Average Values
Mean:  the average of the data  sensitive to outlying data
Median:  the middle of the data  not sensitive to outlying data
Mode:  most commonly occurring value
Range:  the difference between the largest observation and
the smallest
Interquartile range:  the spread of the data  commonly used for skewed data
Standard deviation:  a single number which measures how much the observations vary around the mean
Symmetrical data:  data that follows normal distribution  (mean=median=mode)  report mean & standard deviation & n
Skewed data:  not normally distributed  (meanmedianmode)  report median & IQ Range

49. Average Values
Limit is it is the meaning of edge variant in a variation row
lim = Vmin Vmax

50. Average Values
Amplitude is the difference of edge variant of variation row
Am = Vmax - Vmin

51. Average Values
Average quadratic deviation characterizes dispersion of the variants around an ordinary value (inside structure of totalities).

52. Average quadratic deviation
σ =
simple arithmetical method

53. Average quadratic deviation
d = V - M
genuine declination of variants from the true middle arithmetic

54. Average quadratic deviation
method of moments

55. Average quadratic deviation
is needed for:
1. Estimations of typicalness of the middle arithmetic (М is typical for this row, if σ is less than 1/3 of average) value.
2. Getting the error of average value.
3. Determination of average norm of the phenomenon, which is studied (М±1σ), sub norm (М±2σ) and edge deviations (М±3σ).
4. For construction of sigmal net at the estimation of physical development of an individual.

56. Average quadratic deviation
This dispersion a variant around of average characterizes an average quadratic deviation (  )

57. Coefficient of variation is the relative measure of variety; it is a percent correlation of standard deviation and arithmetic average.

58. Terms Used To Describe The Quality Of Measurements
Reliability is variability between subjects divided by inter-subject variability plus measurement error.
Validity refers to the extent to which a test or surrogate is measuring what we think it is measuring.

59. Measures Of Diagnostic Test Accuracy
Sensitivity is defined as the ability of the test to identify correctly those who have the disease.
Specificity is defined as the ability of the test to identify correctly those who do not have the disease.
Predictive values are important for assessing how useful a test will be in the clinical setting at the individual patient level. The positive predictive value is the probability of disease in a patient with a positive test. Conversely, the negative predictive value is the probability that the patient does not have disease if he has a negative test result.
Likelihood ratio indicates how much a given diagnostic test result will raise or lower the odds of having a disease relative to the prior probability of disease.

60. Measures Of Diagnostic Test Accuracy

61. Expressions Used When Making Inferences About Data
Confidence Intervals
The results of any study sample are an estimate of the true value in the entire population. The true value may actually be greater or less than what is observed.
Type I error (alpha) is the probability of incorrectly concluding there is a statistically significant difference in the population when none exists.
Type II error (beta) is the probability of incorrectly concluding that there is no statistically significant difference in a population when one exists.
Power is a measure of the ability of a study to detect a true difference.

62. Multivariable Regression Methods
Multiple linear regression is used when the outcome data is a continuous variable such as weight. For example, one could estimate the effect of a diet on weight after adjusting for the effect of confounders such as smoking status.
Logistic regression is used when the outcome data is binary such as cure or no cure. Logistic regression can be used to estimate the effect of an exposure on a binary outcome after adjusting for confounders.

63. Survival Analysis
Kaplan-Meier analysis measures the ratio of surviving subjects (or those without an event) divided by the total number of subjects at risk for the event. Every time a subject has an event, the ratio is recalculated. These ratios are then used to generate a curve to graphically depict the probability of survival.
Cox proportional hazards analysis is similar to the logistic regression method described above with the added advantage that it accounts for time to a binary event in the outcome variable. Thus, one can account for variation in follow-up time among subjects.

64. Percentage of Specimens Testing Positive for RSV (respiratory syncytial virus)

65. Descriptive Statistics

66. Distribution of Course Grades

67. Thank you!