Determine the average number of the weight of girls.

Weight in KG.	Frequency(f)	Calculate
15 – 17	20	X Moment
18 – 20	46	δ
21 -23	66	m
24 -26	17
27 -29	1
	Total = 150

VARIANT 2.

Table 17

Determine the average number of the height in 14-year old girls.

Variant (V)	Frequency(f)	Calculate
130 – 134	2	X moment
135 – 139	6	δ
140 – 144	20	m
145 – 149	30
150 – 154	85
155 – 159	35
160 – 164	15
165 – 169	6
170 – 174	1
	Total = 200

VARIANT 3.

Table 18

Determine the average number of the chest circumference in 9 – year old boys.

Variant (V) Chest circumference in cm.	Frequency(f)	Calculate
53 – 55	6	X moment
56 – 58	42	δ
59 – 61	45	m
62 -64	12
65 – 67	5
	Total = 110

VARIANT 4.

Table 19

Determine the average number of the maximal blood pressure in medical students before passing the examinations.

Variant (V)	Frequency(f)	Calculate
100 – 104	2	X moment
105 – 109	2	δ
110 – 114	4	m
115 – 119	5
120 – 124	4
125 – 129	6
130 – 134	9
135 – 139	5
140 – 144	2
	Total = 40

VARIANT 5.

Table 20

Determine the average number of pulse in medical students before the examination.

Variant (V)	Frequency(f)	Calculate
55 – 64	2	X moment
65 – 74	3	δ
75 – 84	10	m
85 – 94	5
95 – 104	22
105 – 114	6
115 – 124	4
125 – 134	3
	Total = 55

VARIANT 6.

 Table 21

Determine the average number of height of 17 – year- old juveniles.

Heights in Cm.	Frequency (f)	Calculate
154 – 156	45	X moment
157 – 159	60	δ
160 – 162	83	m
163 – 165	85
166 – 168	53
169 – 171	6
	Total = 332

VARIANT 7.

Table 22

Determine the average number of then height of 7 – years – old boys.

Variant (V) Growth in Cm	Frequency(f)	Calculate
108 – 109	8	X moment
111 – 113	13	δ
114 – 116	34	X m
117 – 119	40
120 – 122	32
123 – 125	14
126 – 128	9

VARIANT 8.

Table 23

Determine the average number of the level of maximum blood pressure in women at the age of 50 years.

Variant (V) Growth in Cm	Frequency (f)	Calculate
100 – 109	3	X moment
110 – 119	12	δ
120 – 129	21	m
130 – 139	35
140 – 149	62
150 – 159	33
160 – 169	19
170 – 179	15
	Total = 200

VARIANT 9.

Table 24

Determine the average number of the level of maximum blood pressure in women at the age of 25 years.

Variant (V)	Frequency(f)	Calculate
100 – 104	2	X moment
105 – 109	7	δ
110 – 114	21	m
115 – 119	43
120 – 124	75
125 – 129	34
130 – 134	26
135 – 139	25
140 – 144	13
145 – 149	4
	Total = 250.

 

VARIANT 10.

 Table 25

Determine the average number of the head circumference of boys at the age of 2 years.

Variant (V)	Frequency(f)	Calculate
39 – 41	14	X moment
42 – 44	33	δ
45 – 47	46	m
48 – 50	18
51 – 53	9
	Total = 120

THEME 4

PARAMETRIC METHODS OF ESTIMATION

STATISTICAL HYPOTHESES ANDCORRELATION

1. Features of the theme.

Parametric methods of estimation of reliability are necessary in the practical work of doctors by calculation of new methods of treatment in organization of the treatment process.

Aims of studies.

The student must know the finding of average and relative numbers, their kinds, apply them in practical work of doctors, know the rules of complete general and random total and kind correlation.

Education in studies includes the sense of necessary basic knowledge, sense of professional culture, basic professional outlook, the principal logical mentality and dynamic of thinking.

3. Main part.

Reliability statistic indices - power of their thus conformity reflection reality.

Critera estimation of reliability

1. The error is calculated by:

1.1. For average:

1.2. For relative:

2. Confidence limits between average and relative number.

X_general= X_selective ± tm_x,

P_general= P_selective ± tm_p,

Where tm_p = Δ (delta) confidential interval or limit error indices,

t = confidential coefficient

 

3. T coefficient (by Student)

Reliability difference between average and relative number by criteria t

,

 

1. t > 2: perfect prognosis is 95%, in medicine is enough.

2. t> 3: 99.7% is perfect prognosis, in exactly science. (Physics, Mathematics)

3. t< 2: perfect prognosis is less than 95%, in this case parameter is not reliable.

Statistical hypothesis

Zero hypothesis (Ho) is a statement which does not assume the influence of intervention (treatment) in a population. It is used in Biostatistics to check all hypotheses.

Statistical hypothetical checking in Biostatistics -  consists of using data for the realization of a choice of one of two (or more) various opportunities in making decisions in an ambiguous situation.

The result of checking the hypothesis, is that we can receive conclusion if the hypothesis is present or not.

For example: It is necessary to compare the efficiency of two kinds of treatment towards breast cancer. The effect will consist of decrease of 5-years death rate. With this purpose, zero hypothesis and its alternative are formed.

 Zero hypothesis (Ho) shows that the differences between two totalities are appreciated on their average meanings, that is 5-years death rate is identical with different treatment.

The opposite (alternative) hypothesis (Нi) shows, that difference of effects not equal to zero. Acceptance of zero hypothesis means that the obtained difference has only incidental character, the deviation of zero hypothesis - is a non-incidental difference.  

Whether the criteria of checking a hypothesis allow determining enough arguments for rejecting the zero hypothesis. The alternative hypothesis in the latter case is accepted.

When we wrongly reject a zero hypothesis and when we find out differences actually are not present, we will receive a so-called mistake of the first sort (α) also named a significant value. The level of the statistical importance of the found out differences designated as P.

This level the significance value of checking criteria: a hypothesis is rejected, if we received value Р below significant value (α). If Р exceeds the chosen significance value, the hypothesis is accepted.

This probability more often also is resulting in the publications by authors, designating it as «Р <0,05» or «Р <0,01». In medicine and biology, as much as possible admitted probability of such mistake usually is equal to 5 % (0,05) or 1 % (0,01).

If we accept a zero hypothesis, and when the alternative hypothesis shows the presence of differences, we committed a so-called mistake of the second sort (ß).

 In this case probability to find out such difference is equal (1-ß). This also can be named as sensitive or capacity of the statistical criterion.

Capacity is a probability of a deviation of a zero hypothesis when it is false, and it is possible to solve. For example, an analysis as chance (in %) to find out the real clinical effect in the given totality with statistically significant volume. Capacity is fixed at a level of 70 %, 90 % or 95 % and in medico-biological researches should be not less than 80 %.

CORRELATION

Functional, alternative and correlation (statistical) connections are distinguished.

 Functional connection – when the cause is followed by an effect. For example, connection between area of a circle and length of its radius. The more the radius is, the more the area of the circle is.

Alternative or qualitative connection. It is characterized by the presence or the absence of a qualitative feature. For example, a patient is vaccinated – not vaccinated, sick – not sick (other things being equal). Qualitative connection is determined by coefficient of association.

Correlation or statistical connection – is revealed in a mass of big number of observations. For instance, there is a correlation connection between height and weight of a human body. The more is the height, the more, as a rule, is the weight. Correlation connection, or simply correlation, can be direct (with positive sign+) or inverse (with negative sign-). In case of direct correlation, when one phenomenon either increases or decreases the other one increases or decreases respectively. In case of inverse correlation – vice versa, when one phenomenon increases, the other one decreases. For instance, when frequency of preventive examinations increases, number of calls to paramedics decreases.

As a measure of connection closeness serves correlation coefficient. Its value may vary from 0 to ±1. The connection closeness is estimated by the special table (see below).

Table 26