CHAPTER 1

Introduction to statistics

What is Statistics?

•Statistics is the term for a collection of mathematical methods of organizing, summarizing, analyzing, and interpreting

information gathered in a study

Data and Data AnalysisWe have two types of research study

•In quantitative research, data are usually quantitative (numbers) and subjected to

statistical analysis. Mainly the data is collected by close ended questions

•Qualitative research, data are usually narrative and collected by open ended

questions

Example of close ended question (Likert scale) to measure attitude toward mental illness

SA = Strongly agree

A = Agree

D = Disagree

SD = Strongly disagree

= ?? Uncertain

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Strongly disagree

(1)

Disagree

(2)

Uncertain(diversity)

(3)

Agree

(4)

Strongly agree

(5)

ItemsReflect the topic of the study

People who have had Mental illness can become normal and productive citizens after treatment.

Mental ill patient’s who have been in Psychiatric hospital or center should not be

allowed to have children.

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Example of open ended question• What is the perception of you organization

towered female holding high managerial positions? ………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

Where Do Data Come From?•Example 1: Interviews/questionnaires

– Question: On a scale from 0 to 10, please rate your level of fatigue

– Answer (Data): Person 1: 7 Person 2: 3 Person 3: 10 Etc.

Variables

A variable is something that takes on different values

Example of variables –Height, sex, weight, age, level of education, marital status, respiratory

rate, heart rate and etc…

Types of Variables

– Independent variable: The hypothesized cause of, or influence on an outcome

– Dependent variable: The outcome of interest, hypothesized to depend on, or be caused by

the independent variable

Research Questions

•Research questions communicate the research variables and the population(the entire group of interest)

– Example: In hospitalized children (population) does music (IV) reduce stress (DV) ?

Types of Sampling

1. probability Sampling

2. Non- probability Sampling.

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Probability sample

The probability sample means, the probability

of each subject to be included in the study.

There are four types of probability sample

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Four basic kinds of probability samples. a. Simple random sample. The simple random sample is the simplest probability sample, so that every element in the population has an equal probability of being included.

Note

All types of random samples tend to be representative.

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b. Stratified random samples

In a stratified random sample, the population is first divided

into two or more homogenous strata (age, gender, occupation,

level of education, income and so forth) from which random samples are then drawn. This stratification results in greater

representativeness.

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C. Cluster samples

For many populations, it is simply impossible

to obtain a listing of all the elements, so the

most common procedure for a large surveys

is cluster sampling.

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D. Systematic samplesSystematic sampling involves the selection of every (kth) element

from some list or group, such as every 10th subject on a patient

list. If the researcher has a list, or sampling frame, the following

procedure can be adopted. The desired sample size is started

at some number (n). The size of the population must be known or

estimated (N). By dividing (N) by (n), the sampling interval is the

standard distance between the elements chosen for the sample. Dr. Yousef Aljeesh

Example if we were seeking a sample of 200 from a population of 40,000,

then our sampling interval would be as follows: K= 40,000 = 200 200In other words, every 200 the element on the list would be sampled.

The first element should be selected randomly, using a table of

random numbers, let us say that we randomly selected number

73 from a table. The people corresponding to numbers 73, 273, 473, 673, and so forth would be included in the sample.

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2. Non-probability Sample Non-probability sample is less likely than probability

sampling to produce a representative samples. Despite

this fact, most research samples in most disciplines

including nursing are non-probability samples.

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a. convenience sampling (Accidental, volunteer)

The use of the most conveniently available people or subjects in a study. For

example, stopping people at a street corner to conduct an interview is

sampling by convenience. Sometimes a researcher seeking individuals with

certain characteristics will stand in the clinic, hospital or community center to

select his convenience sample. Sometimes a researcher seeking individuals

with certain characteristics will place an advertisement in a newspaper, so the

people or subjects are volunteer to take apart of the study. Dr. Yousef Aljeesh

b. Snowball or network sampling Early sample members are asked to identify and refer other

people who meet the eligibility criteria. or it begins with a few

eligible subjects and then continues on the basic of subjects

referral until the desired sample size has been obtained. This

method of sampling is most likely to be used when the researcher

population consists of people with specific traits who might

otherwise be difficult to identify. Dr. Yousef Aljeesh

C. Quota Sampling Quota sampling is another form of non-probability sampling.

The quota sample is one in which the researcher identifies

strata of the population and determines the proportions of element needed from the various segments of the population,

but without using a random selection of subjects.

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Note: Although there are no simple formulas that indicate how large

sample is needed in a given study, we can offer a simple piece of

advice: you generally should use the largest sample possible.

The larger the sample the more representative of the population it

is likely to be.

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Variable and constant

Variable: is something that varies or takes in different values (weight, sex, blood pressure, and heart rate) are all examples of characteristics that vary from one person to the next. If they did not vary, they would be constants

Discrete Versus Continuous Variables

•Variables have different qualities with regard to measurement potential

–Discrete variables –Continuous variables

Note:- We use non-parametric tests in case of Nominal and Ordinal measurement (Example: Chi-Square test) - Both depend on percentages because Mean

does not make sense

Note In interval scale, there is no real or rational

zero point

Another Example Weight (Zero weight is actual possibility) It is acceptable to say that some one who

weights 100 kg is twice as heavy as some one who weights 50 kg.

NoteInterval and Ratio measurements are continuous

variables and parametric tests should be used in

this situation. Also Mean is applicable

Types of Statistical Analysis •Calculation

– Manual versus computerized

•Purpose– Descriptive versus inferential

•Complexity– Univariate, bivariate, multivariate

Descriptive Statistics•Researchers collect their data from a sample of

study participants—a subset of the population of interest

•Descriptive statistics describe and summarize data about the sample

– Examples: Percent female in the sample, level of education, Income, residency and ect

Example 1 of Descriptive statisticsDistribution of study population according to place of work

Hospital nameTarget

populationRespondents Percentage Response rate

Al-shifa hospital 56 51 35.7 91.07%

Nasser medical complex 21 21 14.7 100%

European Gaza hospital 21 17 11.9 80.95%

Aqsa Martyrs Hospital 14 14 9.8 100%

Kamal Adwan hospital 9 9 6.3 100%

Abu Yousef Al Najjar 12 8 5.6 66.6%

Beit Hanoun hospital 10 10 7.0 90.9%Ophthalmic hospital 7 6 4.2 85.7%Crescent Alemaraty 9 7 4.9 77.7%

Total 159 143 100.0

Calculation of Response Rate

Response Rate (RR) = Respondents (R) 100 Target Population (TP)

RR= 51 100 = 91.07 56

Example 2 of Descriptive statistics Distribution of Study Population According to Height, Weight and BMI (N= 143)

Variables Category Frequency Percentage (%)

Height (cm)

166cm and less than 41 28.7

167 – 176 cm 56 39.2

177 – 186 cm 40 28.0

187cm and above 6 4.2

Weight (kg)

Total 143 100.0

67kg and less than 32 22.4

68-78 kg 39 27.3

79-89 kg 41 28.7

90 kg and above 31 21.7

Total 143 100.0

Body Mass Index

(BMI)

Less than 25 55 0.7

22.5-29.5 33 37.8

30 and more 25 44.1

Total 143 100.0

Age distribution

25.7

45.9

28.4

05

101520253035404550

30 Yrs and less From 31 to 45 Yrs More than 45 Yrs

شرق

Example 3 of Descriptive statistics

Example 4 of Descriptive statistics Gender distribution

Example 5 of Descriptive statistics Distribution of subjects by

governorates % No. Items

13.33 15 North

11.6 13 Khanyounis

50 56 Gaza

11.6 13 Rafah

13.33 15 Mid Zone

100 112 Total

Inferential Statistics •Researchers obtain data from a sample but

often want to draw conclusions about a population

• Inferential statistics are often used to test hypotheses(predictions) about relationships between variables

Example:- Positive, negative, directional hypothesis and etc.

Example of inferential statistics

Association between socio-demographic factors and diarrhea among children aged less than 5 years (N=140)

FactorDiarrhea

χ2 p valueCasesN (%)

ControlN (%)

Father age

(20 – 30) years 33 (47.1) 37 (52.9)

7.371 0.025*(31 – 40) years 34 (48.6) 22 (31.4)

(41 – 59) years 3 (4.3) 11 (15.7)

OVC status

Orphaned 1 (1.4) 2 (2.9)

0.476 0.788Vulnerable 4 (5.7) 3 (4.3)

Not OVC 65 (92.9) 65 (92.9)

Type of familyNuclear family 46 (65.7) 50 (71.4)

0.530 0.466Extended family 24 (34.3) 20 (28.6)

Hypotheses

Definition of hypothesis : It is a statement of

predicted relationship between two or more than

two variables.

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Types of Hypotheses

1. Simple Hypothesis : A hypothesis that predicts the relationship between one dependent variable (DV) and one independent variable (IDV). It is easy to test and analyze it.

Example There is a relationship between smoking and development

of stroke among hypertensive patients in Gaza strip.

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2. Complex hypothesis: (Multivariate hypothesis) : A hypothesis that predicts the relationship between two or

more dependent variables and two or more independent variables.

Example: There is a relationship between high fat diet and smoking

and development of atherosclerosis and stroke among hypertensive patients in Gaza strip.

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3. Directional hypothesis: is one that specifies the expected direction of the relationship between variables. The researcher predicts not only the existence of a relationship but also the nature of the relationship.

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Example

1. There is a positive relationship between Smoking and lung cancer

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4. Statistical hypothesis (Null hypothesis): is one that stated there is no relationship between variables.

Example 1. There is no relationship between Smoking and lung cancer

2. There is no relationship between obesity and Breast cancer.

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