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• Measurement
• Population, Variable, Sample
• Hypothesis
• Types of errors
• Statistical Power
• Sampling
• Descriptive Statistics
• Inferential statistics
• Parametric and Non-parametric Tests
• Appropriate Statistical tests
• Common Statistical tests
• Multivariate Analysis
• Tips on Choosing the appropriate test
• Computer Aided Analysis

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Introduction

As the context of health care is changing due to the pharmaceutical services and technological advances, nurses and other health care professionals need to be prepared to respond in knowledgeable and practical ways. Health information is very often explained in statistical terms for making it concise and understandable. Statistics plays a vitally important role in the research. Statistics help to answer important research questions and it is the answers to such questions that further our understanding of the field and provide for academic study. It is required the researcher to have an understanding of what tools are suitable for a particular research study.  It is essential for healthcare professionals to have a basic understanding of basic concepts of statistics as it enables them to read and evaluate reports and other literature and to take independent research investigations by selecting the most appropriate statistical test for their problems. The purpose of analyzing data in a study is to describe the data in meaningful terms.

Descriptive approach and inferential approach

Depending on the kinds of variables identified (nominal, ordinal, interval, and ratio) and the design of particular study, a number of statistical techniques is available to analyze data. There are two approaches to the statistical analysis of data the descriptive approach and inferential approach. Descriptive statistics convert data into picture of the information that is readily understandable. The inferential approach helps to decide whether the outcome of the study is a result of factors planned within design of the study or determined by chance. The two approaches are often used sequentially in that first, data are described with descriptive statistics, and then additional statistical manipulations are done to make inferences about the likelihood that the outcome was due to chance through inferential statistics. When descriptive approach is used, terms like mean, median, mode, variation, and standard deviation are used to communicate the analysis information of data. When inferential approach is used, probability values (P) are used to communicate the significance or lack of significance of the results (Streiner & Norman, 1996).

Measurement

Measurement defined as “assignment of numeral according to rules” (Tyler 1963:7). Regardless of the variables under study, in order to make sense out of data collected, each variable must be measured in such a way that its magnitude or quantity must be clearly identified. The specific strategy for a particular study depends upon the particular research problem, the sample under study, the availability of instruments, and the general feasibility of the project (Brockopp & Hastings-Tolsma, 2003). A variety of measurement methods are available for use in nursing research.  Four measurement scales are used: nominal, ordinal, interval and ratio.

The nominal level of measurement

The nominal level of measurement is the most primitive or lowest level of classifying information.  Nominal variables include categories of people, events, and other phenomena are named, are exhaustive in nature, and are mutually exclusive. These categories are discrete and noncontinous. In case of nominal measurement admissible statistical operation are counting of frequency, percentage, proportion, mode, and coefficient of contingency.

The ordinal level of measurement

The ordinal level of measurement is second in terms of its refinement as a means of classifying information. Ordinal implies that the values of variables can be rank-ordered from highest to lowest.

Interval Level of Measurement

Interval level of measurement is quantitative in nature.  The individual units are equidistant from one point to the other. The interval data does not have an absolute zero. For example, temperature is measured in Celsius or Fahrenheit.   Interval level of measurement refers to the third level of measurement in relation to complexity of statistical techniques that can be used to analyze data. Variables with in this level of measurement are assessed incrementally, and the increments are equal.

Ratio Level of Measurement

Ratio level of measurement is characterized by variables that are assessed incrementally with equal distances between the increments and a scale that has an absolute zero. Ratio variables exhibit the characteristics of ordinal and interval measurement and can also be compared by describing it as two or three times another number or as one-third, one-quarter, and so on. Variable like time, length and weight are ratio scales and also be measured using nominal or ordinal scale. The mathematical properties of interval and ratio scales are very similar, so the statistical procedures are common for both the scales.

Errors of measurement

When a variable is measured there is the potential for errors to occur. Some of the sources of errors in measurement are, instrument clarity, variations in administrations, situational variations, response set bias, transitory personal factors, response sampling, and instrument format.

Population, Sample, Variable

Population is defined as the entire collection of a set of objects, people, or events, in a particular context. The population is the entire group of persons or objects that is of interest to the investigator. In statistics population means, any collection of individual items or units that is the subject of investigation. Population refers to the collection of all items upon which statements will be based. This might include all patients with schizophrenia in a particular hospital, or all depressed individuals in a certain community.
Characteristics of a population that differ form individual to individual are called variables. A variable is a concept (construct) that has been so specifically defined that precise observations and therefore measurement can be accomplished. Length, age, weight, temperature, pulse rate are a few examples of variables.

The sample is a subset of the population selected by investigator to participate in a research study. A sample refers to a subset of observations selected from the population. It might be unusual for an investigator to describe only patients with schizophrenia in a particular hospital and it is unlikely that an investigator will measure every depressed person in a community. As it is rarely practicable to obtain measures of a particular variable from all the units in population, the investigator has to collect information from a smaller group or sub-set that represents the group as a whole. This sub-set is called a sample.  Each unit in the sample provides a record, such as measurement, which is called an observation. The sample represents the population of those critical characteristics the investigator plan to study.

Dependent and independent variables

An independent variable is presumed cause of the dependent variable-the presumed effect. The independent variable is one which explains or accounts for variations in the dependent variable. An independent variable is one whose change results in change in other variable. In experiments, the independent variable is the variable manipulated by the experimenter. A dependent variable is one which changes in relationship to changes in another variable. A variable which is dependent in one study may be independent in another. Intervening variable is one that comes between the independent and dependent variable.

Hypothesis

Hypothesis is statement or declaration of the expected outcome of a research study. It is based on logical rationale and has empirical possibilities for testing. Hypothesis is formulated in experimental research. In some non-experimental correlational studies, hypothesis may also be developed. Normally, there are four elements in a hypothesis:

• (1) dependent and independent variables,
• (2) some type of relationship between independent and dependent variable,
• (3) the direction of the change, and
• (4) it mentions about the subjects, i.e. population being studied.

It is defined as “A tentative assumption made in order to draw out and test its logical or empirical consequences” (Webster 1968).

Standards in formulating a hypothesis (Ahuja, R. 2001):

• It should be empirically testable, whether it is right or wrong.
• It should be specific and precise.
• The statements in the hypothesis should not be contradictory.
• It should specify variables between which the relationship to be established
• It should describe one issue only.

Characteristics of a Hypothesis

• Characteristics of a Hypothesis (Treece & Treece, 1989)
• It is testable
• It is logical
• It is directly related to the research problem
• It is factually or theoretically based
• It states a relationship between variables
• It is stated in such a form that it can be accepted or rejected

Directional hypothesis predicts an outcome in a particular direction, and nondirectional hypothesis simply states that there will be difference between the groups. There can be two hypotheses, research hypothesis and null hypothesis. The null hypothesis is formed for the statistical purpose of negating it. If the research hypothesis states there is positive correlation between smoking and cancer, the null hypothesis states there is no relation between smoking and cancer. It is easy to negate a statement than establishing it. 

The null hypothesis is statistical statement that there is no difference between the groups under study. A statistical test is used to determine the probability that the null hypothesis is not true and rejected, i.e. inferential statistics are used in an effort to reject the null, thereby showing that  a deference does exists. The null hypothesis is a technical necessity when using inferential statistics, based on statistical significance which is used as criterion.

Types of errors

When the null hypothesis is rejected, the observed differences between groups are deemed improbable by chance alone. For example, if drug A is compared to a placebo for its effects on depression and the null hypothesis is rejected, the investigator concludes that the observed differences most likely are not explainable simply by sampling error. The key word in these statements is probable. When offering this conclusion, the investigator has the odds on his or her side. However, what are the chances of the statement being incorrect?

In statistical inference there is no way to say with certainty that rejection or retention of the null hypothesis was correct. There are two types of potential errors. A type I error occurs when the null hypothesis is rejected when indeed it should have been retained; a type II error occurs if the null hypothesis is retained when indeed it should have been rejected.

Type I Error

Type I errors occur when the null hypothesis is rejected but should have been retained, such as when a researcher decides that two means are different. He or she might conclude that the treatment works or those groups are not sampled from the same population whereas in reality the observed differences are attributable only to sampling error. In a conservative scientific setting, type I errors should be made rarely. There is a great disadvantage to advocating treatments that really do not work.

The probability of a type I error is denoted with the Greek letter alpha (a). Because of the desire to avoid type I errors, statistical models have been created so that the investigator has control over the probability of a type I error. At the .05 significance or alpha level, a type I error is expected to occur in 5 percent of all cases. At the .01 level, it may occur in 1 percent of all cases. Thus, at the .05 a level, one type I error is expected to be made in each of 20 independent tests. At the .01 a level, one type I error is expected to be made in each 100 independent tests.

Type II Error

The motivation to avoid a type I error might increase the probability of making a second type of error. In this case the null hypothesis is retained when it actually was wrong. For example, an investigator may reach the conclusion that a treatment does not work when actually it is efficacious. The probability of a type II error is symbolized by the Greek capital letter beta (B). Here the decision is not to reject the null hypothesis when in actuality the null hypothesis was false. This is a type II error with the probability of beta (B).

Statistical Power

There are several maneuvers that will increase control over the probability of different types of errors and correct decisions. One type of correct decision is the probability of rejecting the null hypothesis and being correct in that decision. Power is defined as the probability of rejecting the null hypothesis when it should have been rejected. Ultimately, the statistical evaluation will be more meaningful if it has high power.

It is particularly important to have high statistical power when the null hypothesis is retained. Retaining the null hypothesis with high power gives the investigator more confidence in stating that differences between groups were non-significant. One factor that affects the power is the sample size. As the sample size increases, power increases. The larger the sample, greater the probability that a correct decision will be made in rejecting or retaining the null hypothesis.

Another factor that influences power is the significance level. As significance increases, the power increases. For instance, if the .05 level is selected rather than the .01 level, there will be a greater chance of rejecting the null hypothesis. However, there will also be a higher probability of a type I error. By reducing the chances of a type I error, the chances of correctly identifying the real difference (power) are also reduced. Thus, the safest manipulation to affect power without affecting the probability of a type I error is to increase the sample size.

The third factor affecting power is effect size. The larger the true differences between two groups, the greater the power. Experiments attempting to detect a very strong effect, such as the impact of a very potent treatment, might have substantial power even with small sample sizes. The detection of subtle effects may require very large samples in order to achieve reasonable statistical power. It is worth noting that not all statistical tests have equal power. The probability of correctly rejecting the null hypothesis is higher with some statistical methods than with others. For example, nonparametric statistics are typically less powerful than parametric statistics, for example.

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