1. College

Basic Statistics for the Health Sciences 2.3 out of 5 based on 0 ratings. An older version of the Basic Statistics book used in a lot of second-rate online statistics classes. By geofflilley in Types > School Work, statistics, and health.

Download Presentation PowerPoint Slideshow about 'BASIC STATISTICS For the HEALTH SCIENCES Fifth Edition' - burian An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. 1.1The Meaning of Statistics Formally defines the term statistics and illustrates by describing what a statistic does 1.2 The uses of statistics Shows how descriptive statistics are used to describe data and how inferential statistics are used to reach conclusions from the analysis of data. 1.3 Why study statistics? Explains how the study of statistics is important for research, for writing publishable reports, for understanding scientific journals, and for discriminating between appropriate and inappropriate uses of statistics. 1.4 Sources of Data Discusses surveys and experiments, two main sources of data, and further classifies surveys as retrospective or prospective and as descriptive or analytical.

1.5 Clinical Trials Describes the use of a clinical trial to determine the value of a new drug procedure. 1.6 Planning of Surveys Previews some hints on how to maximize the value of survey data. 1.7 How to Succeed in Statistics Offers some tips on getting the most out of class and other resources. A.What Does Statistics Mean?. 1.Refers to a recorded number. 2.Denotes characteristics calculated for a set of data.

a.Standard deviation. b.Correlation coefficient. 3.A body of techniques and procedures dealing with the collection, organization, analysis,. interpretation, and presentation of information that can be stated numerically. B.What Do Statisticians Do?. 1.Works on challenging scientific tasks. 2.Primarily concerned with developing and applying methods that can be used in collecting and analyzing data.

3.Tasks are as follows. a.To guide the design of an experiment or survey.

b.To analyze data. c.To present and interpret results. A.Definition: a carefully designed experiment that is generally considered to be the best method for evaluating the effectiveness of a new drug or treatment. B.Protocol. 1.Describes in detail the design of proposed research.

2.Clearly defined hypothesis. 3.Detailed delineation of inclusion and exclusion criteria for study subjects. 4.Descriptions of the proposed interventions and the randomization process. 5.Detailed explanation of how bias may be minimized.

6. Description of the procedures to minimize errors in the collection and analysis of data. 2.1Selecting Appropriate Samples Explains why the selection of an appropriate sample has an important bearing on the reliability of inferences about a population 2.2Why Sample? Gives a number of reasons sampling is often preferable to census taking 2.3How Samples are Selected Explains how samples are selected 2.4How to Select a Random Sample Illustrates with a specific example the method of selecting a random sample using a computer statistical package 2.5Effectiveness of a Random Sample Demonstrates the credibility of the random sampling process 2.6Missing and incomplete Data Explains the problem of missing or incomplete data and offers suggestions on how to minimize this problem.

C.Systematic sampling. 1.used when a sampling frame – a complete, nonoverlapping list of the persons or objects constituting the population is available. 2.randomly select a first case then proceed by selecting every case. D.Stratified sampling – used when we wish the sample to represent the various strata (subgroups) of the population proportionately or to increase the precision of the estimate. E.Cluster sampling.

1.select a simple random sample (number of city blocks). 2.More economical than random selection of persons throughout the city. Assessing all individuals in a population may be impossible, impractical, expensive, or inaccurate, so it is usually to our advantage to instead study a sample from the original population.

To do this, we must clearly identify the population, be able to list it in a sampling frame, and utilize an appropriate sampling technique. Although several methods of selecting samples are possible, random sampling is usually the most desirable technique. It is easy to apply, limits bias, provides estimates of error and meets the assumptions necessary for many statistical tests. Missing or incomplete data can also introduce bias.

Carry-forward analysis is one technique for accounting for missing or incomplete data. The effectiveness of random sampling can easily be demonstrated by comparing sample statistics with population parameters. The statistics obtained from a sample are used as estimates of the unknown parameters of the population. 1.Distinguish between. a.qualitative and quantitative variables.

b.discrete and continuous variables. c.symmetrical, bimodal, and skewed distributions.

d.positively and negatively skewed distributions. 2.Construct and interpret a frequency table that includes class intervals, class frequency, valid percent, and cumulative percent. 3.Indicate the appropriate types of graphs for displaying quantitative and qualitative data. 4. Distinguish which forms of data presentation are appropriate for different situations. A.General Data Organization/Presentation Methods.

1.Tables. 2.Graphs. 3.Numerical Techniques. B.Common Scales used to Measure Data. 1.Qualitative Data –variables that yield nominal level data.

a.Nominal – primarily used for grouping or categorizing data. b.Ordinal – ordered series of relationships. 2.Quantitative Data – numerically measured variables. a.Interval – the number zero is an artificial 0, i.e. Temperature. b.Ratio - the number zero is true or absolute, total absence of the characteristic being measured, i.e. $ in your wallet.

The principles of tabulating and graphing data are essential if we are to understand and evaluate the flood of data with which we are bombarded. By proper use of these principles, statisticians can present data accurately and lucidly. It is also important to know which method of presentation to choose for each specific type of data. Tables are usually comprehensive, but they do not convey the information as quickly or as impressively as do graphs. Remember that graphs and tables must tell their own story and stand on their own.

A.The Mean. 1.the arithmetic or simple mean is computed by sunning all the observations in the sample and dividing the sum by the number of observations. 2.there are also harmonic and geometric means.

3.The arithmetic mean may also be considered the balance point, or, fulcrum. B.The Median. 1.the observation that divides the distribution into equal parts. 2.considered the most typical observation in the a distribution. 3.that value above which there are the same number of observations below. 4.Symbolically the mean is represented. A.Population Mean.

1.defined as the sum of the values divided by the number of observations for the entire population (N). 2.it is the sum of the squared deviations from the population mean, divided by N. 3.The sample mean (x) is an estimate of the population mean and is the sum of values in the sample divided by n, the number of observations in the sample alone. 4.The population variance is the is the sum of the squared deviations from the population mean divided by N, whereas the sample variance is the sum of the squared deviations from the sample mean. 1.Define probability and compute it in a given situation. 2.State the basic properties of probability. 3.Select and apply the appropriate probability rule for a given situation.

4.Distinguish between mutually exclusive events and independent events. 5.Distinguish between permutations and combinations, and be able to compute them for various events. 6.Explain what a probability distribution is, and state its major use. 7.State the probabilities by using a binomial distribution. 8.Interpret the symbols in the binomial term.

A.Rule 1: Number of Ways If event A can occur in n1, distinct ways and event B can occur in n2 ways, then the events consisting of A and B can occur in n1 – n2 ways. B.Rule 2: Permutations. 1.In determining the number of ways in which you can arrange a group of objects, you must first know whether the order of arrangement plays a role. 2.A permutation is a selection of r objects from a group of n objects, taking the order of selection into account. C.Rule 3: Combinations. A selection of a subgroup of distinct objects, with order not being important. Probability measures the likelihood that a particular event will or will not occur.

In a long series of trials, probability is the ration of the number of favorable outcomes to the total number of equally likely outcomes. Permutations and combinations are useful in determining the number of outcomes.

If compound events are involved, we need to select and apply the addition rule or the multiplication rule to compute probabilities. The outcome of an experiment together with its respective probabilities constitutes a probability distribution. One very common probability distribution is the binomial distribution. It presents the probabilities of various numbers of successes in trials where there are only two possible outcomes to each trial. The normal distribution is an important concept for a number of reasons. It has been used to define “normal limits” for clinical variables.

Many variables follow a normal distribution. The assumption of normality proves extremely useful because if the exceptional properties of the distribution. We can quickly reduce any normal distribution to the standard normal distribution by transforming the variable to a Z score.

Because these Z scores and the normal curve areas corresponding to them are conveniently tabulated, we are able to compute the probability of occurrence of various events and this to decide about the degree of uniqueness of those events. A.For a randomly selected sample of size n (n should be at least 25, but the larger n is, the better the approximation) with a mean u and a standard deviation o. 1.The distribution of sample means x is approximately normal regardless of whether the population distribution is normal. From statistical theory come these two additional theories. 2.The mean of distribution of sample means is equal to the mean of the population distribution – that is. 3.

The standard deviation of the distribution of sample means is equal to the standard deviation of the population divided by the square root of the sample size – that is. Is a counterpart of the standard deviation in that it is a measure of variation, but variation of sample means rather that of individual observations.

C.Measures the amount of sampling error. 1.Sampling error differs from other errors because it can be reduced at will, provided you are willing to increase the sample size. D.A nearly universal application of the standard error in medical literature is to specify an interval of, which includes the population mean, , with about 95% probability. E.The central limit theorem is beyond the scope of this book, but we can learn the following:. 1.The mean of the distribution of sample means is nearly identical to the population mean .

2.The standard deviation of the sample means computed by use of the traditional formula is 12.24, very close to the standard error of mean computed by using. This is an impressive result; it is now possible to compute the standard error of the mean knowing only the sample size and the population  or its estimate s. 3.The distribution of sample means is approximately normally distributed. A distinction exists between the distribution of a population’s observables and the distribution of its sample means.

A powerful tool called the central limit theorem gives reassuring results: No matter how unlike normal a population distribution may be, the distribution of its sample means will be approximately normal, provided only that the sample size is reasonably large (n = 30). The mean of the sampling distribution is equal to the mean of the population distribution. The standard error of sample means equals the standard deviation of the observations divided by the square root of the sample size. In sampling experiments, these results are often applied to determine how unusual a sample mean is. 1.Outline and explain the procedure for a test of significance. 2.Explain the meaning of a null hypothesis and an alternative hypothesis. 3.Define statistical significance.

4.Find the value of Z or t corresponding to a specified significance level. 5.Distinguish between a one-tailed and a two-tailed test. 6.Distinguish between the critical value and the test statistic. 7.Determine when to use a Z test and when to use a t test.

8.Calculate and interpret a one-sample Z test ad a one-sample t test. 9.Compute a confidence interval from a set of data for a single population mean. 10.Interpret and explain a confidence interval. 11.Distinguish between a probability interval and a confidence interval.

12.Demonstrate how to narrow the confidence interval. 13.Express results in terms of P values. 14.Calculate a exact P value for Z score.

15.Determine the sample size required to estimate a variable at a given level of accuracy. 16.Explain why it is unethical to choose a one-tailed test after data have been collected and analyzed. 17.Explain the meaning and relationship of the two types of errors made in testing hypothesis.

A.Hypothesis – a statement of belief used in the evaluation of population values. B.Null hypothesis – a claim that there is no difference between the population mean and the hypothesized value. C.Alternative hypothesis – a claim that disagrees with the null hypothesis. If the null hypothesis is rejected, we are left with no choice but to fail to reject the alternative hypothesis that  is not equal to. Sometimes referred to as the research hypothesis.

D.Test Statistic – a statistic used to determine the relative position of the mean in the hypothesized probability distribution of a sample means. E.Critical region – The region on the far end of the distribution.

If only one end of the distribution, commonly termed “the tail”, is involved, the region is referred to as a one-tailed test; if both ends are involved, the region is known as a two-tailed test. Henry rollins the boxed life zip software. When the computed Z or t falls in the critical region, we reject the null hypothesis.

The critical region is sometimes called the rejection region. The probability that a test statistic falls in the critical region is denoted by . F.Critical value – The number that divides the normal distribution into the region where we will reject the null hypothesis and the region where we fail to reject the null hypothesis.

G.Significance level – the level that corresponds to the area in the critical region. By choice, this area is usually small; the implication is that results falling into it do so infrequently. Consequently, such events are deemed unusual or, in the language of statisticians, statistically significant.

H.Nonrejection region – the region of the sampling distribution not included in a; that is the region located under the middle portion of the curve. Whenever a test statistic falls in this region, the evidence does not permit us to reject the null hypothesis. The implication is that results falling in this region are not expected.

The nonrejection region is denoted by (1 – ). I.Test of significance – a procedure used to establish the validity of a claim by determining whether the test statistic falls into the critical region. If it does, the results are referred to as significant. This test is sometimes called the hypothesis test. D.The basis for finding out whether the test statistic supports the null hypothesis is the critical region.

E.The critical region sets guidelines for rejecting or failing to reject the null hypothesis. F.If the computed statistic falls in the critical region of the distribution curve, where it is unlikely to occur by chance, the claim is not supported (conviction). G.If the test statistic falls in the nonrejection region, where it is quite likely to occur by chance, the claim is rejected (possible exoneration).

G.Nor does “statistically significant” imply “clinically significant” as the difference, although technically “significant” may be so small that it has little biological or practical consequence. H.Conventions for interpreting P values. P Value Interpretation. P.05 Result is not significant; usually indicated by no asterisk. P. A.Using data from a one-sample Z test, we can calculate an exact P value. B.The exact P value.001 is a one-tailed probability.

C.Calculating a two-tailed probability. 1.treat the calculated Z, 3.36 as  3.36.

2.still have.0010 in the positive tail, but also have.0010 in the negative tail. 3.add the two numbers together, and you have an exact two-tailed probability of.002. 4. Means that we can expect to find deviations above and below the mean.002,. or.2% of the time. 5.Two-tailed probability is twice that of the one-tailed probability.

A.Whether to use a one-tailed P value or a two-tailed P value is determined by the alternative hypothesis,. B.If is two-tailed, then the exact P value will also be two-tailed. C.Conversely, if is one-tailed, then the exact P value will be one-tailed.

D.Ethical issue – the direction of the alternative hypothesis should be chosen before data is collected – in other words – a one-tailed critical value should not be selected after data is collected and analyzed simply cause it is “easier” to attain significance. A.The determination of exact P values using Z scores is reasonably straight forward because the Z or normal distribution is based on population parameters. B.The t distribution is based on sample statistics and therefore becomes a family of distributions. C.As the sample size increases, the approximations get closer to the normal distribution. D.Researchers use two basic methods to report P values when writing a journal article.

1.First - give the calculated t value and then indicate, by the use of asterisks, the level of significance. 2.Second – display the exact P values. Tests of significance are performed to determine the validity of claims regarding population parameters. From the nature of the claim, we can decide whether the test should be one-tailed or two-tailed. The decision determines how the null and alternative hypotheses are stated, and the manner in which the test is performed. Together with the choice of significance level, this decision defines the critical region. The critical region is the decision-making feature of the test, and the computed test statistic is compared with it.

If the value of the test statistic falls in the critical region, we reject the null hypothesis and fail to reject the alternative; of it falls outside the critical region. We fail to reject the null hypothesis and cannot accept the alternative. In the former case, the evidence supports the claim; in the latter. It is insufficient to support the claim. A point estimate represents a “best guess” at a population parameter. A confidence interval gives a range of values to which we can append a probability statement as to whether the population parameter is included. Based on a sample mean, we can determine the 95% and 99% confidence interval or the range of values for the population mean ().

A randomly selected sample and the resultant calculation of the sample mean, compared with the population mean, can tell us the exact probability that the sample mean differs from the population mean. If we do not wish to define a critical region, it is possible to compute an exact P value, which indicates the probability of the chance occurrence of this or a larger value of the test statistic when the null hypothesis is true. An exact probability can be calculated for Z and t scores. If the P value is smaller than , we will reject the null hypothesis. If it is larger than , we will fail to reject the null hypothesis.

It is possible to commit one of two types of errors in executing these tests. In rejecting a true null hypothesis, we make a type I error ( error); in failing to reject a false null hypothesis, we make a type II error ( error). 1.Write the null and alternative hypotheses. 2.Choose a significance level, a (usually.05 or.01). 3.Compute the test statistic. 4.Determine the critical region. 5.Reject the null hypothesis if the test statistic, t, falls in the critical region (tail).

Fail to reject the null hypothesis if the test statistic falls in the fail-to-reject region. 6.Calculate exact P values (optional – this can be done only by computer). 7.Express the results in P values (P ). 8.Calculate confidence intervals, 95% or 99%. 9.State the appropriate conclusions.

You now should be capable of comprehensively solving a two-sample hypothesis problem. It is first necessary to determine whether the samples are independent or paired and whether the test is one- or two-tailed. Next choose a significance level and calculate the t statistic. Then determine whether your results are significant, and identify the resultant P values. Finally, calculate and interpret the confidence intervals.

Remember that two-sample confidence intervals represent the difference between the means. You should also be prepared to answer the statistician’s toughest and most common heard question: “How large a sample do I need?” The answer is easy and difficult – easy in employing a simple equation, difficult in getting the right input into the equation. 1.Indicate the circumstances that call for ANOVA rather than a t test.

2.Set up an ANOVA table that partitions the total sum of squares into between- group and within-group sums of squares. 3.Compute the F ratio and its appropriate degrees of freedom. 4.List the two assumptions that need to be made to perform an ANOVA. 5.Indicate the type of hypothesis that can be tested with ANOVA.

6.Find the critical region for an F-ratio test. 7.Indicate the reason for performing a post hoc analysis. 8.Apply Turkey’s multiple comparison procedure. 9.Describe an example of randomized block design.

A.Three Assumptions. 1.The observations are independent; that is, the value of one observation is not correlated with the value of another. 2.The observations on each group are normally distributed. 3.The variance of each group is equal to that of any other group; that is, the variances of the various groups are homogeneous, or we have homogeneity of variances.

B.ANOVA is a robust technique, insensitive to departures from normality and homogeneity, particularly if the sample sizes are large and nearly equal for each group. A.A significant F ratio tells us that there are differences between at least one pair of means. B.The purpose of a post hoc analysis is to find out exactly where those differences are. C.Turkey’s HSD is used to test the hypothesis that all possible pairs of means are equal. 1.to perform this multiple comparison test, select an overall significance level, which denotes the probability that one or more of the null hypotheses is false. 2.Those pairs whose differences exceed the HSD are considered to be significantly different. 3.formula.

The analysis of variance is so named because the ANOVA test procedure is based in a comparison of the estimate of the between-group variance with the estimate of the with-in group variance. These two estimates of o2 are obtained by partitioning the overall variance. An F statistic is used to determine the critical region for the test. If the computed F ratio falls in the critical region, we conclude that at least one of the means is significantly different from the others. To determine which specific pairs of means are significant, we utilize a multiple comparison test, not multiple t tests.

To test the hypothesis, we must assume independence of observations, normality of each group, and homogeneous variances. An important interpretation of ANOVA is that it tests whether there is a treatment effect, where the treatment is drug dosage, smoking exposure, or some other factor. In this chapter, we focused on the one-way classification of variance.

To be able to account for the many possible sources of variation in a particular experiment, you may wish to perform a two -way or three-way ANOVA. A.Qualitative data – data for which individual quantitative measurements are not available but that relate to the presence or absence of some characteristic. B.p the estimate of the true proportion, , of individuals who possess a certain characteristic. C.To best understand the difference between the distribution of binomial events (x) and the distribution of binomial proportion (p). 1.Compare these distributions with those in the approximate analogous quantitative situation.

2.The x’s of a binomial distribution with a mean and a standard error. A.In order to compare proportions from two different samples we must:. 1.assume that the proportions are equal, that is, in estimating. 2.learn if, the proportion with the given characteristic in one sample differs significantly from, the proportion with the same characteristic in the second sample. B.Three thing that must be know to determine if the proportions are significantly different. 1.the distribution of the differences -.

2.the mean - . 3.the standard error of this distribution – (SE). C.Statisticians have shown that follows a nearly normal distribution. A.For a given phenomenon, chi-square tests compare the observed frequencies with the expected frequencies. B.Expected frequency is calculated from some hypothesis. C.In comparing the observed frequency with the expected frequency, you need to determine whether the deviations are significant. D.To avoid the problem of deviations being equal, one option is to square each deviation.

This may also generate problems because the same value may be obtained for equal deviations regardless of magnitude. E.The best way to overcome this problem is to look at the proportional squared deviations. Qualitative data may be analyzed by use of a chi-square test. The object of the test is to determine whether the difference between observed frequencies and those expected from a hypothesis are statistically significant. The test is performed by comparing a computed test statistic with a one-tailed critical value found in a chi-square table. The critical value depends on the selected o- and on the number of degrees of freedom, the latter reflecting the number of independent differences computed from the data.

The test statistic is computed as the sum of the ratios of squared differences to expected values. As in other tests of significance, if the computed test statistic exceeds the critical value, the null hypothesis is rejected. A.Two most common methods used to describe relationships between two quantitative variables. 1.Linear correlation – measures the strength of a bivariate association. 2.Linear regression – prediction equation that estimates the value of y for any given x. B.Correlation coefficient – a measure of the strength of the relationship between the two variables, provided the relationship is linear. C.Independent (or input) variable (x) – outcome is independent of the other variable.

D.Dependent (or outcome) variable (y) – its response is dependent on the other variable. A.Correlation coefficient (r) – a measure of the strength of the linear association between two variables, x and y.

A.Scatter diagram indicates that the data do not fit a linear model then the relationship may be curvilinear. B.One possible solution would be fitting a linear regression to a transformed set of variables such as. If the error terms are smaller using, then we have gained some in keeping a simple straight-line model to explain relationship.

C.The object is to obtain a better linear relationship than that given by the original data. D.There is no precise way to determine the best transformation to use. A.A definition for is = 1 – (SSE/SST), where SST represents the total sum of squares and SSE is the sum of squares, representing the overall variability of the response variable y. B.Characteristics about. 1.It is always between 0 and 1. At the extreme value of 0, the regression line is horizontal; that is = 0. 2.The closer is to 1, the “better” the regression line is in the sense that the residual sum of squares is much smaller than the total sum of squares.

For this reason, is usually reported as an overall “figure of merit” for regressional analysis. C.We can interpret as the fraction of the total variation in y (SST) that is accounted for by the regression relationship between y and x.

A.Though it measures how closely the two variables approximate a straight line, it does not validly measure the strength of a nonlinear relationship. B.The reliability of the correlation may also be questionable when n is small (fewer than about 50 pairs of observations). C.It is always useful to plot a scattergram to see if there are any outliners – observations that clearly appear to be out of range of the other observations. D.Outliners have.

1.a marked effect on the correlation coefficient. 2.Often suggest erroneous data. 3.Are likely to give misleading results. E. Most important drawback – a high (statistically significant) correlation can easily be taken to imply a cause-and-effect relationship. D.The regression line always passes through the means of x and y, that is through and therefore makes it simple to superimpose it on the scattergram.

E.A characteristic about a least-squares regression is that. 1.the sum of the deviations about the line is equal to zero. 2.the sum of the scattered deviations is a minimum, that is, there is no other line for which it could be less.

3.it shows the sum of the residuals above the regression line equals the sum of those below the line; that is, or actually.014, which is a tiny round-off error. Correlation analysis and regression analysis have different purposes.

The former is used to determine whether a relationship exists between two variables and how strong the relationship is. The latter is used to determine the equation that describes the relationship and to predict the value of y for a given x. An aid to visualizing these concepts is the scatter diagram. A correlation coefficient (r) can take on values from –1 to +1. The closer r approaches –1 or +1, the stronger the linear relationship. It is important to keep in mind that a high correlation merely indicates a strong association between the variables; it does not imply a cause-effect relationship.

A correlation coefficient is valid only where a linear relationship exists between the variables. After computing the correlation coefficient r and the regression coefficient b, we are obligated to test their significance or set up confidence limits that encompass the population values they estimate. A.Parametric methods – statistical techniques enabling us to determine if there is a significant difference between to sample means with underlying assumptions of normality, homogeneity of variances, and linearity.

B.Nonparametric methods. 1.developed for conditions in which assumptions necessary for using parametric methods cannot be made. 2.sometimes called distribution-free method because it is not necessary to assume that the observations are normally distributed. 3.appropriate for dealing with data that are measured on a nominal or ordinal scale and whose distribution is unknown.

A.Nonparametric advantages. 1.They do not have restrictive assumptions such as normality of the observations.

In practice, data are often nonormal or the sample size is not large enough to gain the benefit of the central limit theorem. At most, the distribution should be somewhat symmetrical.

2.Computations can be performed speedily and easily – a prime advantage when quick preliminary indication of results is needed. 3.They are well suited to experiments of surveys that yield outcomes that are difficult to quantify.

In such cases, the parametric methods, although statistically more powerful, may yield less reliable results than the nonparametric methods, which tend to be less sensitive to the errors inherent in ordinal measures. B.Nonparametric disadvantages.

1.They are less efficient (i.e. They require a larger sample size to reject a false hypothesis) than comparable parametric tests. 2.Hypotheses tested with nonparametric methods are less specific than those tested comparably with parametric methods.

3.They do not take advantage of all the special characteristics of a distribution. Consequently, these methods do not fully utilize the information known about the distribution. C.Should be viewed as complementary statistical methods rather than attractive alternatives.

An inherent characteristic is that they deal with ranks rather than values of observations. A.Counterpart to the paired t test for matched observations, we assume that we have a series of pairs of dependent observations. B.We wish tot test the hypothesis that the median of the first sample equals the median of the second – that is, that there is no tendency for the differences between the outcomes before and after some condition to favor either the before or the after condition. C.Procedure is to obtain the differences between individual pairs of observations. Pairs yielding a difference of zero are eliminated from the computation; the sample size is reduced accordingly. A.One of the simplest of statistical test, it focuses on the median rather than the mean as a measure of central tendency.

B.Only assumption made in performing the test is that the variables come from a continuous distribution. C.It is called the sign test because we use pluses and minuses as the new data in performing the calculations. D.We illustrate its use with a single sample and a paired sample. E.It is useful when we are not able to use the t test because the assumption of normality has been violated. A.The sign test is also suitable for experiments with paired data such as before and after, or treatment and control. B.Only one assumption must be satisfied – the different pairs must be independent; that is, only the direction of change in each pair is recorded as a plus or minus sign. C.An equal number of pluses and minuses if there is no treatment effect.

D.The tested by the paired samples sing test is that the median of the observations listed first is the same as that of the observations listed second in each pair. These are nonparametric methods that correspond to parametric methods such as the t test, paired t test, and correlation coefficient. The primary advantage of these methods is that they do not involve restrictive assumptions such as normality and homogeneity of variance. Their major disadvantage is that they are less efficient than the corresponding parametric methods of five methods described here – the Wilcoxin singed-rank test, Kruskal-Wallis test, the Mann-Whitney U test, the sign test, the Spearman rank-order correlation coefficient, and Fisher’s exact test. These are the nonparametric methods used most frequently in the health sciences. A.Fetal death is defined as the delivery of a fetus that shows no evidence of life (no heart action, breathing, or movement of voluntary muscles) if the 20th week of gestation has been completed or if the period of gestation was unstated. B.Fetal death ration is defined as the number of fetal deaths in a calendar year divided by the number of live births in that year, with the quotient multiplied by 1000.

Note that this ratio only applies to fetal deaths that occur in the second half of pregnancy. No reporting is required for early miscarriages. A.Applies a standard population distribution to the death rates of two comparison groups. B.Sum of the expected deaths for the two groups is then used to compute the adjusted death rate (dividing the expected deaths by the total of the standard population). C.Essential to have bot the age-specific death rates for the populations being adjusted and the distribution of the standard population by age (or by whatever other factor is being adjusted). D.U.S.

Standard Million – a population of 1 million persons that identically follows the age distribution for the entire United States. A.Utilized when age-specific death rates are not available for the populations being adjusted but the age-specific death rates for the standard population are known. B.We compute a Standard Mortality Ration (SMR). (i.e., observed deaths divided by expected deaths) and use it as a standardizing factor to adjust the crude death rates of given populations. C.The SMR increases or decreases a crude rate in relation to the excess of deficit of the group’s composition as compared to the standard population. Public health decision making is a quantitative matter.

The health of a population is assessed by use of its vital statistics and demographic data. Information about demographic characteristics is obtainable from census data, registration of vital events, and morbidity surveys.

Such data are used to calculate vital rates and other statistics that are used to indicate the magnitude of heath problems. Vital rates, ratios, and proportions are classified into measures of mortality (death), fertility (birth), and morbidity (illness). These measures may be crude or specific, the latter referring to calculations for subgroups selected for a common characteristic such as age, sex, race, or disease experience. Comparisons of vital rates, ratios, and proportions among different populations should be made with care and be validated by use if specific or adjusted measures. The choice of the adjustment method depends on the type of data available. Life tables provide excellent means for measuring mortality and longevity.

The current life table shows the effects of age-specific death rates on a group. From this table, measures of mortality and life expectation can be computed. Whereas the current life table presents a hypothetical picture of the effects of present mortality rates, the cohort life table is an actual historical record of the mortality of a group followed through life.

The follow-up life table considers the experiences of persons from event to event during the period of a study. STEP 8: DESIGN THE QUESTIONNAIRE. A.Key principles for questionnaire. 1.easy for respondents to read, understand, and answer. 2.motivate respondents to answer. 3.designed for efficient data processing.

4.have a well-designed, professional appearance. 5.designed to minimize missing data.

STEP 9: PRETEST THE QUESTIONNAIRE – will identify questions that respondents tend to misinterpret, omit, or answer inappropriately. It should be don on a handful of individuals similar to, but not included in, the target population and should utilize the same methodology that will be used in the actual survey. STEP 14: ANALYZE THE DATA. A.Preliminary analysis. 1.review distribution of various variables. 2.provide an item analysis for the variables of specific interest.

3.assess the amount of missing data. STEP 15: REPORT THE FINDINGS. A.Report should include. 1.background information that provides a rationale for the study. 2.indicate the specific objectives that the survey seeks to accomplish. 3.a “methods” section should describe the. a.target population.

b.test instruments. c.sampling design. 4.a “results” section should discuss the findings and possible future implications. OBSERVER BIAS –. increases the likelihood that characteristics will be recorded more for cases than for controls. RESPONSE BIAS –.

Owning to their own health, educational background, and many other reasons, persons who choose voluntarily to participate in research studies are known to differ from those who decline to do so. DROPOUT BIAS –. the mirror image of response bias. Persons who dropout are likely to differ from those who continue. MEMORY BIAS (subjective bias) –. memory for recent events is much more accurate than that for long-ago events. PARTICIPANT BIAS –.

derives from the participant’s knowledge of being a member of the experimental or control group and his or her perception of the research objectives. LEAD-TIME BIAS –. the question – does early detection of chronic disease actually result in improved survival rates, or does it merely provide a longer period between first detection and death?.

KEYS TO SYSTEMATIC APPROACH. A.Research objectives.

1.Does the research report clearly state its objectives?. 2.Do the conclusions address the same objectives. B.Study design.

1.What type of study was it? Was sample election random and appropriate to the study design?. 2.Were cases and controls comparable and drawn from the same reference group?. C.Data collection. 1.Were criteria for diagnosis precisely defined?. 2.Were end points (or outcome criteria) clearly stated?.

3.Were research instruments (whether mechanical or electronic devices, or printed questionnaires) standardized?. 4.Can the study be independently replicated?. KEYS TO SYSTEMATIC APPROACH. D.Discussion of results. 1.Are results presented clearly and quantitatively?. 2.Do tables and figures agree with the text?. 3.Are various tables consistent with one another?.

E.Data analysis. 1.Does the report address the statistical significance of its results?. 2.If not, are you able to draw a reasonable inference of significance (or nonsignificance) from the data as presented?. 3.Were the statistical tests appropriate to the data?. 4.Does the report discuss alternative explanations for what might be spurious statistical significance?.

F.Conclusions. 1.Are the finding justified by the data?. 2.Do the findings relate appropriately to the research objectives set forth? Two fundamental research tools – the health survey and the research report – are inseparable parts of the same process: that of aiding scientists, managers, and public officials in their decision making. Health surveys need careful planning; a systematic, stepwise procedure is the best means of avoiding error in their use. Research reports are read by nearly everyone in the health sciences.

College

It is important to develop a critical eye in order to distinguish between ordinary reports and those of quality. Especially when dealing with human populations, the research is susceptible to many sources of bias. An understanding of the origins of bias, and of the means to avoid bias in whatever form, helps you assess the quality of any research report.