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Friday, December 7, 2012

Sample Size Justification



Students typically struggle with sample size justification, in part because there are 2 types.  One type is based on the population and the second based on a power analysis.  Sample size based on a population is generally not used in dissertations.  It not used in dissertations because the requirement would too exhaustive to stratify the population in terms of geography and the size requirement would be too great. 

The sample size based on a power analysis is used in dissertation and is a required section in your method chapter (and is needed for IRB or URR).  A power analysis essentially says that the researcher has a 80% chance of finding differences or relationships among the variables if they actually do exist.  Sample size based on a power analysis uses the type of statistical analysis you are using such as an ANCOVA, multiple regression, Pearson correlation, etc), the alpha (typically .05), and a small, medium or large effect size.  Effect size has both theoretical and practical considerations.  At a theoretical level, the researcher needs to review other studies that examined the same type of constructs or the same instruments, then see what effect size was found.  If the effect size is not presented, it can be calculated from the means and standard deviations, one-way ANOVAs, frequency counts, correlations, mean gain scores, unstandardized regression coefficients, full sample standard deviations, chi-squares, phi-coefficients, cell frequencies, t-tests, or proportions.  The practical aspect of justifying the sample size is money and time needed to collect data.  For example, if you’re running a multiple regression with 3 predictor variables AND the effect size is small, you’ll need an N=547!   This is in comparison to a regression at a medium effect size with a desired N=76 or a large effect size with an N=34.   Sample size can be calculated by using a free G*Power analysis program or you can purchase a sample size write-up with references from our website by signing on for our Basic Membership for $29.00. 

Monday, November 12, 2012

Multiple Regression Effect Size



Cohen's ƒ2 is a measure of effect size used for a multiple regression.  Effect size measures for ƒ2 are 0.02, 0.15, and 0.35, indicating small, medium, and large, respectively.

Monday, April 18, 2011

Sample Size in Plain English

As a dissertation consultant for over 20 years, I consistently see confusion when it comes to answering a simple question—how many participants do in need? The confusion is reasonable because most programs do not even offer a class in sample size and leave it to the graduate student to figure it out on their own. This post will clear it up once and for all.

Two Types of Sample Sizes

There are two types of sample sizes to determine: one sample size determination is used to find the number to have enough participants to be representative of a population, and the other sample size determination is to achieve statistical power. Let’s talk about these two types.

Sample Size for a Populationwhat researchers and organizations need

This type of sample size determination is an effort to get a representation of the population, such as you see would see in election polling. To determine this sample size, you need to know the population size, confidence interval and confidence level (typically 95%). This is almost never the type of sample size that dissertation students need because you don’t have unlimited time, money, energy to get such as large sample. If you are a funded researcher or organization, and desire this type of sample size, you can view our free calculator at http://www.statisticssolutions.com/products-services/login/free-membership.

Sample Size for Statistical Powerwhat dissertation students need

Statistical power (also called a power analysis and typically set at .80) is the basically the probability of finding statistical differences in your data if in fact they are there. The .80 is saying that you have an 80% chance of finding difference in you data if differences exist. To assess this type of sample size you need to know a few things. First, you need to know what type of statistical analysis you are going to conduct. That is, the sample size calculation for an ANOVA is different than for a correlation or factor analysis. Second, you need to know the effect size, alpha, and desired statistical power. We decided on the conventional .80 power and alpha is usually set at .05 (you’ll recognize the p = .05 in the articles you’ve been reading for several years). Let’s talk about effect sizes and the three sizes they come in: small, medium, and large. Effect size is this context is the ability to detect differences in the data, so, a bit counter intuitively, a large, easily detected effect requires a small sample size to detect it, while a small, difficult to detect effect in the data requires a larger sample size.

How Do You Decide What Effect Size to Choose?

The next question you should be asking yourself is should I choose a small, medium, or large effect size? There are theoretical and practical considerations here. The theoretical answer is to look at the research previously conducted with your types of research questions, variables, and analyses, to see what effect size was found. The problem is that if a small effect size was found (thus requiring a large sample size) it may be impractical for you to find the 300+ participants! On the other hand, just picking a large effect size willy-nilly isn’t quite correct either. What I find is that most dissertation committees go along with are medium effect sizes. You can try to calculate it for free at G-Power http://www.psycho.uni-duesseldorf.de/aap/projects/gpower/ or if you want to find the appropriate sample size with a simple write up and references, you can go to http://www.statisticssolutions.com/products-services/login/basic-membership (while this one is not free—sorry—it’s cheaper than paying us or others $800 to calculate it).

Sample size note. Having said all of this, you should probably recruit as many participants as you can (hence boosting your statistical power).

If you have any sample size questions, or other questions about your methodology or results chapters, feel free to contact us at http://www.statisticssolutions.com . I hope this helps!

Happy Learning,

Statistics Solutions

Thursday, August 6, 2009

Sample Size

The sample size is considered the major part of all statistical analyses. The computation of the appropriate sample size is generally considered the most important and the most difficult step in statistical study. The sample size plays a crucial role in those cases of statistical studies where the statistical studies like sample survey, experiments, observational studies, etc. are involved.

Statistics Solutions is the country's leader in statistical consulting and sample size computation. Contact Statistics Solutions today for a free 30-minute consultation.

The sample size computation must be done appropriately because if the sample size is not appropriate for a particular study, then the inference drawn from the sample will not be true and might cause some serious issues.

Suppose the investigator is working on the study of human or animal related subjects. In this case, he needs to utilize the sample size as this will become an essential issue for the sake of moral reasons. The reason for this is because the sample size that is less than the desired number of sample size will expose the subject who is under study to certain harmful treatments because of a lack of knowledge. On the other hand, if the sample size is more than the desired sample size, there will be a necessary number of subjects who are being exposed to a possible harmful treatment or vice versa.

There are various approaches for computing the sample size. The sample size is determined by specifying the preferred width of the confidence interval. There is also a Bayesian approach for sample size determination, which can be used in cases where the researcher wants to optimize the utility function involving the precision of the estimation or the cost. One of the most popular approaches for sample size is that of power.

The researcher should keep in mind that the sample size requires both the technical skills of a statistics professional and the scientific knowledge of a researcher. Sample size is determinable from a type of cost/benefit analysis. This is because the sample size is related to the cost of an experiment and the sample size is also often directly related to the cost saving during the improvising of the process.

Usually, the study on which the researcher works is often based on a limited budget, so this affects the sample size. An alternative way to get rid of the sample size problem is to make the sample size fixed for certain studies. But this way of keeping the sample size fixed is also not useful when the researcher wants to widen his scope of study in terms of additional suppliers of raw materials, broader demographics of the subjects, etc.

The researcher should keep in mind that there are different types of sample size problems. The sample size problem involving moral issues in an opinion poll is very different from those which involve medical experiments. Also the outcomes of the usage of a sample size more than the desired sample size and the usage of the sample size less than the desired sample size is not the same.

Sample size is generally more crucial in cases that take a huge amount of time while performing data collection.

Wednesday, July 22, 2009

Sample Size

The sample size is considered the major part of all statistical analyses. The computation of the appropriate sample size is generally considered the most important and the most difficult step in statistical study.

Statistics Solutions is the country's leader in statistical consulting and can assist with choosing the appropriate sample size for your research study. Contact Statistics Solutions today for a free 30-minute consultation.

The sample size plays a crucial role in those cases of statistical studies where the statistical studies like sample survey, experiments, observational studies, etc. are involved.
The sample size computation must be done appropriately because if the sample size is not appropriate for a particular study, then the inference drawn from the sample will not be true and might cause some serious issues.

Suppose the investigator is working on the study of human or animal related subjects. In this case, he needs to utilize the sample size as this will become an essential issue for the sake of moral reasons. The reason for this is because the sample size that is less than the desired number of sample size will expose the subject who is under study to certain harmful treatments because of a lack of knowledge. On the other hand, if the sample size is more than the desired sample size, there will be a necessary number of subjects who are being exposed to a possible harmful treatment or vice versa.

There are various approaches for computing the sample size. The sample size is determined by specifying the preferred width of the confidence interval. There is also a Bayesian approach for sample size determination, which can be used in cases where the researcher wants to optimize the utility function involving the precision of the estimation or the cost. One of the most popular approaches for sample size is that of power.

The researcher should keep in mind that the sample size requires both the technical skills of a statistics professional and the scientific knowledge of a researcher. Sample size is determinable from a type of cost/benefit analysis. This is because the sample size is related to the cost of an experiment and the sample size is also often directly related to the cost saving during the improvising of the process.

Usually, the study on which the researcher works is often based on a limited budget, so this affects the sample size. An alternative way to get rid of the sample size problem is to make the sample size fixed for certain studies. But this way of keeping the sample size fixed is also not useful when the researcher wants to widen his scope of study in terms of additional suppliers of raw materials, broader demographics of the subjects, etc.

The researcher should keep in mind that there are different types of sample size problems. The sample size problem involving moral issues in an opinion poll is very different from those which involve medical experiments. Also the outcomes of the usage of a sample size more than the desired sample size and the usage of the sample size less than the desired sample size is not the same.

Sample size is generally more crucial in cases that take a huge amount of time while performing data collection.

Tuesday, July 14, 2009

Sample Size

One of the ordinary objectives of survey research is to collect samples with an appropriate sample size that will be representative of the population. The determination of the sample size involves disregarding sampling error. In quantitative survey design, determining the sample size and dealing with the non response bias are essential.

Statistics Solutions is the country's leader in dissertation statistics consulting and can assist with calculating the sample size for your research project. Contact Statistics Solutions today for a free 30-minute consultation.

According to Peers (1996), sample size is one of the four unified features of a study design that can manipulate the detection of the significant differences, relationships or interactions.
Suppose a researcher has conducted a simple survey on a product. If that survey reveals numerous errors, then it is advisable to check the researcher’s approach in making an appropriate sample size selection.

Most researchers can always benefit from a real life manuscript that describes the common procedure of sample size determination for simple random and systematic random samples. This real life manuscript consists of sample size issues that have been determined in order to solve certain problems.

Krejcie and Morgan’s (1970) developed the formulas for determining the sample size for categorical types of data. These formulas for determining the sample size provide identical sample sizes in cases where the researcher adjusts the tabulated value based on the size of the population, which should be less than or equal to 120.

However, the researcher should always be cautious while using Krejcie and Morgan’s (1970) formulas for the sample size selection. This is because in these formulas, the value of alpha is assumed to be 0.05 and the degree of accuracy is 0.05. Other formulas for sample size selection are also available, but these two formulas for sample size selection are more popular.

Cochran (1977) has given a technique for sample size determination. Cochran (1977) stated that in order to determine the sample size, one has to identify the limits of the errors in the items that have been considered as the most essential items in the survey.

According to Cochran (1977), an estimation of the required sample size is initially made separately for each of the essential items in the survey. After this, the researcher will have a range of sample sizes that include smaller sample sizes for scaled and continuous variables, and larger sample sizes for dichotomous categorical variables. The researcher should make sampling decisions based on the data.

If the range of the sample size is relatively close to the variable of interest, then the researcher can confidently use the largest sample size that would provide him/her the desired result.
A serious component for sample size determination is the estimation of the variance in the significant variables of interest under the study. This is called a serious component in sample size determination because the researcher does not have direct control over the variance and therefore must include the variance estimates.

Cochran (1977) has stated four steps needed to estimate the population variances for sample size determination.

In the first step of estimating the population variances for sample size determination, the researcher obtains the sample in two steps and uses the results of the first step in order to determine the desired number of additional responses to achieve an appropriate sample size based on the variance observed in the data in the first step. In the second step of estimating the population variances for sample size determination, the researcher uses the results of the pilot study. In the third step of estimating the population variances for sample size determination, the data from previous studies of similar populations are used by the researcher. And in the last step of estimating the population variances for sample size determination, the researcher estimates the formation of the population with the help of some logical mathematical results.

Monday, June 29, 2009

Sampling

The general idea behind sampling is the extrapolation from the sample to the population. Sampling must be done in such a manner that the sample that is being drawn from the population should represent the population as a whole. The method of choosing the type of sampling is called design.

Statistics Solutions is the country's leader in statistical consulting and can assist with sampling for your dissertation, thesis or research project. Contact Statistics Solutions today for a free 30-minute consultation.

An appropriate type of sampling involves probability. Sampling that is done with the help of probability methods is called probability sampling. Biased results or estimates are serious problems in sampling, and the researcher can get rid of these with the help of the probability involved in sampling.

In order to conduct sampling by means of probability, it is important to identify the population of interest. The next step is then to create the sampling frame.

There is another kind of sampling that is more flexible and easy to understand to the person not familiar with statistics. This sampling is nothing but simple random sampling. For instance, in order to conduct simple random sampling of 100 units of an item, the researcher chooses one unit at random from the sampling frame, and then the second unit, (and so on) until the 100th unit has been chosen by means of simple random sampling. In each step of this type of sampling, every unit has a similar chance of getting selected.

This type of sampling is generally practically feasible in cases where the population consists of business records. The consequence of this type of sampling would not get affected even when the population is of a larger size.

There are two kinds of errors in sampling, namely random error and systematic error.

Sampling error generally occurs in cases where the researcher gets very few units of a desirable sample from the population. The obvious consequence of this type of sampling error is generally quantified by utilizing the standard error or simply ‘SE.’

In the case of sampling involving probability, the SE can be estimated by using the sample design and the sample data. As the size of the sample in sampling increases, then the SE gets decreased. So, if the population on which the sampling is being carried out is relatively homogeneous, then the SE will be small.

In cases of the sampling involving cluster, there is generally a larger SE. However it should be noted that sampling that involves clusters are generally cost effective.

The non sampling error is generally more serious as the non sampling errors are usually harder to quantify and therefore draw less attention in comparison to sampling errors. This problem of the non sampling error cannot be controlled by increasing the size of the sample. The non sampling error can be categorized into three categories: selection bias, non response bias and response bias.

The first category of non sampling error is selection bias and it is a systematic tendency to exclude one kind of unit from the sample. In cases of sampling that involve probability, this type of bias is generally minimal.

The second category of bias for non sampling errors usually occurs in those cases when the respondents do not respond to sensitive questions. In order to minimize this type of bias of the non sampling error, the response rate should be kept high.

The third category of the bias of the non sampling error occurs in cases when the respondent does not answer the question honestly.

Friday, June 26, 2009

Resampling

Resampling is the method that consists of drawing repeated samples from the original data samples. The method of Resampling is a nonparametric method of statistical inference. In other words, the method of Resampling does not involve the utilization of the generic distribution tables (for example, normal distribution tables) in order to compute approximate p probability values. Resampling involves the selection of randomized cases with replacement from the original data sample in such a manner that each number of the sample drawn has a number of cases that are similar to the original data sample. Due to replacement, the drawn number of samples that are used by the method of Resampling consists of repetitive cases.

Statistics Solutions is the country's leader in statistical consulting and can assist in resampling techniques. Contact Statistics Solutions today for a free 30-minute consultation.

Resampling is also known as Bootstrapping or Monte Carlo Estimation. Resampling generates a unique sampling distribution on the basis of the actual data. The method of Resampling uses experimental methods, rather than analytical methods, to generate the unique sampling distribution. The method of Resampling yields unbiased estimates as the method of Resampling is based on the unbiased samples of all the possible results of the data studied by the researcher.
In order to understand the concept of Resampling, the researcher should understand the terms Bootstrapping and Monte Caro estimation.

The method of bootstrapping, which is equivalent to the method of Resampling, utilizes repeated samples from the original data sample in order to calculate the test statistic.

Monte Carlo estimation, which is also equivalent to the bootstrapping method, is used by the researcher to obtain the Resampling results.

There are certain assumptions that are made by the researcher while conducting the method of Resampling.

This method of Resampling is generally based on nonparametric assumptions.

This method of Resampling generally ignores the parametric assumptions that are about ignoring the nature of the underlying data distribution. Therefore, Resampling is based on nonparametric assumptions.

Sample size assumption of the Resampling: In Resampling, there is no specific sample size requirement. Therefore, the larger the sample, the more reliable the confidence intervals generated by the method of Resampling.

In the method of Resampling, there is an increased danger of over fitting noise in the data. This type of problem can be solved easily by combining the method of Resampling with the process of cross-validation.

In SPSS, the researcher can perform the method of Resampling in the following manner:

After selecting “Nonparametric Tests” from the analyze menu, the researcher clicks on “Two Independent Sample tests,” where the researcher finds an "Exact" button. This button in SPSS is used to conduct the process of Resampling, and allows the researcher to make a choice between the types of significance estimates. One such choice the researcher can make includes the method of "Monte Carlo," which is also a Bootstrapping and Resampling method.

Monday, June 15, 2009

Sample Size Calculation

A sample is a subset of the population. It is through samples that researchers are able to draw specific conclusions regarding the population. Sample size is the size of that sample. Sample size is very important in statistics.

Statistics Solutions can assist in choosing the correct sample size for your dissertation, thesis or research. Contact Statistics Solutions today for a free 30-minute consultation.

Sample size calculation ascertains the correct sample size that would represent the population as a whole. A larger sample size is required while making decisions when more information is needed. As the sample size increases, the information obtained has to be obtained with precision. The degree of precision may be measured in terms of the standard deviation of the mean. The standard deviation is inversely proportional to the square root of the sample size. Sample size calculation is very important in statistical inference and findings.






Determining Sample size:

There are many ways to determine the sample size. Sample size calculation for different statistical testing varies depending on the formulae used. Sample size calculation cannot be performed with only one method or technique.

Sample size calculation is legitimate for most relevant tests, like the t test, z test, f test, etc. To show this in an example, let us take an example of hypothesis testing.



Let us assume that Xi (i=1, 2, …n), where ‘n’ is the independent number of observations drawn from N (µ,σ2).



Here, H0: µ= 12 X'> i.e. there is no significant difference in the mean of the sample drawn from the population.



H1: µ= µ*, for some 'smallest significant difference' μ* >0.



While observing some significant differences, the smallest value can be considered.



To estimate our hypothesis, we must do as follows:

Zα = √n ( 12X-µ) / σ'> . Here, Zα is the value of standard normal distribution at α level of significance.



If the tabulated value of Zα > calculated value of Zα , then we accept H0 at α level of significance. Otherwise we reject it.

In order to determine the value of ‘n,’ we have the following formulae:
n= (Zα σ)2 / ( 12X-µ)'> 2

Sample size calculation depends on the different statistical tests that are to be carried out, because with a change in statistical tests, the results are also dissimilar. Depending on the size of the population or the accuracy of the result, the size of the sample in sample size calculation varies.



Sample size calculation depends on many factors that are more commonly known as qualitative factors. These are important to help calculate any kind of sample size calculation and determination. These factors are the importance of decision, the resource Constraints, the number of variables, the sample sizes used in similar studies, the nature of the research, and the nature of the analysis.



In qualitative research, the sample size in sample size calculation is usually small. Larger samples would be required for conclusive research, such as descriptive surveys. Again, if the data collected is on a large number of variables, then the samples should also be large.
In market research, sample size is used for problem solving research, problem identification research, TV, radio, print advertising, test-market audits, focus groups, etc.

Tuesday, June 9, 2009

Estimation

A statistical inference is basically a process that involves the inference of the data in a statistical manner. There are basically two types of statistical inferences, namely estimation and the test of the hypothesis.

Statistics Solutions can assist with estimation and sample size calculation, click here for a free consultation.

Estimation serves the purpose of determining the true value of the population that is based on the observations or the samples that are collected by sampling. To carry out estimation, the researcher needs to utilize certain statistics.

Estimation involves the use of two popular terms that a researcher should understand. The two terms that are used extensively by the researcher in estimation are the estimator and the estimate. These two terms, called the estimator and the estimate, can be explained with the help of an example. It is assumed in estimation that x1 x2 x3 (and so on) are the collection of the sample from the population having ‘s’ as their parameter. If the T=T(x) is a statistic then E(T(x))= s is the estimation. In this manner, estimation of the statistic is done. In this case of estimation, the estimator is the statistic T, and the estimate is the parameter called ‘s.’
It is important to understand the properties of estimators in estimation theory.

In estimation theory, unbiasedness is the first property that is assumed for an ideal estimator.
The Unbiasedness property of the estimators in estimation theory is basically those types of estimators that give their outcome as zero bias for all the values of the parameter. If the researcher considers the example above, then T in the theory of estimation is said to be unbiased only if its estimate is simply ‘s.’

The second property in estimation theory is that of the consistent estimators that involve the estimation that is consistent in nature. In other words, it can also be said that the consistent estimators in the theory of estimation should have a higher degree of concentration as the value of the random variable increases. In the theory of estimation, the sufficient condition of consistency explains that an estimator is supposed to be consistent only if the estimation of its expected value gives an unbiased estimate and the variance of the estimator is zero. In estimation, these two conditions are fulfilled only when the number of random variables tends to infinity.

There is another property for the ideal estimator in the theory of estimation called efficiency. According to the condition of this property in the theory of estimation, the consistent estimators should be distributed by normal distribution. This condition is introduced in the theory of estimation because there is some possibility that the estimators, which satisfy the sufficient conditions of consistency, may not be an efficient estimator.

The last property of the ideal estimator in the theory of estimation is the property of sufficiency. An estimator in the theory of estimation is said to be sufficient only if the joint conditional distribution function of the sample or the observation falls under the condition where T1 T2 T3 T4 (and so on) are the values under the function of the estimator ‘T.’ Thus, this joint conditional distribution in estimation should be independent of the parameter‘s.’

An estimator in estimation is considered to be the best estimator only if it is a minimum variance unbiased estimator (MVUE). By minimum variance in estimation, we mean that the estimator has less variability as compared to the other estimators.

Thursday, May 21, 2009

Sample Size

Sample Size for a given survey is determined by its measurement objectives. If the survey is being carried out to estimate the changes in indicators over time, or if a survey is being carried out to estimate the differences between the indicators, then the required number for the sample size for each phase of the survey will depend upon five factors.

  • The number of the measurement units in the target population is the first factor on which the approximation of the sample size will depend.
  • The second factor on which the determination of the sample size depends is the initial level of the indicator.
  • The third factor on which the approximation of the sample size depends is the magnitude of the change or comparison group differences that are expected to be reliably measured.
  • The degree of confidence with which it can be expected that a significant change or a significant group difference will not have occurred by chance is the fourth factor on which the sample size depends.
  • The degree of confidence for which it is expected that the significant change will be detected is the fifth factor on which the sample size depends.

For assistance in calculating your dissertation or research project sample size, click here.


The first two factors on which the sample size depends belong to the population characteristics. The last three factors on which the sample size depends are chosen by the evaluator or the survey designer.

Generally, the requirements for each indicator are considered in approximating the sample size needs for any particular survey. However, this task in relation to the sample size is tedious if the number of indicators is large.

This problem can be addressed with the help of the following two approaches:

The first approach is to approximate which of the indicators is expected to be most demanding in terms of the sample size, and to use the sample size required for that indicator. The biggest advantage to this type of approach is that it will automatically assure an adequate sample size for all the indicators to be measured.

The second approach is to identify a small number of indicators that are thought to be more important for any particular evaluation purpose and to limit the sample size computations. This approach assures an adequate sample size for the key indicators.

The drawback of this type of approach is that an adequate number of sample sizes might not be the same for other indicators that are more demanding in terms of sample size requirements.

An appropriate approximation of the sample size is crucial for economical reasons. If the investigator extracts a sample size that is smaller than the desired sample size, then the inference of the sample will not be appropriate or valid. If, on the other hand, the investigator extracts a sample size that is much larger than the desired sample size, then obtaining the inference of the sample would cost the researcher a lot and be tedious as well.

Generally, there is a budget for the study and this also affects the sample size to a great extent. Knowledge about the sample size is crucial in cases when data collection is expensive.

According to Peers (1996), sample size is referred to as one of the unified features of a study design that can influence the effect of significant differences, associations, or interactions.

Tuesday, May 19, 2009

Sample Size

Sample size has been regarded as a study plan which can influence and control the recognition of important distinctions, relationships or dealings. Gathering samples of appropriate sample size representing the population or other collectives is a regular goal for the researcher. In this method, the researcher determines the sample size by ignoring the sampling error. Sample size determination and the relation with the non response bias are essential statistics.

For a free consultation on determining the sample size for your research project or dissertation, click here.

While a researcher conducts a simple survey on any given product, the survey is most likely to uncover a large number of errors. Thus, it is important for the researcher to check his approach by making a suitable sample size selection. The common technique of sample size determination for simple and random samples profits most researchers through real life documents that illustrate the techniques. These documents or real life manuscripts consist of sample size issues that have been determined to solve certain drawbacks.

Cochran (1977) has given a modus operandi for sample size determination. In order to decide upon the sample size, according to Cochran, the researcher has to be able to make out the boundaries of mistakes and errors in the items which have been considered crucial in the survey. Cochran holds that an approximate guess of the required sample size is made disjointedly for each item in the survey. The researcher who is undertaking the task will then use the help of a wide range of sample sizes which includes smaller sample sizes for dichotomous categorical variables. Sampling decisions should be made by the researcher based on the data acquired. The researcher uses the largest sample size if the range of the sample size is close to the variable of interest.

When the researcher does not have direct influence over the variance, he must take in the variance estimates. This is called a serious component in sample size determination. This is because the estimation or approximation of the difference in the important variables of interest under the study is an essential module for sample size determination.

To estimate the population for sample size determination, Cochran followed four steps. In the first step of estimating the population variances and differences for sample size determination, the researcher obtains the samples in two steps. He uses the results of the first step in order to settle on the desired number of extra responses to achieve an appropriate sample size based on the differences studied in the first step. Secondly, while determining the sample size, the researcher estimates the population variances for sample size determination by using the results of the pilot study. Next, the data from prior studies of the population is used by the researcher to determine the sample size. Finally, the researcher makes the required estimation for sample size determination by the formation of the population using the assistance of some logical mathematical results.

Another developed mode of determining the sample size for the categorical type of data is that of Krejcie and Morgan’s (1970). For the determination of sample size, these formulas provide identical sample sizes in instances where the researcher modified the charted or tabulated value established on the size of the population which should be below or equivalent to 120.
The researcher should, however, take care while using these formulas for the sample size selection. While these are the two important and more popular formulas amongst many others in sample size determination, the researcher always has to be cautious with the process of determining the sample size.

Thursday, May 7, 2009

Dissertation Statistics

Dissertation statistics are an essential part of any dissertation, as dissertation statistics provide the proof of what it is the researcher (in this case, the student) is proving. Dissertation statistics are the most important aspect of the dissertation because without these dissertation statistics, the dissertation cannot make a valid and provable point.

Because dissertation statistics are so important, it is essential that these dissertation statistics are acquired accurately and precisely. The first step in acquiring dissertation statistics is to gather information. This gathering of information can be very time consuming as it is an arduous task to get enough information upon which to base a student’s dissertation statistics.

The collection of data for dissertation statistics must be done according to rules, guidelines, assumptions, parameters and formats. For example, the sample size plays a major role in acquiring data for dissertation statistics. The sample size tells the researcher how many people need to be studied in order to draw certain conclusions. There are different sample sizes for every single thing being studied, and thus, the researcher must follow precise sample size rules in order to obtain accurate dissertation statistics. In other words, there are rules governing sample size justification and if these rules are not followed, the dissertation statistics will be invalid and incorrect.

Once the sample size has been decided, the student must gather the proper data for the dissertation statistics. Data can be gathered in many, many ways, but here again, there are exact rules and regulations regarding this gathering of data. Questionnaires, studies, research, interviews, phone interviews and surveys are just some of the ways to gather information. The questions on these surveys, however, must lead to accurate and precise data. Otherwise the dissertation statistics will be invalid and incorrect.

After the data has been gathered properly, it can then be analyzed and interpreted. This is not easy, and improper analysis of the data will lead to inaccurate and invalid dissertation statistics. In the analysis of the data, the researcher (or student) must be able to discern trends and relationships. Here again, there are rules, guidelines, tests, formats and procedures to interpret the data collected, and improper interpretation of the data will skew the dissertation statistics.

Because there is an extensive amount of rules and regulations revolving around dissertation statistics, it is important for a student to get help while working with these statistics. This is especially true for students who are writing their dissertation for the first time. Students who are new to the process of writing the dissertation often make little mistakes that completely nullify their dissertation statistics. This results in much time wasted doing and redoing tests, data collection, data analysis, data interpretation, etc. Further, it is not the student’s fault that they struggle with the dissertation statistics part of their research as oftentimes statistics is not what the student has spent years and year studying. Instead, it is simply something that they need to do in order to finish their dissertation.

Clearly then, it is important for a student to be sure that the dissertation statistics are done properly, accurately, and on-time. With the help of experts trained in statistics, students can ensure that their dissertation statistics are accurate and valid. Because dissertation statistics are such an important part of the dissertation, it is essential that students have statisticians working for them. Without this help, dissertation statistics can be skewed as there are many places where a little mistake can completely invalidate dissertation statistics. With help, students can ensure that they receive their doctoral degree because with accurate dissertation statistics, their dissertation will be accepted and approved.

Wednesday, May 6, 2009

Statistical Consulting Firms

Statistics is a science and it involves the collection, classification and interpretation of data. Because it is a science, it is both very precise and detailed. Statistics can help with a number of things as statistics is a crucial aspect to anything that requires the interpretation of data.

Not everyone who needs to use statistics is well versed in the science of statistics. This, however, is precisely where statistical consulting firms come into play as statistical consulting firms are staffed with experts trained in all things regarding statistics. Thus, statistics consulting firms can help anyone who needs guidance with statistics.

Statistical consulting firms can be invaluable to many people and organizations. Businesses, for example can use statistical consulting firms to study, analyze and interpret data regarding their business products and services. Statistical consulting firms, then, can be an asset to businesses as they can study the business and their objectives and provide much needed feedback. One such feedback comes in the form or market research and statistical consulting firms can do all that needs to be done in terms of market research. Because market research involves statistics, statistical consulting firms can help. Statistical consulting firms can acquire the proper data and information needed for market research. Once this is complete, statistical consulting firms can analyze that data and provide information regarding what products will work, what price these products should be sold for, what the demands for these products are, etc. Thus, statistical consulting firms can provide valuable feedback needed for companies to maximize their research.

Just as statistical consulting firms can provide valuable guidance to businesses, statistical consulting firms can provide valuable guidance to students who need to do any kind of statistics. Oftentimes, statistics are needed when a student researches his/her topic for a dissertation. Much like the business that is not trained in statistics (and therefore needs the help of statistical consulting firms) students are oftentimes not trained in statistics and can benefit from statistical consulting firms. The dissertation is a big undertaking because it involves the gathering of an extensive amount of information and research. Statistical consulting firms can help students in the gathering of information and additionally, statistical consulting firms can help students interpret the results once they have this information and data. Because the dissertation is one of the most important aspects of attaining a doctoral degree, and because statistics plays a major role in that dissertation, statistical consulting firms can be an essential part of any student’s success.

Finally, people and organizations involved in the medical field can also benefit from statistical consulting firms. Because much research and statistics need to be gathered, analyzed and interpreted when it comes to the medical field, statistical consulting firms can play a crucial role in this field. Statistical consulting firms can help, for example, when it comes to analyzing the results of a particular drug. Because these results can be a crucial part of an individual’s life, the statistics gathered and interpreted must be extremely precise. There can be no error when it comes to the medical field, and statistical consulting firms are well aware of this fact.

Clearly, statistical consulting firms can help with any aspect of statistics as statistical consulting firms are staffed with experts that are trained statisticians. The need for statistical consulting firms, then, cannot be overstated as statistical consulting firms provide invaluable services when it comes to the collection, classification, interpretation and analysis of data. When a business, student or organization seeks the help of a statistical consulting firm, they ensure their success as statistical consulting firms provide extremely valuable information, feedback, guidance and assistance.

Wednesday, April 29, 2009

Dissertation Help

Dissertation help provides help to students who face challenges in submitting their dissertation. Dissertation Help is very useful to students in all fields, most of whom are stuck in their dissertation work. Dissertation help provides statistical help in various fields, like business, psychology, medicine, etc.

Let us discuss in detail how Dissertation Help provides statistical guidance in such fields.

In the field of business, Dissertation Help provides immense help in the field of market research. Dissertation Help provides detailed case studies on how market research is carried out on a particular product. Dissertation Help provides information about the methods by which data is to be retrieved. Dissertation Help also provides information on how a questionnaire is to be prepared in order to get valid data. Dissertation Help provides information on the various statistical techniques used during market research. Dissertation Help provides information about the correlation between good data and a valid inference after the analysis. Dissertation Help is generally provided by professors who have attained their doctorates in the statistics field. It is also provided by other statistical consultants.

Dissertation Help guides people on financial modeling. Dissertation Help, in this case, is generally provided by some expert financial analysts. Dissertation Help gives information on how to write a report, which can describe an opinion on a company’s investment potential. Dissertation Help provides information on various financial models, like Discounted Cash Flow model, Binomial Pricing Model, etc.

In the field of medicine, Dissertation Help provides immense help as it gives information on the analytical techniques being used. These analytical techniques include Meta analysis while performing clinical trials on a particular drug. Dissertation Help provides information about various statistical operations on pre-clinical programs, drug production, launch management, contract research, manufacturing management, drug process development, optimization, regulatory and quality management, validation of the drug, package development, line integration of the drug, and manufacturing engineering of the drug. Dissertation Help provides information about the phases that a drug undergoes during clinical trials. Dissertation Help also provides knowledge about survival analysis, which helps in knowing that a fraction of the population would have survived in the past at a certain point of time. Dissertation Help gives a mathematical interpretation of this technique, which says that the probability of a person dying at time ‘T’ is much later than the specified time ‘t.’ Dissertation Help also provides information about the assumptions of survival analysis, which approaches zero as age increases.

In the field of psychology, Dissertation Help provides information about two types of statistical distributions, which are continuous statistical distribution and discrete statistical distribution. Dissertation Help provides information about the major difference between these statistical distributions. Dissertation Help provides information that discrete distribution is designated as probability mass function (pmf) and continuous distribution is designated as probability density function (pdf). Dissertation Help provides information about which samples are countable (for example, the number of bulbs) and fall under discreet distribution, and information about which samples cannot be counted (for example, the intensity of power) and fall under continuous distribution. Dissertation Help provides information about various distributions falling under discreet statistical distribution like Poisson distribution, Binomial distribution, Bernoulli distribution, etc. Dissertation Help provides information about various distributions falling under continuous statistical distribution, like uniform distribution, hyper geometric distribution, etc.

Dissertation Help makes sincere efforts in making student’s work better. But Dissertation Help should not be misinterpreted as a medium by which students do not need to work after submitting their work to Dissertation Help. On the contrary, students should also work hard and make sincere efforts as they receive Dissertation Help.