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.

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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.

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.

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.

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.

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.

Sample Size

Sample size plays a very crucial role in conducting statistical tests and analyses in various fields, such as business, medicine, nursing, psychology, etc. Sample size is correlated to making an appropriate decision or inference about the product from which the sample has been drawn. In other words, if the sample size is too small, then a systematically conducted study can fail to detect the important effects, associations or correlations. In the same manner, if the sample size is too large, then the study would be complex and tedious. Thus, an optimum sample size is the most important part in any statistical study. This document, therefore, will detail the role played by sample size in business, medicine, nursing, and psychology fields.

In the field of psychology, if one has to compare the difference of means of two populations with a particular sample size, or has to test for a single mean with some sample size, or has to compare the means from two different populations with some sample size using the t-test, then the sample size should be less than 30. If one has to compare the differences of means of two populations with some sample size, or has to test for a single mean with some sample size, or has to compare the means from two different populations with some sample size using the Z- test, then the sample size should be greater than 30. If one has to perform regression analysis in order to predict the attitude of teenagers, generally the sample size should be 10 for each independent variable, defined during that analysis. This means that if there are two independent variables in that study, then the sample size should be at least 20. If, in this study, the data is of categorical type, then the sample size should be more in order to perform the same analysis. In the case of focus group studies, the sample size should be around two from the population and it should have 6-15 groups.

In the field of business, for example in the case of market research studies, the sample size varies from study to study. If one is performing a problem- identification market research study, then the minimum sample size should be around 500 from a population of the size of 1000-2500. If one is performing a problem-solving market research study, then the sample size should be around 200 from a population of the size of 300-500. If one is performing a TV / radio advertising market research study, then the minimum sample size should be around 150, from a population of the size of 200-300. If one wants to test market audits, then the sample size of the stores should be around 10 from a population of 20 stores.

In the field of medicine / nursing, getting a correct sample size is very important. An example can clearly show just how important sample size is in research. In this example, if a researcher wants to know whether or not there is any difference in the curability rate of drug A and drug B, a sample size of 150 patients must be applied to test the two drugs. If in this example there is no difference observed between the two drugs, then a sample size of 150 patients could be the problem. This would be known as a Type II error and this kind of error is very dangerous.
Thus, a larger sample size will avoid this serious error. Sample size, then, plays a crucial role as it is used to avoid Type II errors.

Generally, one should always keep in mind that if the population size is smaller, then one should have a bigger sample size and if the population is large, then one should have a smaller sample size.

For more information on calculating sample size, click here.

Sample Size Justification

Sample size justification deals with the justification of the sample size. Sample size justification is very important because it affects the results of the research. If, for example, the sample size is too small, then even if everything else has been carried out perfectly, the inferences drawn will not be valid or perfect. On the other hand, sample size justification is also important in the case of a sample size being too large. In this case, if the sample size is too large, the results can also provide a false statistical inference. Therefore, sample size justification is important in order to make a valid inference about the product being tested. Sample size justification is important in the field of psychology, business and medicine and nursing.

In the field of psychology, sample size justification is important if one is trying to compute the difference of means from two populations using a t-test. Sample size justification implies that in this case, the sample size should be less than 30. Sample size justification is also important if one is trying to compute the difference of means from two populations using the z test. Sample size justification implies that in this case, the sample size should be more than 30. Sample size justification is also important in the case of regression analysis. Sample size justification is important if, for example, one is trying to predict the behavior of a child in his teenage years given some other dependent variables. Sample size justification implies that in regression analysis, there should be at least 10 samples for each independent variable.

In the field of business, sample size justification plays a crucial role in the case of market research study. Sample size justification is important in this case, when one is performing a problem of identification in market research study. Sample size justification implies that the minimum sample size should be around 500 from a population of the size of 1000-2500. Sample size justification is also important when one is performing problem solving in market research study. Sample size justification implies that the sample size should be around 200 from a population of the size of 300-500. For example, sample size justification is important, let’s say, if one is performing TV / radio advertising market research study. Sample size justification implies that the minimum sample size should be around 150 from a population of the size of 200-300. Sample size justification is equally important if one wants to test market audits. Sample size justification implies that the sample size of the stores should be around 10 from a population of 20 stores.

In the field of medicine / nursing, sample size justification is important when a researcher wants the curability effect of two drugs, say, drug A and drug B. Sample size justification implies that this test should be carried out on more than 150 patients, otherwise this may result in a Type II error. Thus, sample size justification can prevent a researcher from getting a Type II error, which is the most serious error in the field. If a researcher goes against the sample size justification in this case, i.e. by not conducting the test on 150 patients, then the result will say that there is no difference in drug A and drug B—and this is a serious error called Type II error. Thus, the researcher must deal properly with sample size justification.

It is important for a researcher to always keep sample size justification in mind. The researcher must always be aware of sample size justification, otherwise the results of their research will not be valid.

Sample Size Calculation

Sample size calculation plays a very important role in statistics analysis. Sample size calculation refers to how much data we need for particular research to make a correct decision. If we have more data, then our decision will be more accurate, and there will be less error of the parameter estimate. Some of the factors that affect the sample size calculation are the type of data, including the Power of the sample size, the Technique used for analysis, the Marginal error, the Level of Significance, the Standard Deviation, the Missing value, etc. First of all, we should consider the type of data level and the measurement of a specific sample size.

There are four types of data level:

(1) nominal data

(2) ordinal data

(3) interval data

(4) ratio data

Nominal data is simply categorical data. Ordinal data is the data when ranks are assigned to the data. Interval data is the data when an interval is given between the cases. Ratio data is metric or continuous data, on which we can perform all analysis which we cannot perform on nominal, ordinal and interval data. In determining the sample size calculation, we should consider the level of significance or the level of alpha. For instance, two tailed test alpha level is 5%, which is equal to 1.96. When the sample size calculation is done, we should consider the marginal error as well. Marginal error is simply the error that a researcher is willing to accept for a particular sample size. For example, in continuous data t value of alpha for 5% is 1.96 and SD in population is 1.167, and marginal error is .21. Then we can calculate the sample size by using the following formula:

N=

N= sample size

t= level of alpha

S= standard deviation

D= marginal error

When the data is categorical, then we can use the probability of method instead of the standard deviation. For example, when we have two categories for samples, then we can use .5 probability of the first category and .5 probability for the second category. We can use the following formula in the case of categorical data:

N=

N= sample size

t= level of alpha

P= probability of event happening

Q= probability of second event happening

D= marginal error

These are some basic formulas for sample size calculation. But sample size calculation differs from technique to technique. For example, when we are comparing the means of two populations, if the sample size is less than 30, then we will use the t-test. If the sample size is greater than 30, then we will use the Z-test for comparing the two populations’ sample means. As a rule of thumb, in regression analysis, there should be 10 cases for each independent variable. For example, if we have two independent variables, then the minimum sample size should be 20 in order to reach a correct decision about the regression parameter. If the sample size is less than the given criteria, then the decision will not be correct. When data are categorical and the level of alpha decreases, then the sample size should be bigger for the same technique. If the population size is smaller, then we need a bigger sample size, and if the population is large, then we need a smaller sample size as compared to the small population. Sample size will differ with different margin error. Missing value also affects the sample size. When data has missing value, we need bigger sample sizes as compared to the non-missing value sample. In an analysis of variance test, we need to determine how many covariates we can use for a particular treatment variable. We can use sample size to determine the covariate. For example, with a sample size of 50, and a number of groups in 3 treatment factor, we can use only 3 covariates in an analysis of variance study. Variance also affects the sample size. When variance is more for the variable taken into study, then the sample size needs to be bigger to reach a correct decision about the parameter estimate. When we do not know the population standard deviation, then we can use the range to know the standard deviation. Sample size also depends on the power. With more power, we need a bigger sample size.

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Statistical Power

One can interpret or conjecture about data statistically, with the help of statistical inference. Thus, statistical inference is to infer about something statistically. Statistical inference basically involves Estimation and Testing of Hypothesis.

Since our discussion involves Statistical Power, we shall discuss Testing of Hypothesis. Hypothesis Testing consists of null and alternative hypothesis, typically denoted as H₀ & H₁ respectively. Null hypothesis is a statement in which no difference or effect is expected. Thus, if H₀ is rejected, then one can say that there is no significant difference in the tested data. H₁ is the complement of H₀, i.e.; if H₁ is accepted, then one can say that there is some significant difference in the tested data.

The acceptance or rejection of the null and alternative hypothesis results in errors. There are basically two types of errors: Type I and Type II. Type I error is the event of rejecting a null hypothesis when a null hypothesis is true. The probability of a type I error is called the significance level. Type II error is when a researcher fails to reject a null hypothesis when a null hypothesis is false. In practical study, Type II is a more serious error than Type I, especially in Pharmaceutical research (involving drugs).

Due to the Type II error, Statistical Power has been created. Statistical Power is the probability (1-β) of rejecting null hypothesis when it is false, and this null hypothesis should be rejected in order to avoid Type II error. Therefore, one needs to keep the Statistical Power correspondingly high, as the higher our Statistical Power, the fewer Type II errors we can expect.

The analysis on Statistical Power, i.e. Power Analysis, can be done either upon the prior-collected-data or the post-collected-data.

Statistical Power usually depends upon:

-The desired power level

-The desired level of significance in the test

-The strength of association or the effect size in the population

-The sensitivity of the data

· -The size of the sample

In Statistical Power, the power level specifies the level or the chance of not making a Type II error. Usually, the researcher takes the power level as 0.80. In other words, the researcher has an 80% chance of not making a Type II error.

In Statistical Power, the level of significance is the minimum possible chance that a sample is likely to get associated with the population. Suppose the level of significance is 5%. This means that the sample drawn from the population should have at least 5% of the characteristics of the population from where it has been drawn.

In Statistical Power, the effect size or the strength of association is basically the strength of the relation between the two variables. Thus, the greater the effect size, the greater its Statistical Power. Thus, there are more chances that the test is valid. Therefore, a greater effect size emphasizes a greater Statistical Power.

In Statistical Power, the sensitivity is referred to the number of true positives out of the total of true positives and false negatives. In layman’s language, sensitivity recognizes the truly correct data. This means that a high sensitivity will yield good data and therefore a high Statistical Power, which means data having less number of Type II errors. Therefore, the sensitivity of data is a very important factor for Statistical Power.

In Statistical Power, the determination of the sample size of the prior data is a very crucial factor. It is a sample size which keeps the value of Statistical Power high. This means that the larger our sample size, the greater the Statistical Power.

Sample Size Calculation

Sample size calculations are required for a majority of quantitative studies involving surveys and statistics. It is a necessity to consider sample size calculations in order to ensure that analyses have adequate statistical power and that the results obtained are accurate and useful. If samples are too large in size, researchers could waste time, money and resources. On the other hand, if samples are too small, the results obtained may not be accurate or reliable. A sample size calculation is not necessarily complicated or unnerving, though it does tend to strike several statisticians as either a minor technicality or a huge undertaking. There is no mystery involved in estimating the sample size. It is a relatively straightforward task for the equipped and experienced researcher. However, considering it’s tremendous importance in the overall project setting, it may be best left to an expert statistician.

One of the benefits of performing a sample size calculation is that it helps in setting a project on the right foot. A proper sample size ensures that analyses conducted will produce reliable and usable results. Before calculating the sample size, it is necessary to develop a thorough knowledge of the requirements of the project and the nature of the statistical analysis to be conducted. This feeds into the method by which the sample size will be calculated. Nowadays, there is a plethora of online sample size calculators that can simply calculate your sample size. These may seem useful but are more like a band-aid. It is recommended that unless one is an expert, one does not attempt such calculation short cuts without a thorough understanding of the underlying methodologies.

There isn’t a single standard sample size equation. The best equation is one that addresses the needs of the project analysis, types of variables and intended outcomes. For instance, two different sample size equations are available for use in continuous variable and categorical data.

The first and foremost thing that must be kept in mind is that a sample size is essentially a function of effect, significance level and power. In other words, it signifies that effect, significance and power are the three levels on which the sample size is going to depend. If any one of the three measures is changed, then sample size will also change as a result.

Sample size calculation largely relies on the statistical tests that are intended to be conducted. This is because there will be differences in the effect depending on the statistical test(s) being conducted.

In addition to the statistical method in question, there are several other factors on which the sample size calculation depends. These factors are important to consider for any kind of sample size calculation.

· Type of data

· The requisite level of significance

· The desired power

· The standard deviation of continuous outcome variables

· The effect size

· The one and two sided tests of significance

· Other various aspects of design of the study

In case of sample size calculation where continuous data are involved, categorical formulas for sample size calculation must be used. The following formula will be applied to such requirements.

n_o = ( t)² * (s)²

^{_____________}

(d)²

Where t = value of selected alpha level

n_o = required return sample size

s= estimate of standard deviation in the population

d = acceptable margin for error in mean

Where the data or variable(s) are categorical, sample size calculation will differ in terms of approach. The following sample size calculation formula will be applied in that case.

n_o = ( t)² * (p) (q)

^{__________________}

(d)²

Where t = value of selected alpha level

(p) (q) = value of selected alpha level

s = estimate of standard deviation in the population

d = acceptable margin for error in mean

Click here for more assistance with Sample Size.

Sample Size Calculation for One-Way ANOVAs in Dissertations and Theses

I'm sure there are some of you out there looking for the minimum sample size necessary to find the analyses of variance (ANOVAs) in your dissertation or thesis significant. Sample size calculation for ANOVAs can be complicated if it's a factorial ANOVA or mixed ANOVA, so we'll start slow and focus on an ANOVA with only one independent variable.

What is the Power used in calculating the sample size of the ANOVA being used in my dissertation or thesis?

For the purposes of this example, we are going to looking for the minimum sample size to give us a power of 0.80. To read more about this, click here. This is going to give us a 20% probability of falsely accepting the null hypothesis, or a 20% probability that we missed something. We're okay with this, since missing something is typically less severe than finding something that isn't really there. Click here for help with determining the appropriate power for your dissertation or thesis.

What is the level of significance used in calculating the sample size of the ANOVA being used in my dissertation or thesis?

This is the probability of falsely rejecting the null hypothesis. The statistical significance for the purposes of calculating the sample size for the ANOVA is going to be 0.05. This means we are looking for less than a 5% probability that our results are due to chance. Get help with determining the ANOVA level of significance for the sample size calculation in your dissertation or thesis.

What is the effect size used in calculating the sample size of the ANOVA being used in my dissertation or thesis?

There are a couple things involved in determining this. Since choosing a small effect size will require that we gather thousands of observations to find our ANOVA significant, and choosing a large effect size will mean fewer people but not a very good chance of finding the test significant if the groups are not hugely different.

What we need here is something in the middle…the medium effect size. For the purposes of the dissertation or thesis, this is definitely acceptable. Get help with determining the ANOVA effect size for the sample size calculation in your dissertation or thesis.

What is the sample size needed for the ANOVAs in my dissertation or thesis?

Using the criteria above, the sample size needed for the one-way ANOVA, testing for differences on one independent variable with two groups, is 128, the same as the independent samples t-test. The sample size will vary with the number of groups in the independent variable, but for the independent variable with 3 groups, you will need 156 or approximately 52/group. Get help with a custom sample size calculation for your dissertation or thesis.

Sample Size for Bivariate Correlation, Pearson Correlation, and Pearson Product Moment Correlation

To satisfy some of the requests of my blog readers, I am covering sample size calculation for a bivariate correlation or the Pearson correlation. This test might also be called the Pearson product-moment correlation.

I am going to assume that you know what a Pearson correlation is and its function, if not check out this blog entry on dissertation statistics help featuring bivariate correlation. In a nutshell we are testing for a significant relationship between two variables. Please keep reading, but if you are just looking for someone to help you calculate the sample size for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation using bivariate correlation, Pearson correlation, or Pearson product-moment correlation, or to justify the sample you already have, click here.

Sample Size for Bivariate Correlation or Pearson Correlation

There are some things we have to understand prior to calculating the sample size of our bivariate correlation or Pearson correlation. We have to first understand why we are calculating the sample size. If you are looking for some more information on these things, check out this blog entry.

Significance

Sample size is calculated for the bivariate correlation or the Pearson correlation so we know how many people we have to survey, poll, or sample to find the test significant at the level of significance we have set. This is the probability of committing a Type I error. Usually the level of significance is set at 0.05. This means there is a 5% probability that our results are due to chance. Get help with determining the correct level of significance for your bivariate correlation, Pearson correlation, or Pearson product-moment correlation.

Power

Power is the opposite of significance and is probability of falsely accepting the null hypothesis or… in plain English… the probability that we missed something and the test we ran was significant even though the result was not significant. This is the probability of committing a Type II error. Usually this is set at 0.80, making the probability 20% or four times as likely as committing a Type I error (measured by our level of significance). Get help with determining the correct power for your bivariate correlation, Pearson correlation, or Pearson product-moment correlation.

Effect Size

This circumstance is slightly different than other tests, in that there is no causality or direction in a sense. Effect size in this case is measured as r and represents the strength of the relationship. These r effect sizes for the bivariate correlation and the Pearson correlation are 0.10 for a small effect size, 0.30 for a medium effect size, and 0.50 for a large effect size. Just to make sure credit is given where credit is due, these effect sizes are courtesy of Jacob Cohen and his fantastically helpful article A Power Primer. For this example we will use a medium effect size. Get help with determining the correct effect size for your bivariate correlation, Pearson correlation, or Pearson product-moment correlation.

Now that we have determined these factors – and these numbers are the numbers that will be used 98% of the time in a Master's thesis, Master's dissertation, Ph.D. thesis, and Ph.D. dissertation – the rest of the sample size calculation for the bivariate correlation or the Pearson correlation is easy. For this we will refer again to A Power Primer by Jacob Cohen. If you are looking for this journal article you will find it here.

What is the sample size needed for a significant bivariate correlation or a significant Pearson correlation (Pearson product-moment correlation)?

Here it is…. 85. For a significant Pearson product-moment correlation at a 0.05 level of significance, a power of 0.80, and a medium effect size, we need 85 people. This number will fluctuate with changes in any of those measures, including power, which is sometimes set at 0.90. To have me calculate the sample size needed for your bivariate correlation, Pearson correlation, Pearson product-moment correlation, or for that matter any correlation or test, click here.

Sample Size Calculation for Dependent Samples t-test

A Priori Sample Size for Dependent Samples t-test

Sample Size Calculation for Dependent Samples t-tests are not as simple as sample size calculation for the independent samples t-test. While the sample size requirement is smaller because the two samples are related or correlated, the calculation is somewhat complicated. In order to calculate the minimum sample size for the dependent samples t-test being used in your Master's thesis, Ph.D. thesis, Master's dissertation, or Ph.D. dissertation, you are going to need some information or have a good idea of values for key pieces of information.

What is my thesis power analysis or dissertation power analysis for a dependent samples t-test or paired samples t-test?

For the purposes of this example, I will refer to a Jacob Cohen book, Statistical Power Analysis for the Behavioral Sciences. We are going to define power analysis for the dependent samples t-test as the sample size necessary to…

1. Achieve a Power of 0.80
   
2. Detect a reasonable difference between the groups with a medium effect size of 0.50
   
3. Detect a significant difference between the groups at a 0.05 level of significance
   

Important to understand is that each of the four items mentioned (Sample Size, Power, Effect Size, and Level of Significance) are a function on one another, meaning that changing any one of these things is going to change the value of the other three. So we have determined values for Power (0.80), Effect Size (0.50), and Level of Significance (0.05), and we are trying to figure out how many people we need to actually achieve all of these values. Get help with your thesis power analysis or dissertation power analysis

How is sample size calculation for a dependent samples t-test or paired samples t-test different than that of an independent samples t-test?

Before, we found the sample size for an independent samples t-test by looking at a simple table. This time, the groups are related and we need to take that into account in our sample size calculation. Before we continue, however, I would like to tell you the good news… The sample size requirements for the independent samples t-test are much larger than that of the dependent samples t-test. If you have calculated the independent samples t-test sample size and power analysis for your dissertation or thesis, can obtain that many pairs of participants, and are not under a lot of pressure from your college or university to justify the sample size, then...

Stop Here.

If you are like the rest of the world, please continue. For your dissertation or thesis using dependent samples t-test, your sample size is not going to be measure in participants, but in pairs of participants. Get help with your thesis power analysis or dissertation power analysis

How do I calculate the sample size for dependent samples t-tests or paired samples t-test?

Since we have established that we are conducting a dependent samples t-test, and are assuming the scores for the pairs are related or correlated, we need to know the degree to which they are correlated. Since this is an a priori power analysis for a dissertation or thesis, we could not possibly know the exact correlation between pairs in the sample we are going to obtain and must estimate the degree to which these pairs are going to be correlated.

If this is a dissertation or thesis following other research designs and there is empirical research information available, then look for a correlation coefficient from some of these other studies. For instance, if four of the studies you have read found a strong correlation (0.90) between childhood obesity prior to dieting and after dieting, then we can assume that we are going to find the same thing in our study. We would assume that the correlation would be 0.90. Get help with your thesis power analysis or dissertation power analysis

What is the equation for calculating sample size for dependent samples t-test?

Here it is in all of its mathematical glory…

n= n_(.10)/(100d^(2 ) )+ 1

where, n_.10 = 1571 and is the necessary sample size for the given a or α and Power, d = 0.645 and is the ES index for t tests of means in standard unit calculated by the equation:

d= d_(4^' )/√(1-r)

where
= the medium effect size of 0.50 and
r = 0.40
is the estimation of the correlation within the pairs.
This yields d = 0.645 = 0.05/√ (1 – 0.40).

OR

Just tell them you need 39 pairs of participants or scores. Better yet, get professional help with your thesis or dissertation power analysis. Let us give you a customized power analysis for your Master's thesis, Ph.D. thesis, Master's dissertation, or Ph.D. dissertation.