Statistics is the science that deals with collection, organization, analysis and interpretation of a study group of data. The science of statistics is also concerned with planning of data for various purposes such as experiments and surveys. Statistics knowledge is necessary for good statistical analysis (Pearson, Karl 2007). Statistical thinking involves recognizing sources of variations that may come in the process of data collection and recording, this is because data collection process always precedes data analysis and data collection (Pearson, 2007). The sciences of statistics always tend to follow criteria of some basic fundamental principles: all the study calculations always follow an interconnected processing system; all the interconnected processes always have variations in them and a successful statistics process is to understand and reduce the variations. These statistical interconnected are essential tools in the prediction and forecasting through the use of data.
Analyzing quantitative research
Quantitative research is a method used to investigate quantitative properties of a certain given phenomena with an aim to develop a mathematical side of view and to develop a hypothesis as well (Pearson, 2007).
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Taking focus in the Resent National Science Teachers Association (NSTA) (2004), a study to understand a scientific construction at Aquariums, Zoos and nature centers was conducted, through a scientific field trip (Miller, 2009). The study carried out at an aquarium and zoo in the United States. Teachers and students who had gone to the state facilities were used for the study. A group of different teachers from different various 18 schools who had visited the facilities took part in the study. The teachers took part in a seminar that was used to discuss constructivism and inquiry in the learning of the science subject in order to help the growth and development of easy understanding of science. From the author's text we find that after the seminar, students adopted the methodology to develop data observation and collection structures to the physical sites at the aquarium and at the zoos. The teachers received training on a constructivist observation instrument while divided into six groups. The training programs involved observations of different parameters in the zoos and aquariums such as what were the frequencies of children to read graphics to the chimpanzee's habitats? What is the frequency of children to inquire the docents at a manatee habitat? And what are the frequency of and the kind of questions that were asked about the aquarium instructors? The teachers observed while coding the visitors behaviors using the above question factors in different aquariums and zoos.
Different groups went round the different physical places until they all were done with the study sites. The observations were based on interactions between children and adult interactions, child to child interactions or between the children alone (Dodge, 2003). This kind of data differentiation by the type of social group is essential in determination of the future studies to enhance efficient differentiation of a study group by different categories. This study was carried out over a period of four months with the different groups rotating in the sites repeatedly so as to accommodate all the seasons of the zoos and aquarium visitation periods.
The data from different groups were then collected together and compiled for analysis processes for the validation of the study hypothesis. Various observations were observed from the collected data in the study conducted.
The author states that it was observable that the total tallied results were 3,132 at all the study sites in the different. An independent study group was consisted of either an adult with a child or a child with a child or just the children alone, as the group of data presented for analysis. The data analyzed were presented into two different groups: the different groups between the different types of observations on the different stations by the visitors and the control for the different types of the respective observations. The researcher found that exhibits done with living animals were more liked than static exhibits.
From the studies it was conclude that various previous studies have been encouraged to enhance activities in the public facilities to facilitate outdoor informal type of education in the different scientific physical environments. The zoos and aquariums are all well reputable for their sources of education sector as well as recreation centers as well. These sites should then be regarded as important sources of information that should be conserved and should be supported. It was also observed that visitors preferred to view an animal first before reading the graphics unlike reading the graphics after viewing the exhibit; this was observed by noticing that the mere site of the animal alone created a desire for the visitors to know more about the animal which lead to the visitor reading the graphics for further information.
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Analyzing Qualitative Research
Qualitative research is method used to inquire a deeper and more detailed understanding of a given identified human character and the underlying causes of the characters by examination, analysis and interpretation. Analysis of a qualitative research is aimed at investigating a particular case study by trying to answer the why and how factors of the parameters to reveal the underlying meanings and patterns of the questions relationships together with the classifications of the various types of the occurrence of events and the entities involved.
A study was conducted to research to determine the nature and characteristics of reflective practices among the teachers education faculty. There is a high demand for national accountability and venture into assessing and documenting the results of education (Seymour & Mark, 2008). This factor has contributed to the universities focusing their attention on teaching and focusing on the instructional performance on college teachers.
The author also notes that the focus on the college teaching is not precedent and that the actual student learning had been neglected. It is also indicated in the text that education qualities were directly linked to the input measures (Nicholas & Catherine, 2004). Factors such the library presence and the size, institutional endowment and standardization of the students joining the institutions were determinants of academic performances in the degrees of faculties. According to Nicholas and Catherine (2004), stakes are high these days in the higher education sectors with offers of funding and highly ranked competition among nontraditional providers and pressures from global market place. He further notes that the higher education today is has more profound changes in a shorter period of time than in the previous times, with these changes being noted by the need of the universities to educate a larger magnitude of students.
Qualitative data was collected to determine the nature and characteristics of the reflective practices in the physical education centers to determine the association of the effects of the variables. The researcher conducted his study by recruiting a sample of those who were willing to take part in the stud from a public university in the United States. From the text we find that the researcher established that teachers are reflective decision makers who are seen as to come up with theory and practice, they have ethical characters, value in individual and unit basis, value tradition and change and give acknowledgement to the service of education. The control for the study was an initial study that was developed prior to the study. The data was collected by answering some structured questions such as; what are the characteristics of reflective system? Can scaffolding and guidance affect the nature of reflection? What typologies of reflection are evidenced in the COE among faculty? What is professional development for a college faculty member and the evidence that the reflective process results in profession development. Does an individual's stage in the profession development continuum affect the nature of reflection? Those who participated in the study were asked to compose a response to the following item in the box on the survey instrument.
Analysis of the survey indicated that reflection for the participants is a process that uses the brain as the primary tool. External planning documents, formalized data collection or analysis or journals were not laterally involved in the study. The main idea of the study was to test the participant's beliefs and practices using a cognitive means (Robert & Patricia, 2001). Various reflective studies have indicated that collaborative action researches have been positively perceived by both the researchers and the teachers with an agreement to adopt the changes in the teaching methods (Underhill & Bradfield, 1998). This finding lead to a major contribution by experienced teachers taking part in the study, including the feeling of leadership and professionalism.
An area that arose for the need of further research was the questions that can the reflective process be detached from evaluation or judgment? It is also an observation by Gharhramani (2000) that an area that needs further studies is that if reflective studies were applicable to individual persons, for any given level for any given event for any behavior, is it in the exact order to follow the criteria through the lower stages as a cognitive activity or can they bypass directly to the optimal level? Other studies conducted by Robert and Patricia (2001) suggested the use of videotaped classroom vignettes as a cognitive tool for preserves and in service graduate work and professional development. Another issue that arose as in need of furthers research was the linking of reflection to a personal improvement in somewhat of an evaluative frame of reference. It was noted that the need for improvement in the quality of college teaching from the faculties with the support of the society that is around the university fraternity; the students, state legislate, governing boards and even the parents have a great concern for quality education offered in the colleges, but there is a point everyone differs in terms of their reasoning (Gauss, 2006).
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Comparing quantitative and qualitative research
Although there are certain arguments on the probability that there exists little differences between qualitative and quantitative research, the use of a contemporary research has indicated the actual differences and similarities between the two theories of research. For instance, using the research on return to zoo, several comparisons and contrasts can be highlighted. For instance, describing the methodology, qualitative method has been shown in this research to focus on the use of focus groups as well as interviews and review of the existing papers. On the contrary, quantitative methods focus on the use of surveys, and observations as described in this research. In addition, the contemporary quantitative methods include structured interviews as well as reviews of the existing documents for numeric information. Although the document reviews may seem similar between the two or methodologies, the major difference is that review in qualitative research aims at obtaining the types of themes in these documents, while on the contrary, the aim of the quantitative review of documents aims at obtaining the numeric information within these documents.
Looking at this research paper on the return to zoo, it is conclusive that research methodologies also differ on the basis of formulating the study hypotheses. The qualitative methods are normally inductive, as they use an inductive process of formulating the study hypotheses. On the contrary, the quantitative methodologies are generally deductive, as they use a test or pre test method of measuring pre specific constructs, concepts and the hypotheses that will be used to make up a theory.
Qualitative methods, as described in this paper, seem to be more subjective than objective. This implies that the qualitative methods normally describe the problem or condition from the persons who experience the very problem. On the contrary, the quantitative methods are more objective than subjective (Pearson, 2000). This implies that the methods provide the observed effects of a given program concerning a problem or a condition. This is normally as described or interpreted by the researchers. Moreover, the qualitative methods have been shown to be text based rather than number based, while the inverse is true for quantitative methods.
While qualitative methods are suitable in research studies that require in depth searching of information on only one or a few cases, quantitative methods requires that the breadth of the information be more broad, and that it should include a large number of cases under study. The quantitative methods also do not need to focus on deep information about each case; rather just a simple description for each case is used for generalization (Robert R Johnson and Patricia J). In the qualitative research methods, researchers have the choi8ce of making both unstructured and semi-structured responses (Robert R Johnson and Patricia J). However, in the quantitative methods of research, the researchers are not in a position to make any other type of responses apart from the fixed options provided (Gauss, 2006).
Statistical tests are not a necessity in the qualitative methods of study. On the contrary, quantitative research requires that the researchers develop comprehensive statistical tests on the data obtained in the research. The skills and the rigor displayed by the researcher shows some effect on the validity and reliability of the qualitative research (Gauss, 2006). The study has been shown to depend largely on the researcher's vigor and the ability to direct he research in a desired manner, a fact that is quite contradictory in the quantitative research methods. The latter depends largely on the instrument or measurement device used in the data collection part of the research. In addition, qualitative methods have their time schedule in such a way that more time is spent during the analysis phase, while less timed is spent on the planning phase. The opposite is true for the quantitative methods, where more time is spent on the planning phase and less spent on the analysis phase (Robert R Johnson and Patricia J). Research methods further differ on the abilities to be generalized, where in qualitative methods; generalization is less possible as compared to quantitative methods.
There are known similarities between quantitative and qualitative research, both these approaches are basically different in their ability to ensure the validity and reliability of their findings. (Nicholas & Catherine, 2004)
A lot of quantitative data can be tends to be confirmatory and deductive, but there is plenty of quantitative research that can be classified as exploratory. Consequently, while the quantitative research does tend to be exploratory giving the chance to be used in be used to make conclusions in the verification of specific deductive hypothesis. Both the quantitative and qualitative procedures act on epistemological assumptions from quantitative researchers (Robert & Patricia, 2001). This can be elaborated by the belief by some researchers who tend to believe that the best way to obtain a quantitative result is to view the samples physically and view it in its full context, while for other researchers the best way to obtain qualitative information is to become immensely attached into the information being solicited.
Any researcher used to the qualitative tradition would notice that that the issues of qualitative and quantitative approaches, it is not possible to separate a research assumptions from the obtained study data. Some researchers will notice that the perspective of data being based on assumptions common to qualitative and quantitative approaches are based on assumptions from the collected data samples. Other researchers would argue that it doesn't matter if the recorded data are coded mathematically or quantitatively because they would do either of the approaches, by recognizing the inherent limitations and the complex assumptions beneath all numbers. Both quantitative and qualitative approaches are backed up by in depth fundamental and philosophical assumptions with the nature of the study. This sided debate can further be enhanced by social research which is richer for a wider variety of varied views and methods that the debate might generate.
Return to the zoo
The visit to the zoo and the aquarium involved a number of statistical calculations and statistical terms. A number of variables were observed such as; the frequency of children to inquire the docents at a manatee habitat, and what the frequency of and the kind of questions that were asked about the aquarium instructors, that teachers observed while coding the visitors behaviors using the above question factors in different aquariums and zoos. The identification of the visits to the zoo required a control that would act as the guiding factors; previous results that had been used in relevant studies were used as the controls in the study. The previous studies were identified as the controls so as to keep the current study in truck as the others. The constants in the study was the number of times the researchers had to go round the zoos and the aquarium, the number was 9 times which was common to all the groups who had taken part in the study.
Introduction to probability
Probability calculations are used to determine the number of occurrences of an event based on the value of related known probability. Probability calculations help with the framework to define a problem. It is a way of putting down a belief that an event will occur or has occurred. An experiment in probability is involving a chance or probability that leads to results called outcomes (Gauss, 2006). A probability calculation refers to the connection between mathematical calculations and the application of these calculations for a decision making in the day to day activity. Probability is applicable in the preparation to interpret, calculate and understand a situation which is under the probability calculation study. A probability calculation is presented in a subject in the statistical calculation, with the intensions to carry out a research to those who require a more contextual understanding of statistical interpretation.
The probability which is the likelihood of an event according is calculated by dividing the number of ways of achieving success by the total number of possibility of achieving success. Probability can be used to determine single events occurrence or double events (Gauss, 2006). In the single event it can be calculated by trying to determine the chance that only one event is going to take place, this can be considered when we have a bag with six balls with different colors, we can determine the chance of picking just one ball of a specific color is a typical case of just one event probability. A multiple event probability can be described as independent and dependent event probabilities (Gauss, 2006). A two event occurrence can be described as independent if the outcomes of the events do not affect the outcome of the other.
We can describe this by throwing up two dice; the probability of getting a number 3 on the second die is the same, regardless of what the first die figure was. The values in the dice were independent regardless of the other die results, and the values of both the probabilities remain constant as 1/6. The dependent probability calculation is in a case where we have a bag containing 4 red balls and 4 yellow balls, if we pick two of the balls, there is a probability of picking either a red or a yellow ball, when the first ball has been picked is red, the probability of picking a yellow ball is dependent on the color of the first ball picked. This kind of probability is known as dependent probability (Gauss, 2006).
Possibility spaces can be evaluated when calculating the probability of two events taking place. The probability space is the other possibilities that can be expected after noting the first occurrence, the remaining percentage of the possibilities forms the possibility space. The possibility space is helpful in prediction of possible further occurrences (Gauss, 2006). These probabilities can be determined by calculations or by drawing probability trees. Probability calculations have some basic rules that are followed during their calculations; the first rule states that if two events A and B are independent, then the probability of the entire occurrence is calculated by multiplying the probability of event A by the probability of event B occurrence. The second rule of probability is that if we have two events A and B and there is no possibility of both events taking place, then the probability of either of an event A or B taking place is the probability of event A occurring + the probability of event B occurring. These rules are referred to as the 'AND' and 'OR' rules respectively (Gauss, 2006).
Probability trees can be drawn using vertical lines from the points of origin of the curve. This line is the mathematical median and mean when we have a perfect curve that denotes a normal distribution of data the area above and below the line is always equal to a 50% to 50% of the population. These lines can always be used to represent the medians (Seymour & Mark, 2008).
Mean and standard deviation
Standard is different from the ranges; standard deviation is used to measure a variable or diversity in calculations, while mean refers to the average of all the data numerical, it is the characteristic of the central tendencies meaning that it is greatly influenced by outliers. The sample mean is used in the approximation of the entire population mean. The population mean is always a random value that can be one of the sample values in the population. There are different kind of mean values in a population sample; weighted mean which is one that the mean faction is a positive digit to a positive digit. Unweighted mean is one which the mean value equals the weight, and the convert unweighted mean to weighted mean is just unweighted mean that can be turned into a weighted mean by repeating the sample elements (Underhill & Bradfield, 1998)
Statistical measures of spread are as median, mode and the interquartile range. The standard deviation of a population can be calculated by examining a random sample taken from a given study population. The standard deviation is of a sample can be presumed to be equal as the population of a discreet random variable (Underhill & Bradfield, 1998). For a given data set, the mean of the data set is the sum of all the values divided by the number of values, if the data set were based upon a series of observations obtained by sampling a population. Standard deviation is used to show how much variant is from each measurement is from the average value which is the mean value. Standard deviation is used to find information of the collected data that are in analysis and also to understand the normal distribution of data (Dodge, 2003). The normal distribution of data is used to indicate the samples in a given set of data are closely related in value to the average while other samples vary widely from the mean.
In the demonstration graph, the x axis is the value that determines the standard deviation in any data set and the y axis which is the horizontal line is the number of data points for each of the data points for each of the values in the x axis which is the horizontal line. Different data sets give different types of curves where some curves can be steep while others can be flat curves. Other data sets can give irregular graphs that are not coherent, but normal distributed information will give a bell shape curve (Underhill & Bradfield, 1998).
Standard deviation is a static that enables one to know how closely all the data samples are clustered around the mean value of the whole data sets. In various cases a standard deviation may serve as a measure of uncertainty, taking a case study in the science where numerous experiments performed can be analyzed by finding the standard deviations, standard deviations can also be used to compare the practical and the theoretic notions in a given kind of study the reported result (Robert & Patricia, 2001).
A small standard deviation will be observed when the data set values are close to the mean value and as a result a steep graph will be observed, a large standard deviation will lead to a flat graph this indicating a large standard deviation (Underhill & Bradfield, 1998). If the mean and the standard deviation of two overlapping samples are known as the point of intersection, then the standard deviation is the aggregation sample can still be calculated. One standard deviation from either the horizontal or the vertical axis accounts for a 68% of the total sample population. 2 standard deviations from these lines accounts for 92% of the total populations in the study sample (Miller, 2009). A flat graph will give a 68% of the total population sample. The standard deviation is then important in the determination of a sample population in a given data set of a study. The standard deviation has been used in various studies to determine the comparison test scores for different schools; the standard deviation lets one to know how diverse the test scores for different schools have. This helps in the ranking and grading of the schools performances (Dodge, 2003).
Standard deviations can assist someone to answer some common questions as to why the data achieved is as it is. Standard deviation has then also proved efficient in the evaluation of studies. The worth of a scientific research is an evaluation based on calculations of the standard deviation, this save someone from seeking other statisticians by paying them off in order to know the worth of a study.
In the calculations of standard deviation, there are some common terms that should be understood; where x will be one of data in a set of the sample data.
Avg (X) is the mean (average) of all the values in the values X in the set of data
N is the total number of values of X in the data set.
The whole calculation process can be summarized into four main steps.
The initial step is to calculate the mean, after which we calculate the intermediate value table. The intermediate value is then divided by the number of points in the set of data samples minus one. The squire root of the obtained number is the calculated. This becomes the standard deviation of the data set.