Understanding Statistics - Essay Example

? Understanding Statistics Understanding Statistics Scales of Measurement Scales of measurement determines the criteria for ifying various variables. The scales of measurements are more applicable in the academic and research scenarios as compared to the ordinary life situations. The scales of measurements include nominal, ratio, ordinal and interval. The nominal scales are the simplest scales in this case because they involve the marking of variables without the consideration of any quantitative value.The nominal scales are reciprocally exclusive and they are not associated with any numerical significance.The nominal scales may refer to objects as male, female, brown or black among others. The ordinal scales provide no evident variation amongst the variables. This scale only evaluates the order of the values. The ordinal scales measure the concepts that are not numeric such as fulfillment, jovialness and discomfort among others. In any analysis, an individual can elucidate that number four is better than number three though the extent is not clear again, it is not easy to determine the variation between ok and happy. The interval scales encompass numeric scales that besides providing the order, they also provide the accurate differences between the variables in question. A standard example is the Celsius temperature such as the disparity between 30 and 40 degrees is 10 degrees. Time can also provide precise variations where the disparity between six and four minutes is two minutes. Ratio scales are essential in statistical evaluations to its flexibility for alterations seeking accuracy. The ratio scale can be multiplied, added, divided or subtracted and the central tendency measures estimated. A discrete variable involves well determined set of predetermined set of probable values-states. The variables include the provision that is either “true” or ”false”, the team that will win and the number of dime in a pouch amongst others. Nonetheless, the variables might appear to be discrete at one point and continuous at a different perspective. The continuous variable opts to take on a position between two extreme positions or values. Continuous variables encompass the indoor temperature, direction travelled or the water used. The discrete variable tends to depict a digital quantity whilst the continuous variable tends to be analog in quantity. According to the explanations provided on the above scales, the different statistical research studies can select any of the according to suitability for application. The continuous and the discrete variables have significance on the selection of the research methodologies to use since the experimental method would be appropriate with discrete data whilst the researches dealing with conventional aspects might find it appropriate to employ continuous variables in the research activity. The area under the normal distribution is proportional to the overall area. The total area covered in the normal curve is equivalent to one. The curves never attain the situation Y = 0 but move to the positive infinity and the negative infinity. The shape assumed by the normal curve is infinite and depends on the mean and the standard deviation. The z-score is a critical tool in data evaluation and is used to determine the extent to which a point x is high or below the population mean ?. It is the providence of the T-statistic with predetermined mean and the standard deviation. In case of interference with the degree of freedom to an extent of assuming population mean and the standard deviation from the availed sample, then it fails to be T-statistic. The percentile rank of a normally distributed population can be estimated readily through the use of z- scores. In the e vent that the area under a curve is apportioned above and below the mean, the partitions obtained are the similar to the probability picking a value in the similar range. For instance, the area between the standard deviation above and below the mean when the values are subtracted from the population mean a number is obtained that provides a percentile of the values found in the predetermined range. This information is essential to the counselors since it enables them to handle larger amounts of data effectively and determine the statistical relationships on the methods of data collection and in the eventual presentation of the information. The counselors can make decisions depending on the statistical principles to prove or disprove the hypothesis. The first step in hypothesis testing is highlighting the research question. The process defines the subject populations to the researcher, the variable parameters investigated together with the hypothesized values. The procedure assists the researcher to determine the variable parameters to be used in sample data collection and the form of variable and hence the statistical test that can be done on the set of data gathered. Step 2 is the specification of the null (H0) and alternative (HA) hypotheses. The null hypothesis is the populace parameter, µ and might be designated a value. The alternative hypothesis is also a population parameter. However, it should not be equal to the null hypothesis parametric value. The research should also choose a significant point-type one error and practically alpha used at the initial levels of 0.05 or else 0.01. The type II error is also selected at this stage. This step is important in setting the research question as a matter of statistical evaluations and analyzes the suitability of all the assumptions. Step 3 is the calculation of the test statistic. The statistic calculated here has to be analogous to the previously set in the null hypothesis. The hypothesis might had determined the population mean to be µ but in this case the mean is to be depicted by the xbar, and the standard deviation as s. the approximation of the expectation in its distribution would be represented by a histogram. This process also attempt to determine the essence of the different means in the research. z = xbar-µ (hypothesized)        standard error of xbar Step 4 involves the computation of probability of T- statistic or the rejection region. This process attempts to calculate the p-value that infers the t- statistical probability of both tails in the two tailed evaluation. The null hypothesis is rejected in the event that the probability is either less or equal to the significance level. Conversely, the null hypothesis is not rejected in the event that the outcome is not statistically significant. Step 5 involves stating of the conclusion. As the eventual step, the process attempts to describe the outcome and outline perfect statistical conclusions in a suitable means that can be understood. The conclusions entail descriptions of both the results of null and alternative hypotheses. To determine the group differences analysis, experiments can be one of the methods employed. In this situation the samples can be constant but different variables can be applied. For instance, in the case where the research may aim at understanding the effect of different stimulants in an individual, different stimulants might be used on the individual then the effect would be assessed. The independent variables are the variables that might be manipulated by the researcher while the dependent variable is influenced by independent variables. In cases of experiments, the independent variables depend on the researcher performing the experiment. In the analysis of size of individuals, one mat realizes that the weight depends on the height and not vice versa. Weight is therefore a dependent variable. In the situation where the research aims at determining the effect of a substance in an individual, then the substance can be administered to the individual and response evaluated through the individual’s ability in performing tasks such as mathematical calculations. Here, performance is a dependent variable that depends on the state of mind of the subject. The nonparametric techniques in the case of only two levels are the non-parametric descriptive statistics and statistical tests. Here, the linear regression as well as the linear disanalysis methods is used. However in the case of more than two levels of the factor, canonical correlation analysis and statistical models as well as inferences can be employed. The non-parametric techniques are robust, have higher levels of efficiency due to their simplicity and provide distinct information. Conversely the parametric techniques rely on assumptions. The parametric methods can be more accurate in case the assumptions that define them are correct. The methods include formula and calculations in their operations. The technique provides that one can predict the distribution through the mean and the standard deviation. The assumptions in parametric techniques depend on the fixed formulas of determining the tendencies and the probability of distributions. The parametric distributions are accurate in the event that the experiment meets all the standards of the situations. The non-parametric techniques are realistic since they depend on the actual evaluations and performance of the research activity. The methods of handling a "nuisance variable" include i) blocking: this method involves incorporating the nuisance variable into the system as a distinct independent variable. In such a situation the nuisance variable will not pose alterations to the subject variables in question. ii) Randomization can be used to handle the nuisance variable by ensuring that the every event is assigned to the experiment or the standard condition. This method is essential in neutralizing the influences of nuisance variable. iii) Statistical control: this involves the employment of statistical fools such as evaluations of covariance and partly correlation to regulate the nuisance variable. The statistical control is effective since it ensures that the nuisance variable obtains the right position in the experiment and converts it to be useful in research. However, the method can lead to increased negative effects on the experiment if it fails to be implemented in the right way in the experiment. Correlation is a measure in statistics that shows the degree to which more than one variable vary together. Positive correlation shows the exact difference with which the variables have and how they increase or fall unitarily. The negative correlation depicts one variable rise as the contrary variable falls. The parametric assumptions concerns the datasets. The assumptions involve the manner in which the data is formed, the location of the quantities and the overall rationale on the information. However, the nonparametric variables are limited assumption and have fewer experiences of errors basing on the assumptions. The parametric methods can be used to answer questions concerning the hypotheses and assumptions whilst the nonparametric methods are applied in the situations of decision rules and computations. The multiple regressions tries to formulate the relationship amidst two or more evaluator variables together with the response variable by fixing a linear equation to the information present while discriminate function analysis is the statistical evaluation targeting the prediction of a classifying dependent variable. Point out whether these are parametric or non-parametric techniques, and what the relevant assumptions are to use them. The multiple regression aims at the provision of the connection between the variables while the discriminate function analysis primarily deals with the categorization and the binary dependence amongst the variables. Discriminant function analyses are employed when the priorities are known by the researchers whilst the multiple regression endeavors to determine the priorities. The scales of measurements appropriate for the discriminant function analysis are ratio and ordinal scales. The ratio scale in this case is the might originate from the known source or priority of variables. The discriminant function analysis can be used with the questions on experiments whilst the multiple regression is appropriate when answering the questions on hypotheses in the research study in question. References Miles, J., & Banyard, P. (2007). Understanding and using statistics in psychology: A practical introduction : or, how I came to know and love the standard error. Los Angeles: SAGE Publications. Read More