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Psychological Statistics mainly concerned with the compilation, collection and interpretation of the numerical data. Generally, it refers to a numbers, theorems and laws to psychology. It involves the various statistical applications viz. learning theory, human development, abnormal psychology, personality test, perception, psychological tests, and many more. Psychological Statistics field deals with the various topics, such as Z-Scores and Percentile Ranks, Percentiles and Percentile Ranks, Sign Test and Hypothesis Testing, Correlation and Regression, and many others.

SPSS software is the majorly used in the Psychological Statistics field. This software mainly used for non batched and logical batched statistical analysis. SPSS is mainly used by marketing organizations, health researchers, market researchers, education researchers, data miners, and others. Two important features of SPSS software is used in the Statistics field which includes data documentation and data management.

Two major statistical tests that involved in the psychology are as follows:

- Parametric tests: parametric statistics is defined as the sub disciplines of statistics which relies on the parameterized families of probability distribution. It assumes about the population that specifically based on the probability distribution and if the assumption is correct, then its method provides the efficient results. Parametric formulae is faster to compute and easier to
- Non-parametric tests: A statistics which doesn’t depend on the parameterized families of probability distributions is termed as Non-parametric Statistics. Non-parametric Statistics usually do not make any kind of assumptions and includes inferential and descriptive statistics. Few representative parameters re variance, mean, etc.

Descriptive statistics is mainly used to explains and summarize the data in a significant way. It enables user to summarize the data graphically or numerically. It can summarize the large set of data and decrepit into measures of variability, spread and measures of central tendency. Measures of the variability involve skewness, maximum variables, minimum variables, standard variance and kurtosis.

Inferential statistics permits user to discover the inferences about the population by using sample of data that. Inferential Statistics evaluate the relationship between dependent and independent variables. It acts as a useful term when there is difficult to examine the each member of population.

T-test is used to determine the estimates between two different levels. The estimate depends on the distinction among the sample means. T-test is of two types:

- Independent t-test
- Paired t-test

Chi-square mainly concerned with one categorical data and also known as Goodness-of-Fit test. Difference between the acquired and expected variables can be compute by using One-variable Chi-square and association among the two categorical variables can be changed by 2*2 Chi-Square.

Moreover, General Linear Model is defined as a procedure which used the least square regression to determine the relationship between continuous response variable. It can also determine the relationship between one or more predicators, whereas predicators may be covariates or factors. To discover the significant differences, GLM done the numerous comparisons among the factor level. GLM majorly involves the various statistical analyses that can be used in the social and applied research. Three main component of GLM are as follows:

- Systematic component
- Random Component
- η or g(μ)

Factorial ANOVA is one who is responsible for determining a fact that a bunch of independent variables forecasts the value of a dependent variable. It also determines that independent variables which are evaluated by the ANOVA test. In dependent variables, a user can measure the effect of various factors by using factorial ANOVA.

Dispersion is defined as the method which is used to disperse the values among the central tendency. There are two types of measures involved in the Dispersion, one is range deviation and second is standard deviation. Range deviation is easy to calculate and standard deviation elaborates the process of spreading the scores among the mean of the sample.

Spearman’s rho test refers to a non-parametric correlational analysis which is generally used to determine the correlation between the ranked data and ratio data.

Multilevel Modeling is defined as a method that is used for analyzing the nested data. For example, in school, data is analyzed by many students, in office by numerous clients, and many other places. MLM involves the various steps:

- Elucidate the research question
- Select the specific parameter estimator
- Determine the requirements for MLM
- Creating the first level model
- Creating the second level model
- Effective reporting
- Likelihood ratio model testing

Furthermore, Statistics is a vast field and numerous students are pursuing their higher level studies in this field and Psychological Statistics field is also using the applications of statistics to Psychology. Some of the higher level topics that students commonly study in this field are Statistical Notation, Summation, and Computations, Sampling Distributions, Z-tests, Power, Measures of Center and Spread, and many more. Along with these topics, Psychological Statistics involve the various Progressive topics which are listed as below:

- Multiple Regression
- Trend Analysis
- NonParametric procedures
- Factorial Designs
- Hierarchical and Nested Designs
- Repeated Measures

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**APPLICATIONS OF STATISTICAL METHODS IN PSYCHOLOGY**

- measures of central tendency and variability, probability and distributions, confidence intervals and hypothesis testing, t-test and analysis of variance, correlation and regression, χ2 tests, data collection, statistics in psychological science, visual displays of data, characterizing distributions: central tendency, characterizing distributions: variability
- scores, and the normal distribution, sampling and probability, logic of hypothesis testing, significance testing, statistical tests using the Z distribution, confidence intervals, std error of measurement, statistical power, influences on, statistical, power, logic of analysis of variance, hypothesis tests and comparisons in ANOVA, power and effect size in ANOVA
- raw score approach to ANOVA, interaction effects in, factorial ANOVA, correlation, simple regression, logic of multiple, regression, Distributions, with graphs; Distributions with numbers, normal distributions, Scatterplots and Correlation, Regression, Producing Data, probability, Sampling distributions, Confidence Intervals, Tests of significance, Inference in Practice, Inference about a Population Mean, Two-Sample Problems, Two Categorical Variables: The Chi-square Test, One-Way Analysis of Variance

**Topics for Psychological Statistics**

- Descriptive statistics, central tendency and variability , Standard deviation, z scores, normal distribution , Variables and Relationships, Hypothesis testing, sampling distribution of the mean, Hypothesis testing, z & t test for a single mean, Research Designs, Parameter estimation, statistical power , t-tests for, independent samples, Internal and External Validity
- Analysis of variance, Artifacts and bias , Correlation, Simple Linear Regression , Controlling Extraneous Variables, Chi square tests for categorical data, choosing appropriate tests , Reading Research Critically , statistics and frequency distributions, Central tendency and variability, z-scores and probability, Distribution of sample means, hypothesis testing, hypothesis testing, t statistic , t test
- ANOVA and correlation , Chi-square statistic, descriptive and inferential statistics, parametric and nonparametric statistics, distinguish between a population and a sample, distinguish between statistics and parameters, Compute statistical tests , measures of central tendency , Compute and explain variability, range, variance, standard deviation, standard z scores, normal distribution tables.
- correlation coefficients using the Pearson and the Spearman, regression and predict y-values, interpret standard error of the estimate, proportion of variance, hypothesis testing, type I and type II errors, power of an analysis, sampled t-tests, determine significance, F-test, one-way ANOVA, two-way ANOVA, non-parametric, Mann-Whitney U, Wilcoxin rank test, Chi Squares,