Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what's going on in our data.
Here, I concentrate on inferential statistics that are useful in experimental and quasi-experimental research design or in program outcome evaluation.
Perhaps one of the simplest inferential test is used when you want to compare the average performance of two groups on a single measure to see if there is a difference. You might want to know whether eighth-grade boys and girls differ in math test scores or whether a program group differs on the outcome measure from a control group. Whenever you wish to compare the average performance between two groups you should consider the t-test for differences between groups.
Most of the major inferential statistics come from a general family of statistical models known as the General Linear Model. Given the importance of the General Linear Model, it's a good idea for any serious social researcher to become familiar with its workings. The discussion of the General Linear Model here is very elementary and only considers the simplest straight-line model.
However, it will get you familiar with the idea of the linear model and help prepare you for the more complex analyses described below. One of the keys to understanding how groups are compared is embodied in the notion of the "dummy" variable. Inferential statistics are necessary to draw conclusions of this kind. Inferential statistics allow the researcher to begin making inferences about the hypothesis based on the data collected. This means that, while applying inferential statistics to data, the researcher is coming to conclusions about the population at large.
Inferential statistics seek to generalize beyond the data in the study to find patterns that ostensibly exist in the target population. This course will not address the specific types of inferential statistics available to the researcher, but a succinct and very useful summary of them, complete with step-by-step examples and helpful descriptions, is available here. Conducting Research in Psychology: Measuring the Weight of Smoke, 3rd Edition. Wadsworth Publishing February 27, All Rights Reserved Worldwide.
The units of measurement are equal throughout the full range of the scale. Ratio scales are similar to interval scales, in that equal differences between scale values have equal quantitative meaning.
However, ratio scales also have a true zero point, which gives them an additional property. For example, the system of centimetres is an example of a ratio scale. There is a true zero point and the value of 0 cm means a complete absence of length. The thyromental distance of 6 cm in an adult may be twice that of a child in whom it may be 3 cm.
Descriptive statistics[ 4 ] try to describe the relationship between variables in a sample or population. Descriptive statistics provide a summary of data in the form of mean, median and mode. Inferential statistics[ 4 ] use a random sample of data taken from a population to describe and make inferences about the whole population. It is valuable when it is not possible to examine each member of an entire population.
The examples if descriptive and inferential statistics are illustrated in Table 1. The extent to which the observations cluster around a central location is described by the central tendency and the spread towards the extremes is described by the degree of dispersion. The measures of central tendency are mean, median and mode. Mean may be influenced profoundly by the extreme variables.
For example, the average stay of organophosphorus poisoning patients in ICU may be influenced by a single patient who stays in ICU for around 5 months because of septicaemia.
The extreme values are called outliers. The formula for the mean is. Median[ 6 ] is defined as the middle of a distribution in a ranked data with half of the variables in the sample above and half below the median value while mode is the most frequently occurring variable in a distribution. Range defines the spread, or variability, of a sample. If we rank the data and after ranking, group the observations into percentiles, we can get better information of the pattern of spread of the variables.
In percentiles, we rank the observations into equal parts. The median is the 50 th percentile. Variance[ 7 ] is a measure of how spread out is the distribution. It gives an indication of how close an individual observation clusters about the mean value. The variance of a population is defined by the following formula:. The variance of a sample is defined by slightly different formula:. Each observation is free to vary, except the last one which must be a defined value.
The variance is measured in squared units. To make the interpretation of the data simple and to retain the basic unit of observation, the square root of variance is used. The square root of the variance is the standard deviation SD.
The SD of a sample is defined by slightly different formula:. An example for calculation of variation and SD is illustrated in Table 2. Most of the biological variables usually cluster around a central value, with symmetrical positive and negative deviations about this point. It is a distribution with an asymmetry of the variables about its mean. In a negatively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the right of Figure 1.
In a positively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the left of the figure leading to a longer right tail. In inferential statistics, data are analysed from a sample to make inferences in the larger collection of the population. The purpose is to answer or test the hypotheses. A hypothesis plural hypotheses is a proposed explanation for a phenomenon.
Hypothesis tests are thus procedures for making rational decisions about the reality of observed effects. Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 where 0 indicates impossibility and 1 indicates certainty. Alternative hypothesis H 1 and H a denotes that a statement between the variables is expected to be true. The P value or the calculated probability is the probability of the event occurring by chance if the null hypothesis is true.
The P value is a numerical between 0 and 1 and is interpreted by researchers in deciding whether to reject or retain the null hypothesis [ Table 3 ]. However, if null hypotheses H0 is incorrectly rejected, this is known as a Type I error. Numerical data quantitative variables that are normally distributed are analysed with parametric tests.
However, if the distribution of the sample is skewed towards one side or the distribution is unknown due to the small sample size, non-parametric[ 14 ] statistical techniques are used.
Non-parametric tests are used to analyse ordinal and categorical data. The parametric tests assume that the data are on a quantitative numerical scale, with a normal distribution of the underlying population. The samples have the same variance homogeneity of variances.
The samples are randomly drawn from the population, and the observations within a group are independent of each other. Student's t -test is used to test the null hypothesis that there is no difference between the means of the two groups. It is used in three circumstances:. The group variances can be compared using the F -test.
If F differs significantly from 1. The Student's t -test cannot be used for comparison of three or more groups. The purpose of ANOVA is to test if there is any significant difference between the means of two or more groups. The within-group variability error variance is the variation that cannot be accounted for in the study design. It is based on random differences present in our samples. However, the between-group or effect variance is the result of our treatment.
Inferential Analysis: From Sample to Population Introduction Inferential analysis is used to generalize the results obtained from a random (probability) sample back to .
With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. Analysis of Covariance (ANCOVA), regression analysis, and many of the multivariate methods like factor analysis, multidimensional scaling, cluster analysis, discriminant function analysis, and so on. An understanding of that.
Module 5: Data Preparation and Analysis Preparing Data. After data collection, the researcher must prepare the data to be analyzed. Organizing the data correctly . Research Methodology Sample Paper on Inferential Statistics Inferential Statistics Inferential statistics is a procedure used by researchers to draw conclusions based on data that is beyond simple description (Clayton, ).
This article explains the difference between descriptive and inferential statistic methods. In short, descriptive statistics are limited to your dataset, while inferential statistics attempt to draw conclusions about a population. When it comes to statistic analysis, there are two classifications: That’s enough on market research. terminology of data analysis, and be prepared to learn about using JMP for data analysis. Introduction: A Common Language for Researchers Research in the social sciences is a diverse topic.