Basic Concepts of Inferential statistics
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Know what inferential statistics is and its process. Also discover about various sampling techniques.
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STA 222 Lecture 1 Introduction to Statistical Inference.pptx
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- Statistic describes a characteristic of the sample (known)
Probability sampling methods, like simple random sampling, give every member of the population a known chance of being selected in the sample. This allows estimating sampling error and making statistical inferences about the population. Non-probability sampling does not give all members an equal chance of selection.
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statistical inference.pptxsuerie2 This chapter introduces statistical inference and how it is used to make statements about population characteristics based on sample data. It discusses the differences between descriptive and inferential statistics, and how inferential statistics is used for estimation and hypothesis testing. It also explains key concepts like random sampling, sample statistics, population parameters, sampling distributions, sampling error, and how the central limit theorem allows inferring characteristics of the population from a sample as long as the sample size is at least 30.
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- 1. Basic Concepts of Inferential Statistics Statisticsconsultation.co
- 2. WHAT IS INFERENTIAL STATISTICS? Inferential statistics is a technique used to draw conclusions about a population by testing the data taken from the sample of that population. It is the process of how generalization from sample to population can be made. It is assumed that the characteristics of a sample is similar to the population’s characteristics. It includes testing hypothesis and deriving estimates. It focuses on making statements about the population. Statisticsconsultation.co
- 3. THE PROCESS OF INFERENTIAL ANALYSIS Raw Data • It comprises of all the data collected from the sample. • Depending on the sample size, this data can be large or small set of measurements. Sample Statistics • It summarizes the raw data gathered from the sample of population • These are the descriptive statistics (e.g. measures of central tendency) Inferential Statistics • These statistics then generate conclusions about the population based on the sample statistics. Statisticsconsultation.co
- 4. SAMPLING METHODS Random sampling is the best type of sampling method to use with inferential statistics. It is also referred to as probability sampling. In this method, each participant has an equal probability of being selected in the sample. In case the population is small enough then everyone can be used as a participant. Another sampling technique is Snowball sampling which is a non-probability sampling. Snowball sampling involves selecting participants on the basis of information provided by previously studied cases. This technique is not applied for inferential statistics. Statisticsconsultation.co
- 5. IMPORTANT DEFINITIONS Probability is the mathematical possibility that a certain event will take place. They can range from 0 to 1.00 Parameters describe the characteristics of a sample of population. (Variables such as age, gender, income, etc.). Statistics describe the characteristics of a sample on the same types of variables. Sampling Distribution is used to make inferences based on the assumption of random sampling. Statisticsconsultation.co
- 6. SAMPLING ERROR CONCEPTS Sampling Error: Inferential statistics takes sampling error (random error) into account. It is the degree to which a sample differs on a key variable from the population. Confidence Level: The number of times out of 100 that the true value will fall within the confidence interval. Confidence Interval: A calculated range for the true value, based on the relative sizes of the sample and the population. Sampling error describes the difference between sample statistics and population parameters. Statisticsconsultation.co
- 7. SAMPLING DISTRIBUTION CONCEPTS The variables of a sample taken from the population should be the same for the population also. Due to sampling error, the sample mean can be varied. The amount of this variation in the sample mean is referred to as standard error. Standard error decreases as the sample size increases. Statisticsconsultation.co
- 8. TYPES OF HYPOTHESES Alternative hypothesis: It specifies expected relationship between two or more variables. It may be symbolized by H1 or Ha. Null hypothesis: It is the statement that says there is no real relationship between the variables described in the alternative hypothesis. In inferential statistics, the hypothesis that is actually tested is the null hypothesis. Therefore, it is essential to prove that the null hypothesis is not valid and alternative hypothesis is true and should be accepted. Statisticsconsultation.co
- 9. HYPOTHESIS TESTING PROCESS State the research hypothesis State the null hypothesis Choose a level of statistical significance Select and compute the test statistic Make a decision regarding whether to accept or reject the null hypothesis. Statisticsconsultation.co