Tiêu đề 13. BASICS OF TESTING HYPOTHESIS.pdf ✅

PHARMD GURU Page 1 INTRODUCTION: The process of acquiring on unknown information from what is known is called inference. The various methods are also developed in statistical inference to measure the validity of the inference in terms of probability. It is broadly classified into two categories: 1) Estimating of parameters 2) Testing of hypothesis 1)ESTIMATION OF PARAMETER: The estimation of parameters deals with methods of determining numbers that may be taken as the values of the unknown parameters, as well as with the determination of intervals that will contain the unknown parameters with a specified probability based on a sample taken from the population. Statistical estimation procedures provide us with the means of obtaining estimates of population parameters with a desired degree of accuracy. The statistic used to estimate the population parameter is known as an estimator. The value of the estimator for a particular sample is known as an estimate. OBJECTIVES OF ESTIMATION: 1) Distinguish between a point estimate and an interval estimate. 2) Calculate the confidence interval. 3) Calculate the sample size if the confidence intervals are known. 4) Describe the types of estimators. Since statistical inference works with the estimation of parameters and the testing of hypotheses, we define characteristics of populations from information contained in samples. Also, we infer something about a population from information taken from a sample. To calculate the exactness of the mean would be an impossible goal. So, we try to make an estimate and implement some controls to avoid as much of the error as BASICS OF TESTING HYPOTHESIS

PHARMD GURU Page 3 2) CONFIDENCE INTERVAL (INTERVAL ESTIMATE): In interval estimation, we provide a range (or interval) based on sample values for estimating the population parameters, and the process is called interval estimation. EXAMPLES: 1. Estimating the population means birth weight of newborns in interval estimation will give a range based on sample values. In interval estimation, we will find two statistics t 1 and t 2 (where t 1 < t 2 ) such that the probability that the interval (t 1 ,t 2 ) will contain the correct value of unknown parameters has a pre-assigned probability α or confidence coefficient. 2. Confidence Interval Example: o If we report that we are 99% confident that the mean of the population of failures of students in the final exam will lie between 50 and 100, then the range 50 - 100 is our confidence interval. 2)TESTING OF HYPOTHESIS:  A hypothesis is an assumption that we make about the population parameter (which is not necessarily based on statistical data).  Testing of Hypothesis is a procedure or process by which we accept or reject a statistical hypothesis based on a sample taken from the population.  In statistics, we are mainly concerned with studying a population. The most important aspect of a population that is statistically studied is:  The form of the distribution or  The value of the parameters involved in it.  A statistical hypothesis is a statement or assertion about the value of the parameters of a population or the form of the distribution of the population. OBJECTIVES OF HYPOTHESIS: 1. Describe the basic concept of hypothesis testing. 2. Identify and describe the test for a particular problem.
PHARMD GURU Page 4 3. Analyze the types of errors. TYPES OF TESTING OF HYPOTHESIS: For each situation, there are two types of statistical hypotheses: a) Null Hypothesis (H 0 ) b) Alternative Hypothesis (Ha ) a) NULL HYPOTHESIS (H0):  A null hypothesis defines a test where there is no difference between the assumed value and the actual value of the parameter.  It provides a natural idea about the relationship between the variables under study.  It is denoted by H 0 . EXAMPLES: 1. If you want to test whether the Hb% of patients is 12 or not, we can frame the null hypothesis: H 0 : The mean Hb is 12 2. If we want to compare the mean of two groups, we can frame the null hypothesis as: H 0 : There is no difference between the means of the two groups for example, H 0 : The IQ of boys and girls is the same b) ALTERNATIVE HYPOTHESIS (Ha):  When we contradict the null hypothesis, another statement is true (valid).  This is called the alternative hypothesis.  If the null hypothesis is rejected, we accept the alternative hypothesis.  It is denoted by Ha (or H1 , etc.). Examples:  The IQ of boys is greater than girls.