《统计学》课程教学资源（PPT课件讲稿）Chapter 07 定量变量的假设检验 hypothesis testing for quantitative variable

Chapter-7hypothesiststing for quantitative variable 2021/1/29 1

2021/1/29 1

●●● ●●●● ●●●●● contents ●●●● ●●0●● ●●●● ●●●● 1 introduction 2. Hypothesis testing 2. 1 One sample t test 2.2 two independent-samples t test 2.3 Paired-samples t test 21/1/29

2021/1/29 2 contents 1. introduction 2. Hypothesis testing 2.1 One sample t test 2.2 two independent-samples t test 2.3 Paired-samples t test

●●● ●●●● Hypothesis testing ●●●●● ●●●● Aim: Is the average English score of students from 2 0000 ●●●● schools different or same? Methods 1. Compute and compare two population mean directly ≠ XINI 21/1/29

2021/1/29 3 Hypothesis testing Aim: Is the average English score of students from 2 schools different or same? Methods1. Compute and compare two population mean directly 1 2 1 2 = 

●●● ●●●● Hypothesis testing ●●●●● ●●●● Aim: Is the average English score of students from 2 0000 ●●●● schools different or same? Methods 2 Do a sampling study and then do hypothesis testing =100 X1=82,S1=9.5 =150 X2=81 8.3 XINI 2021/1/29

2021/1/29 4 Hypothesis testing Aim: Is the average English score of students from 2 schools different or same? Methods 2 Do a sampling study and then do hypothesis testing 82, 9.5 100, 1 1 1 = = = X S n 81, 8.3 150, 2 2 2 = = = X S n 1 2 = 

●●● ●●●● ●●●●● ●●●● The reason that81≠82 ●●0●● ●●●● ●●●● y True difference between two population means √ Chance( sampling error So the hypothesis task is to differentiate that the difference between two samples is from the true difference between two population means or from chance 21/1/29

2021/1/29 5 The reason that ✓ True difference between two population means. ✓ Chance (sampling error) So the hypothesis task is to differentiate that the difference between two samples is from the true difference between two population means or from chance. 81 82

Section I Introduction ●●●●● 21/1/29

2021/1/29 6 SectionⅠ Introduction

●●● ●●●● ●●●●● ●●●● ●●0●● ●●●0 ●●●● The purpose of hypothesis testing is to aid the clinician researcher or administrator in reaching a conclusion concerning a population by examining a sample from the population r "Is the effect of the new drug significant than the old drug? which one is better between the two operations? Did the large amounts of advertising describe the benefits of new drugs?” 21/1/29

2021/1/29 7 The purpose of hypothesis testing is to aid the clinician, researcher, or administrator in reaching a conclusion concerning a population by examining a sample from the population. ✓ “Is the effect of the new drug significant than the old drug?”, ✓ “which one is better between the two operations? ” ✓ “Did the large amounts of advertising describe the benefits of new drugs?

●●● ●●●● ●●●●● ●●●● 1 What does statistic test do? ●●0●● ●●●0 ●●●● EXAMPLE们] General the average height of7 years old° children increases 4cm in one year. Some researcher let 100 of 7 years old children get a bread appended lysine in everyday. After one year the average height of 100 children increases 5cm. and the standard deviation is 2cm Basing on the data can we think: lysine benefits growth of stature of 7 years old children? 21/1/29

2021/1/29 8 1 What does statistic test do? [EXAMPLE1] General the average height of 7 years old children increases 4cm in one year. Some researcher let 100 of 7 years old children get a bread appended lysine in everyday. After one year the average height of 100 children increases 5cm, and the standard deviation is 2cm. Basing on the data can we think: lysine benefits growth of stature of 7 years old children?

●●● ●●●● ●●●●● ●●●● ●●0●● ●●●● ●●●● Suppose ↓=0 Compute Ts Find p-value 21/1/29

2021/1/29 9 Suppose ＝0 Compute T.S Find P-value

●● ●● STEPS。 2 Steps of hypothesis testing The statisticians have made a set of steps as fixed as legal procedure, and made some formulas to calculate test statistic (Ts) 21/1/29

2021/1/29 10 2 Steps of hypothesis testing The statisticians have made a set of steps as fixed as legal procedure, and made some formulas to calculate test statistic (T.S). STEPS