Introduction To Statistics Lectures PDF

Introduction To Statistics  Why we are studying statistics? 1. Data are everywhere 2. Statistical techniques are used to make many decisions that affect our lives 3. No matter what your career, you will make professional decisions that involve data. An understanding of statistical method...

Introduction To Statistics  Why we are studying statistics? 1. Data are everywhere 2. Statistical techniques are used to make many decisions that affect our lives 3. No matter what your career, you will make professional decisions that involve data. An understanding of statistical methods will help you make these decisions efectively Applications of statistical concepts in the business world  Finance – correlation and regression, index numbers, time series analysis  Marketing – hypothesis testing, chi-square tests, nonparametric statistics  Personel – hypothesis testing, chi-square tests, nonparametric tests  Operating management – hypothesis testing, estimation, analysis of variance, time series analysis  Statistics  The science of collectiong, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions ‫ علم جمع البيانات وتنظيمها وتقديمها وتحليلها وتفسيرها للمساعدة في‬ ‫اتخاذ قرارات أكثر فاعلية‬  Statistical analysis – used to manipulate summarize, and investigate data, so that useful decision-making information results. ، ‫ يستخدم لمعالجة التلخيص والتحقيق في البيانات‬- ‫ التحليل اإلحصائي‬.‫بحيث تكون نتائج معلومات صنع القرار مفيدة‬  Types of statistics  Descriptive statistics – Methods of organizing, summarizing, and presenting data in an informative way ‫ طرق تنظيم وتلخيص وعرض البيانات بطريقة إعالمية‬- ‫ اإلحصاء الوصفي‬  Inferential statistics – The methods used to determine something about a population on the basis of a sample ‫ الطرق المستخدمة لتحديد شيء ما عن مجموعة‬- ‫ اإلحصائيات االستداللية‬ ‫سكانية على أساس عينة‬  Population –The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest  Sample – A portion, or part, of the population of interest Difference between Population and Sample  Population  The entire group of individuals is called the population.  For example, a researcher may be interested in the relation between class size (variable 1) and academic performance (variable 2) for the population of third-grade children. 8  Sample  Usually populations are so large that a researcher cannot examine the entire group.  Therefore, a sample is selected to represent the population in a research study.  The goal is to use the results obtained from the sample to help answer questions about the population. 9  Inferential Statistics ‫اإلحصاء‬ ‫االستنتاجي‬  Estimation  e.g., Estimate the population mean weight using the sample mean weight  Hypothesis testing  e.g., Test the claim that the population mean weight is 70 kg Inference is the process of drawing conclusions or making decisions about a population based on sample results ‫االستدالل هو عملية استخالص النتائج أو اتخاذ القرارات بشأن مجموعة سكانية بنا ًءا على نتائج العينة‬  Inferential Statistics  Inferential statistics are methods for using sample data to make general conclusions (inferences) about populations.  Because a sample is typically only a part of the whole population, sample data provide only limited information about the population.  As a result, sample statistics are generally imperfect representatives of the corresponding population parameters. 12  Sampling‫أخذ العينات‬ -The sample should have the same characteristics as the population it is representing..‫يجب أن يكون للعينة نفس الخصائص مثل السكان الذين تمثلهم‬ Sampling can be:  with replacement: a member of the population may be chosen more than once (picking the candy from the bowl)  without replacement: a member of the population may be chosen only once (lottery ticket)  Sampling methods Sampling methods can be:  random (each member of the population has an equal chance of being selected))‫(لكل فرد من السكان فرصة متساوية في االختيار‬  nonrandom -The actual process of sampling causes sampling errors..‫ العملية الفعلية ألخذ العينات تسبب أخطاء في أخذ العينات‬- -For example, the sample may not be large enough or representative of the population..‫ قد ال تكون العينة كبيرة بما يكفي أو ال تمثل السكان‬، ‫ على سبيل المثال‬- -Factors not related to the sampling process cause nonsampling errors..‫ تتسبب العوامل غير المرتبطة بعملية أخذ العينات في حدوث أخطاء غير متعلقة بأخذ العينات‬- -A defective counting device can cause a nonsampling error..‫ يمكن أن يتسبب جهاز العد المعيب في حدوث خطأ في عدم أخذ العينات‬-  Random sampling methods 1- Simple random sample (each sample of the same size has an equal chance of being selected) )‫ عينة عشوائية بسيطة (كل عينة من نفس الحجم لها فرصة متساوية في االختيار‬ 2- Stratified sample (divide the population into groups called strata and then take a sample from each stratum) ‫عينة طبقية (ق ّسم السكان إلى مجموعات تسمى طبقات ثم أخذ عينة‬ )‫من كل طبقة‬ 3- Cluster sample (divide the population into strata and then randomly select some of the strata. All the members from these strata are in the cluster sample.) ‫ جميع األعضاء‬.‫ضا من الطبقات بشكل عشوائي‬ ً ‫سم السكان إلى طبقات ثم اختر بع‬ ّ ‫عينة عنقودية (ق‬ ).‫من هذه الطبقات في العينة العنقودية‬ 4- Systematic sample (randomly select a starting point and take every n-th piece of data from a listing of the population) )‫ عينة منهجية (حدد عشوائيا ً نقطة بداية وأخذ كل جزء ن من البيانات من قائمة السكان‬  Descriptive Statistics  Collect data  e.g., Survey  Present data  e.g., Tables and graphs  Summarize data  e.g., Sample mean = X i n  Descriptive Statistics  Descriptive statistics are methods for organizing and summarizing data.  For example, tables or graphs are used to organize data, and descriptive values such as the average score are used to summarize data. ‫ تُستخدم الجداول أو الرسوم البيانية لتنظيم‬، ‫على سبيل المثال‬.‫ ويتم استخدام القيم الوصفية مثل متوسط الدرجة لتلخيص البيانات‬، ‫البيانات‬  In the descriptive Statistics a descriptive value for a population is called a parameter and a descriptive value for 17 a sample is called a statistic.  Statistical data  The measurements obtained in a research study are called the data.  The goal of statistics is to help researchers organize and interpret the data.  Statistical data are usually obtained by counting or measuring items.  Primary data are collected specifically for the statistical analysis  Secondary data have already been compiled and are available for statistical analysis  The data can be: A variable is an item of interest that can take on many different numerical values.  A constant has a fixed numerical value.  Variables  A variable is a characteristic or condition that can change or take on different values.  Most research begins with a general question about the relationship between two variables for a specific group of individuals. 19  Types of Variables  Variables can be classified as discrete or continuous.  Discrete variables (such as class size) consist of indivisible categories ‫ (مثل حجم الفصل) تتكون من فئات غير قابلة للتجزئة‬.....‫المحددة‬..‫ المتغيرات المنفصلة‬  continuous variables (such as time or weight) are infinitely divisible into whatever units a researcher may choose. ‫ المتغيرات المستمرة (مثل الوقت أو الوزن) قابلة للقسمة بال حدود إلى أي وحدات قد يختارها‬.‫الباحث‬  For example, time can be measured to the nearest minute, second, half-second, etc.  Measuring Variables  To establish relationships between variables, researchers must observe the variables and record their observations..‫ يجب على الباحثين مالحظة المتغيرات وتسجيل مالحظاتهم‬، ‫ إلنشاء عالقات بين المتغيرات‬  This requires that the variables be measured.  The process of measuring a variable requires a set of categories called a scale of measurement and a process that classifies each individual into one category.  Types of Measurement Scales 1- A nominal scale is an unordered set of categories identified only by name. -Nominal measurements only permit you to determine whether two individuals are the same or different..‫المقياس االسمي هو مجموعة غير مرتبة من الفئات المحددة باالسم فقط‬ ‫تسمح لك القياسات االسمية فقط بتحديد ما إذا كان شخصان متماثالن أو‬.‫مختلفان‬  Types of Measurement Scales 2- An ordinal scale is an ordered set of categories. - Ordinal measurements tell you the direction of difference between two individuals..‫ المقياس الترتيبي هو مجموعة مرتبة من الفئات‬-2.‫ تخبرك القياسات الترتيبية اتجاه االختالف بين شخصين‬-  Types of Measurement Scales 3- An interval scale is an ordered series of equal-sized categories. -Interval measurements identify the direction and magnitude of a difference. -The zero point is located arbitrarily on an interval scale..‫مقياس الفاصل الزمني هو سلسلة مرتبة من الفئات المتساوية الحجم‬-.‫تحدد قياسات الفترات اتجاه وحجم االختالف‬-.‫تقع نقطة الصفر بشكل تعسفي على مقياس فاصل‬-  Types of Measurement Scales 4- A ratio scale is an interval scale where a value of zero indicates none of the variable. - Ratio measurements identify the direction and magnitude of differences and allow ratio comparisons of measurements..‫مقياس النسبة هو مقياس فاصل حيث تشير القيمة صفر إلى عدم وجود متغير‬-.‫ تحدد قياسات النسبة اتجاه وقيمة الفروق وتسمح بمقارنات نسبية للقياسات‬-