Presentation on theme: "Introduction to Educational Statistics"— Presentation transcript:
1 Introduction to Educational Statistics Joseph Stevens, Ph.D., University of Oregon(541) ,
2 WHAT IS STATISTICS?Statistics is a group of methods used to collect, analyze, present, and interpret data and to make decisions.
3 POPULATION VERSUS SAMPLE A population consists of all elements – individuals, items, or objects – whose characteristics are being studied. The population that is being studied is also called the target population.
4 POPULATION VERSUS SAMPLE cont. The portion of the population selected for study is referred to as a sample.
5 POPULATION VERSUS SAMPLE cont. A study that includes every member of the population is called a census. The technique of collecting information from a portion of the population is called sampling.
6 POPULATION VERSUS SAMPLE cont. A sample drawn in such a way that each element of the population has an equal chance of being selected is called a simple random sample.
7 TYPES OF STATISTICSDescriptive Statistics consists of methods for organizing, displaying, and describing data by using tables, graphs, and summary measures.
8 TYPES OF STATISTICSInferential Statistics consists of methods that use information from samples to make predictions, decisions or inferences about a population.
9 Basic DefinitionsA variable is a characteristic under study that assumes different values for different elements. A variable on which everyone has the same exact value is a constant.
10 Basic DefinitionsThe value of a variable for an element is called an observation or measurement.
11 Basic DefinitionsA data set is a collection of observations on one or more variables.A distribution is a collection of observations or measurements on a particular variable.
12 TYPES OF VARIABLES Quantitative Variables Discrete VariablesContinuous VariablesQualitative or Categorical Variables
13 Quantitative Variables cont. A variable whose values are countable is called a discrete variable. In other words, a discrete variable can assume only a limited number of values with no intermediate values.
14 Quantitative Variables cont. A variable that can assume any numerical value over a certain interval or intervals is called a continuous variable.
15 Categorical Variables A variable that cannot assume a numerical value but can be classified into two or more categories is called a categorical variable.
16 Scales of MeasurementHow much information is contained in the numbers?Operational Definitions and measurement proceduresTypes of ScalesNominalOrdinalIntervalRatio
17 Descriptive Statistics Variables can be summarized and displayed using:TablesGraphs and figuresStatistical summaries:Measures of Central TendencyMeasures of DispersionMeasures of Skew and Kurtosis
18 Measures of Central Tendency Mode – The most frequent score in a distributionMedian – The score that divides the distribution into two groups of equal sizeMean – The center of gravity or balance point of the distribution
19 MedianThe calculation of the median consists of the following two steps:Rank the data set in increasing orderFind the middle number in the data set such that half of the scores are above and half below. The value of this middle number is the median.
20 Arithmetic MeanThe mean is obtained by dividing the sum of all values by the number of values in the data set.Mean for sample data:
21 Example: Calculation of the mean Four scores: 82, 95, 67, 92
32 Normal distribution with mean μ and standard deviation σ x
33 Total area under a normal curve. The shaded area is 1.0 or 100%μx
34 A normal curve is symmetric about the mean Each of the two shaded areas is .5 or 50%.5.5μx
35 Areas of the normal curve beyond μ ± 3σ. Each of the two shaded areas is very close to zeroμ – 3σμμ + 3σx
36 Three normal distribution curves with the same mean but different standard deviations σ = 5σ = 10σ = 16xμ = 50
37 Three normal distributions with different means but the same standard deviation σ = σ = σ = 5µ = µ = µ = x
38 Areas under a normal curve For a normal distribution approximately68% of the observations lie within one standard deviation of the mean95% of the observations lie within two standard deviations of the mean99.7% of the observations lie within three standard deviations of the mean
42 Converting an X Value to a z Value For a normal random variable X, a particular value of x can be converted to its corresponding z value by using the formulawhere μ and σ are the mean and standard deviation of the normal distribution of x, respectively.
43 The Logic of Inferential Statistics Population: the entire universe of individuals we are interested in studyingSample: the selected subgroup that is actually observed and measured (with sample size N)Sampling Distribution of a Statistic: a distribution of samples like ours
44 The Three Distributions Used in Inferential Statistics I. PopulationIII. Sampling Distribution of the StatisticII. Sample