PRED 354 TEACH. PROBILITY & STATIS. FOR PRIMARY MATH Lesson 2 Variables, Scales of Measurement, Frequency Distribution and its Shape, Percentiles

Variable is a characteristic or condition that changes or has different values for different individuals. Independent variable Dependent variable Confounding variable (is uncontrolled variable that is unintentionally allowed to vary systematically with the IV)

Variable Class AClass B IVlecturingTeaching with discovery DVFinal exam scores CVProf. YProf. X

Scales of measurement Nominal scale consists of a set of categories that have different names. (categorize observations, but do not make any quantitative distinctions between observations) EX: Describe your occupation! Its lists: “sales”, “professional”, “skilled trade”, and “other”

Scales of measurement Ordinal scale consists of a set of categories that are organized in an ordered sequence. (rank observations in terms of size or magnitude) EX: a job supervisor is asked to rank employees in terms of how well they perform their work.

Scales of measurement Interval and ratio scales IS: consists of ordered categories where sll of the categories are intervals of exactly the same size. RS: is an interval scale with additional feature of an absolute zero point. (Ratios of magnitude)

Scales of measurement Interval and ratio scales EX: Measurements of height for a group 8-year-old boys. 44, 51, 49 and so on. Convert this initial measurement into a new scale. A child who is 1 cm taller than avegare now gets score +1. A child who is 4 cm taller than avegare now gets score +4. A child who is 2 cm shorter than avegare now gets score -2.

Frequency Distributions It is an organized tabulation of the number of individuals located in each category on the scale of measurement. EX: The following set of N=20 scores was obtained from a 10 point statistics quiz. 8, 9, 8, 7, 10, 9, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8,

Frequency Distributions Proportions and Percentages It measures the fraction of the total group that is associated with each score proportion p = f/N

Frequency Distributions Grouped frequency distribution tables Rule 1. The grouped frequency distribution table should have about 10 class intervals. Rule 2. The width of each interval should be relatively simple number. Rule 3. The bottom score in each class interval should be a multiple of the width. Rule 4. All intervals should be the same width.

Frequency Distributions Grouped frequency distribution tables EX: An instructor has obtained the set of N=25 exam scores shown here. Scores: 82, 75, 88, 93, 53, 84, 87, 58, 72, 94, 69, 84, 61, 91, 64, 87, 84, 70, 76, 89, 75, 80, 73, 78, 60,

Frequency Distributions Real limits When a continous variable is measured, the resulting measurements correspond to intervals on the number line rather than single points.

Frequency Distribution Graph Histograms Bar Graphs Frequency Distributions Polygon

Frequency Distribution Graph Histograms 1. The height of the bar corresponds to the frequency. 2. The width of the bar extends to the real limits of the score xf EX:

Frequency Distribution Graph Bar graphs 1. The height of the bar corresponds to the frequency. 2. There is a space seperating each bar from the next. Personality type f A10 B5 C20 EX:

Frequency Distribution Graph Frequency distribution polygons 1. The dot is centered above the score. 2. The height of the dot corresponds to the frequency. EX: xf

The Shape of a Frequency Distribution Graph 1. Shape. 2. Central tendency. 3. Variability

The Shape of a Frequency Distribution Graph Type of Shape 1. Symmetrical distribution. 2. Skewed distribution (the scores tend to pile up toward one end of the scale)

Percentiles, Percentile Ranks and Interpolation The rank or percentile rank of a particular score is defined as the percentage of individuals in the distribution with scores at or below the particular value. When a score is identified by its percentile rank, the score is called a percentile.

Percentiles, Percentiles Ranks and Interpolation EX: 1. Complete the table! 2. What is the 92nd percentile? 3. What is the percentile rank for X=6.5? Xfcfc%

Percentiles, Percentiles Ranks and Interpolation The values that are not specifically reported in the table can be estimated through intermediated values by using a standard procedure known as interpolation. Upper/lower real limits, EX: 1. What is the percentile rank for X=7? Xfcfc%

Percentiles, Percentiles Ranks and Interpolation EX: 1. What is the 50 th percentile? Xfcfc%