İSTATİSTİK I

The outcomes obtained on all variables for one element in the data set is called a case. In this table, the outcomes on the four variables for John constitutes a case. name,gender, age, salary= John, Male, 52, 4300

Ordinal scales of measurement have the property of both classifying and magnitude. Subjects are categorized into different rank ordered groups. Each value on the ordinal scale has a unique meaning, and it has an ordered relationship to every other value on the scale. From the table,  we can conclude that the customer prefers historical fiction to science fiction, science fiction to detective fiction, detective fiction to romance. However, even though the differences in the consecutive numbers of the ranks are equal, we cannot say that how much the customer prefers one type of book over another type. That is, consecutive categories do not represent equal differences of the measured attribute.

In observational studies, researchers observe subjects and measure variables of interest without any intervention to the subjects. In this case, the teacher wants to learn if the new strategy affects the learning. The researcher needs to manipulate some of the variables and try to determine how the manipulation influences other variables.

Rated responses generally include three-point, five-point, and seven-point scales. A rating scale should provide more than two options. The mostly used rating scale is five-point Likert (1932) type scale. Likert type scale can be designed in the following forms.
• Strongly Agree - Agree – Undecided / Neutral - Disagree - Strongly Disagree
• Always - Often - Sometimes - Seldom - Never
• Extremely - Very - Moderately - Slightly - Not at all
• Excellent - Above Average - Average - Below Average - Very Poor

Sample in statistics means a small part of the targeted population. A sample must be representative of the population. Sampling methods must be used to achieve a representative sampling. Otherwise, the sampling does not represent the targeted population and the results yield biased or inaccurate information.

Error in population specification occurs when the researcher determines an inappropriate population from which to collect data.

Error in measurement can be described as any discrepancy between the actual result obtained and the correct result that would be provided by an ideal procedure. From a statistical point of view any observation is composed of the true value plus some random error value. However, all error is not random. The error component of any observation can be divided into two subcomponents, random error and systematic error.
Random errors are caused by unknown and unpredictable factors that randomly affect measurement of the variable across the sample. For example, a school teacher conducted a particular survey on the students to measure their performances. Some students may be feeling in a good mood and others may be depressed. This may artificially deflate performance scores of the depressed students. Random error does not have any consistent effects across the entire sample. Instead, it affects observed scores up or down randomly. Random error adds variability to the data and it is sometimes called noise.
Systematic errors are reproducible inaccuracies that shift measurements from their true value by the same amount and consistently in the same direction. This type error arises from problematic, poor calibrated or incorrectly used equipment. For example, an industrial scale showed heavier weights than it should be for a particular product because it was not calibrated properly and thereby provided incorrect measurements.

Sometimes raw data in a frequency distribution table yield more useful information. To construct a frequency distribution table, the measurement categories and the number of responses within a given measurement category are used.

Interpretation of the frequency distribution table can be easier or clearer when we use the percentage of the frequency. Percentage representation of frequency can also be displayed in the frequency distribution table. Percentage of frequency is called the relative frequency and the table is called relative frequency distribution table. Relative frequency can be used for both quantitative and qualitative variables. The relative frequency for a class is calculated as follows: Relative Frequency = fi/ n where, fi is the frequency for class i and n is the sample size. In this case, fi is 21and n is 85. The percentage of relative frequency is 24,7.

We can obtain such information by using cumulative frequency. Cumulative frequency is used to determine the number of elements that falls above or below a particular value in a given class interval. The cumulative frequency of a class is calculated by adding its frequency to the sum of all predecessor class frequencies. Consequently, the last value must be equal to the sample size.

In this table, there are two categorical variables. One is the variable gender which has two categories, female and male. The other categorical variable is the variable excel knowledge which has two categories, yes and no. Thus, there are two categorical variables.

Ifa data set includes two different categorical variables, we use a two-way table (contingency table) todemonstrate the relationship and interaction of the two categorical variables. A two-way table of counts  organizes data about two categorical variables measured from the same set of individuals. A contingency table is a special type of frequency distribution table, where two variables are shown simultaneously and
it is used to determine if one categorical variable is related to another categorical variable.

When we create the contingency table with row and column percentages, within the people who do not have technical knowledge (No) the percentage of male and female are 50% and 50%, respectively.

Variable-Observation-Case

Career Plans: Nominal scale

Age: Ratio scale

1

2

The independent variable s are the length of time spent sleeping, studying and the number of questions solved while the dependent variable is the exam score.

Observational study

Rated responses

Sampling error

0,43

40% under 30 years old.

60% of them 30 & over.