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Summary  Applied statistics for the behavioral sciences

1.1 The meaning and role of statistics

What does statistics mean to the researcher in the behavioral sciences?
Statistics are a collection of theory and methods applied for the purpose of understanding data

Statistics are the methods or procedures that researchers apply in an attempt to understand data.

1.2.1 The summation operator

What is the summation operator and what does it stand for?
The summation operator is denoted by the Greek capital sigma: , which stands for 'the sum of'.

indicates the summing of whatever immediately follows in the expression.

The subscripts on the Xs mean that they stand for different numbers.
Xi (cap X, subscript i; X, sub i) is the general symbol for a number.
The notation under the indicates the first number in the summation, and the number above indicates how far the summation continues. When the number above is N, this means that the summation concludes with the Nth, or last number.

Waar staat Xi (X, sub i) voor?
Xi is het algemene symbool voor een nummer.

1.2.2 Special indicators of arithmetic operations

The square root: squaring a number is multiplying a number by itself. The square is denoted Y2 (Y^2), or Y to the second power. The number 2 is called the exponent, the power to which the number is raised. If Y is raised to the fourth power, Y4, we have Y^4 = (Y)(Y)(Y)(Y) = (5)(5)(5)(5) = 625.
The square root (36) = 6, because (6)(6) = 36.
The absolute value of a number is the value of the number without regard to its algebraic sign. The absolute number of 7, which is denoted 7, is 7.

1.2.3 Order of operations

1. Perform any operations in parentheses or brackets or braces. If there are parentheses within brackets, perform the operations from the inside out.
2. Perform operations with exponents, such as squares or square roots, if they were not contained within the parentheses.
3. When the operations are complete, clear the expression of parentheses, do the multiplications and divisions, then the additions and subtractions.

1.2.4 Rounding numbers

After every arithmetic operation that yields a fraction, carry the decimal to three places and round to two places more than there were in the original data.
If the number beyond the last digit to be reported is equal to or greater than 5, increase the last digit to the next higher number. If the number beyond the last digit is less than 5, the last digit remains the same.

1.3 Variables

A constant is a characteristic that assumes the same value for all members of a group under study. A variable if a characteristic that can take on different values for different members of a group being studied.

Independent variables are variables that the researcher controls or manipulates in accordance with the purpose or the investigation. They can be either manipulated or classifying variables.
A dependent variable is a measure of the effect of the independent variable. As the independent variable is changed or varied, the researcher observes the change in the dependent variable to determine how it is associated with changes in the independent variable.

1.4 Scales of measurement

Measurement scales of variables are classified in a hierarchy based on their degree of precision. This hierarchy includes the nominal, ordinal, interval, and ratio scales.

1.4.1 Nominal scale

In nominal measurement there is no logical ordering of the categories. We cannot order these categories from lowest to highest in any other kind of numerical ordering. A nominal scale simply classifies, nothing more.
1. Data categories are mutually exclusive: an object can belong to only one category.
2. Data categories have no logical order.

1.4.2 Ordinal scale

The ordinal scale not only classifies objects or characteristics, but also gives a logical order to the classification.
1. Data categories are mutually exclusive.
2. Data categories have some logical order.
3. Data categories are scaled according to the amount of the particular characteristic they possess.
Latest added flashcards
Xi is het algemene symbool voor een nummer.
The summation operator is denoted by the Greek capital sigma: , which stands for 'the sum of'.
Statistics are a collection of theory and methods applied for the purpose of understanding data