# Statistics in Research: Introduction Measurement for ACET 2021

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## Statistics

- The word statistics comes from the Italian word statista, a person dealing with affairs of state (from stato, “state” ) . It was originally called “state arithmetic,” involving the tabulation of information about nations, especially for the purpose of taxation and planning the feasibility of wars
- statistics is a branch of mathematics that focuses on the organization, analysis, and interpretation of a group of numbers
- Playing with numbers
- SPSS
- descriptive statistics procedures for summarizing a group of scores or otherwise making them more understandable.
- inferential statistics procedures for drawing conclusions based on the scores collected in a research study but going beyond them

## Variable, Value and Score

- How stressed have you been in the last weeks, on a scale of 0 to 10, with 0 being
*not at all stressed*and 10 being*as stressed as possible?* - level of stress is a variable, which can have values from 0 to 10, and the value of any particular person՚s answer is the person՚s score
- variable characteristic that can have different values.
- values possible number or category that a score can have.
- score particular person՚s value on a variable.

## Level of Measurement

- Numeric variables are also called quantitative variables
- An equal-interval variable is a variable in which the numbers stand for approximately equal amounts of what is being measured - age
- ratio scale. An equal-interval variable is measured on a ratio scale if it has an absolute zero point. An absolute zero point means that the value of zero on the variable indicates a complete absence of the variable – two times siblings
- rank-order variable, is a variable in which the numbers stand only for relative ranking. (rate something)
- nominal variable are values that are categories (that is, they are names rather than numbers) . Also called categorical variable – gender, religion

## Discrete and Continuous Variable

- A discrete variable is one that has specific values and cannot have values between the specific values. Nominal variables, such as gender, religious affiliation, and college major can also be considered to be discrete variables
- With a continuous variable, there are in theory an infinite number of values between any two values. Age, height, weight, and time are examples of continuous variables

## Frequency Table

- 30 Students and Stress rating of all
- The 30 students′ scores (their ratings on the scale) are: 8, 7, 4, 10, 8, 6, 8, 9, 9, 7, 3, 7, 6, 5, 0, 9, 10, 7, 7, 3, 6, 7, 5, 2, 1, 6, 7,10, 8,8.
- frequency table because it shows how frequently (how many times) each score was used (mark from lowest to highest values, mark scores, from lowest to highest) - makes it easy to see the pattern in a large group of scores
- A frequency table that uses intervals is called a grouped frequency table. – information more directly understandable (inclusive series and exclusive series)
- Histogram: barlike graph of a frequency distribution in which the values are plotted along the horizontal axis and the height of each bar is the frequency of that value; the bars are usually placed next to each other without spaces, giving the appearance of a
__city skyline__

## Unimodal, Bimodal and Multimodal

- In the stress ratings study, the most frequent value is 7, giving a graph only one very high area. This is a unimodal distribution. If a distribution has two fairly equal high points, it is a bimodal distribution. Any distribution with two or more high points is called a multimodal distribution.
- a distribution with values of all about the same frequency is a rectangular distribution

## Symmetrical and Skewed Distribution, Kurtosis

**symmetrical distribution** (if you fold the graph of a symmetrical distribution in half, the two halves look the same) . A distribution that clearly is not symmetrical is called a **skewed distribution**

__The side with the__*fewer*__scores (the side that looks like a tail) is considered the direction of the skew__- A distribution that is skewed to the right is also called
*positively skewed*. A distribution skewed to the left is also called*negatively skewed* *skew*comes from the French*queue*, which means line or tail. Thus, the direction of the skew is the side that has the long line, or tail.- floor effect: situation in which many scores pile up at the low end of a distribution (creating skewness to the right) because it is not possible to have any lower score. (a family cannot have fewer than zero children)
- ceiling effect situation in which many scores pile up at the high end of a distribution (creating skewness to the left) because it is not possible to have a higher score. (distribution of adults′ scores on a multiplication table test)
- bell-shaped standard or normal curve
- Kurtosis is how much the shape of a distribution differs from a normal curve in terms of whether its curve in the middle is more peaked or flat than the normal curve
- Distributions with a flatter curve usually have fewer scores in the tails of the distribution than the normal curve

## Misleading Graphs

- Not using equal intervals
- Exaggeration of Proportions

✍ Manishika