Types of measurements, continuous and discrete measurement, descritive statistics and disribution

define measure of shape?

For distributions summarizing data from continuous measurement scales, statistics can be used to describe how the distribution rises and drops. e.g.Symmetric, scew (negative or positive).

define measure of spread

Getting to know the range, interquartile range and standard deviation. The three most important measures of dispersion are defined as follows: ... Dev. or SD) is the average deviation (spread) of scores in your data set from their mean score for a particular variable. The mean score is the average of scores on a variable.

what is interval data?

Interval data is like ordinal except we can say the intervals between each value are equally split. The most common example is temperature in degrees Fahrenheit. The difference between 29 and 30 degrees is the same magnitude as the difference between 78 and 79 (although I know I prefer the latter). With attitudinal scales and the Likert questions you usually see on a survey, these are rarely interval, although many points on the scale likely are of equal intervals.

define kurtosis

Kurtosis - Like skewness, kurtosis has a specific mathematical definition, but generally it refers to how scores are concentrated in the center of the distribution, the upper and lower tails (ends), and the shoulders (between the center and tails) of a distribution. Mesokurtic - A normal distribution is called mesokurtic. The tails of a mesokurtic distribution are neither too thin or too thick, and there are neither too many or too few scores in the center of the distribution. Platykurtic - Starting with a mesokurtic distribution and moving scores from both the center and tails into the shoulders, the distribution flattens out and is referred to as platykurtic. Leptokurtic - If you move scores from shoulders of a mesokurtic distribution into the center and tails of a distribution, the result is a peaked distribution with thick tails. This shape is referred to as leptokurtic.

what is norminal data?

Nominal basically refers to categorically discrete data such as name of your school, type of car you drive or name of a book. This one is easy to remember because nominal sounds like name (they have the same Latin root).

define mesures of location

Often it is not possible to list all the data or draw a histogram; it would be nice to have one number which best represents a data set. Often where the data lies is of interest, for which purpose a measure of location is useful. There are several measures of location. for example, mean, median and mode.

what is ordinal data?

Ordinal refers to quantities that have a natural ordering. The ranking of favorite sports, the order of people's place in a line, the order of runners finishing a race or more often the choice on a rating scale from 1 to 5. With ordinal data you cannot state with certainty whether the intervals between each value are equal. For example, we often using rating scales (Likert questions). On a 10 point scale, the difference between a 9 and a 10 is not necessarily the same difference as the difference between a 6 and a 7. This is also an easy one to remember, ordinal sounds like order.

define histogram

a form of a bar graph used with interval or ratio-scaled data. Unlike the bar graph, bars in a histogram touch with the width of the bars defined by the upper and lower limits of the interval. The measurement scale is continuous, so the lower limit of any one interval is also the upper limit of the previous interval.

define box plot

a graphical representation of dispersions and extreme scores. Represented in this graphic are minimum, maximum, and quartile scores in the form of a box with "whiskers." The box includes the range of scores falling into the middle 50% of the distribution (Inter Quartile Range = 75th percentile - 25th percentile)and the whiskers are lines extended to the minimum and maximum scores in the distribution or to mathematically defined (+/-1.5*IQR) upper and lower fences.

what is continuous data?

A continuous variable is one that can take any value between two numbers. For example, between 62 and 82 inches, there are a lot of possibilities: one participant might be 64.03891 inches tall, and another person might be 72.67025 inches tall. And, there are literally millions of other possible heights between 62 and 82 inches.

define distribution

A normal distribution is a bell-shaped frequency distribution curve. Most of the data values in a normal distribution tend to cluster around the mean. The further a data point is from the mean, the less likely it is to occur.

what is the definition of discriptive statistic?

Descriptive Statistics. Descriptive statistics is the term given to the analysis of data that helps describe, show or summarise, orginise data(i.e. the sample) in a meaningful way such that, for example, patterns might emerge from the data. ... They are simply a way to describe our data.

define interquartile range

Provides a measure of the spread of the middle 50% of the scores. The IQR is defined as the 75th percentile - the 25th percentile. The interquartile range plays an important role in the graphical method known as the boxplot. The advantage of using the IQR is that it is easy to compute and extreme scores in the distribution have much less impact but its strength is also a weakness in that it suffers as a measure of variability because it discards too much data. Researchers want to study variability while eliminating scores that are likely to be accidents. The boxplot allows for this for this distinction and is an important tool for exploring data.

what is ratio data?

Ratio data is interval data with a natural zero point. For example, time is ratio since 0 time is meaningful. Degrees Kelvin has a 0 point (absolute 0) and the steps in both these scales have the same degree of magnitude.

define skewness

Refers to the degree of asymmetry in a distribution. Asymmetry often reflects extreme scores in a distribution. Positively skewed - A distribution is positively skewed when is has a tail extending out to the right (larger numbers) When a distribution is positively skewed, the mean is greater than the median reflecting the fact that the mean is sensitive to each score in the distribution and is subject to large shifts when the sample is small and contains extreme scores. Negatively skewed - A negatively skwed distribution has an extended tail pointing to the left (smaller numbers) and reflects bunching of numbers in the upper part of the distribution with fewer scores at the lower end of the measurement scale.

define mode

The mean is the most common measure of central tendency and the one that can be mathematically manipulated. It is defined as the average of a distribution is equal to the SX / N. Simply, the mean is computed by summing all the scores in the distribution (SX) and dividing that sum by the total number of scores (N). The mean is the balance point in a distribution such that if you subtract each value in the distribution from the mean and sum all of these deviation scores, the result will be zero.

define median

The median is the score that divides the distribution into halves; half of the scores are above the median and half are below it when the data are arranged in numerical order. The median is also referred to as the score at the 50th percentile in the distribution. The median location of N numbers can be found by the formula (N + 1) / 2. When N is an odd number, the formula yields a integer that represents the value in a numerically ordered distribution corresponding to the median location. (For example, in the distribution of numbers (3 1 5 4 9 9 8) the median location is (7 + 1) / 2 = 4. When applied to the ordered distribution (1 3 4 5 8 9 9), the value 5 is the median, three scores are above 5 and three are below 5. If there were only 6 values (1 3 4 5 8 9), the median location is (6 + 1) / 2 = 3.5. In this case the median is half-way between the 3rd and 4th scores (4 and 5) or 4.5.

define mean

The mode of a distribution is simply defined as the most frequent or common score in the distribution. The mode is the point or value of X that corresponds to the highest point on the distribution. If the highest frequency is shared by more than one value, the distribution is said to be multimodal. It is not uncommon to see distributions that are bimodal reflecting peaks in scoring at two different points in the distribution.

define range

The simplest measure of variability to compute and understand is the range. The range is the difference between the highest and lowest score in a distribution. Although it is easy to compute, it is not often used as the sole measure of variability due to its instability. Because it is based solely on the most extreme scores in the distribution and does not fully reflect the pattern of variation within a distribution, the range is a very limited measure of variability.

define standard deviation

The standard deviation (s or s) is defined as the positive square root of the variance. The variance is a measure in squared units and has little meaning with respect to the data. Thus, the standard deviation is a measure of variability expressed in the same units as the data. The standard deviation is very much like a mean or an "average" of these deviations. In a normal (symmetric and mound-shaped) distribution, about two-thirds of the scores fall between +1 and -1 standard deviations from the mean and the standard deviation is approximately 1/4 of the range in small samples (N < 30) and 1/5 to 1/6 of the range in large samples (N > 100).

define variance

The variance is a measure based on the deviations of individual scores from the mean. As noted in the definition of the mean, however, simply summing the deviations will result in a value of 0. To get around this problem the variance is based on squared deviations of scores about the mean. When the deviations are squared, the rank order and relative distance of scores in the distribution is preserved while negative values are eliminated. Then to control for the number of subjects in the distribution, the sum of the squared deviations, S(X - `X), is divided by N (population) or by N - 1 (sample). The result is the average of the sum of the squared deviations and it is called the variance.

can norminal data be discrete or continuous?

discrete

can interval data be discrete or continuous?

either

can ratio data be discrete or continuous?

either

what are the visualising data?

histogram, distribution, skewness, kurtosis and box plot

can ordinal data be discrete or continuous?

normally discrete but... tied ranks are possible eg. 6,6,6 (not dicrete) some long scale of measurement can be in intervals

what are the levels of measurements?

norminal, ordinal, interval and ratio

what is descrete data?

you want to measure how many siblings a person has and see if people with more siblings have higher IQs. The number of siblings a person has is a discrete variable, or a variable that has only certain values. For example, a person isn't going to have 2.34978 siblings; he will have two siblings or three siblings. Remember how we said that continuous variables are measured but not counted? Well, discrete variables are counted.