Skip to main content

Skewed Distributions

 

Skewed Distributions*



Skewed distributions have one tail that is longer than the other tail compared to the "normal" distribution, which is perfectly symmetrical. Skew affects the location of the central values of the mean and median.

Positive Skew

Below is an image of positive skew, which is also called right skew. Skew is named for the "tail." If you had statistics, you may have heard a professor say, "the tail tells the tale." The tail is the extended part of the distribution close to the horizontal axis.

The large "hump" area to the left represents the location of most data. In behavioural science, the high part often refers to the location of most of the scores. Thus, in positively skewed distributions, most of the participants earned low scores and few obtained high scores as you can see by the low level of the curve, or the tail, to the right.



Negative Skew

As you might expect, negatively skewed distributions have the long tail on the left thus, they are also called left-skewed distributions. A negatively skewed distribution of test scores illustrates an easy test--just what students want. Teachers used to talk about grading on a curve. You can see that such grading could be good or bad for students depending on what curve the teacher uses.



Skewed distributions are nonnormal by definition. 

Recall that in the normal curve, the mean, median, and mode are all at the same point in the middle of the distribution. The value of skew in a normal distribution is zero. 

In skewed distributions, the mode is at the high point and it represents the most frequent value or test score. The mean is pulled in the direction of the long tail and the median falls between the mode and the mean.

Common test questions ask what happens to the mean in skewed distributions. Keep in mind that the mean is "pulled" toward the tail. The mean is an average and, as such, it is most susceptible to extreme scores.

Skew and Data Analysis

Most statisticians accept small deviations from normality when analysing data using procedures designed for a normal distribution like the Pearson r, t tests, and the parametric ANOVAs

The question of acceptable ranges of skew will yield different answers from different sources. A range of +1.5 to -1.5 is a common rule of thumb. An important consideration is the "true" nature of the measured variable. Scientists may argue for flexibility in analysing data from a sample if the variable is known to be normally distributed in the population.

Skewed data can be adjusted and should be adjusted before using parametric tests. One method of adjustment is to convert all scores to logarithms and perform the data analysis on these transformed values.

If the data are too skewed and it is inappropriate to transform the data, then analysts should use nonparametric statistical methods.

Moments

In statistics, the concept of moments is taken from physics. Moments refer to central values. The first moment is found by calculating the value of the mean. The first moment is zero.

The second moment is seen in the calculation of variance, which uses squared values.

The third moment is found by calculating skew and the fourth moment results in the calculation for kurtosis.


Learn more about behavioural statistics in Applied Statistics Concepts for Counselors on AMAZON   or   GOOGLE








Learn More about analyzing data  in Creating Surveys on AMAZON or GOOGLE








Please check out my website   www.suttong.com

   and see my books on   AMAZON       or  GOOGLE STORE

Also, consider connecting with me on    FACEBOOK   Geoff W. Sutton    

   TWITTER  @Geoff.W.Sutton    

You can read many published articles at no charge:

  Academia   Geoff W Sutton     ResearchGate   Geoffrey W Sutton 


*Photo credit- From Bing images labeled "Free to share and use."

Comments

Popular posts from this blog

Personal Self-Concept Questionnaire (PSQ)

  The Personal Self-Concept Questionnaire  ( PSQ )   Overview The Personal Self-Concept Questionnaire (PSQ) measures self-concept based on ratings of 18 items, which are grouped into four categories: Self-fulfilment, autonomy, honesty, and emotional self-concept. Subscales : The PSQ has four subscales 1. Self-fulfilment (6 items) 2. Autonomy (4 items) 3. Honesty (3 items) 4. Emotional self-concept (5 items)  👉 [ Read more about Self-Concept and Self-Identity] The PSQ is a Likert-type scale with five response options ranging from totally disagree to totally agree. Reliability and Validity In the first study, coefficient alpha = .85 and in study two, alpha = .83. Data analysis supported a four-dimensional model (see the four categories above). Positive correlations with other self-concept measures were statistically significant. Other notes The authors estimated it took about 10 minutes to complete the PSQ. Their first study included people ages 12 to 36 ( n = 506). In the second s

Student Self-Efficacy

  Assessment name:  STUDENT SELF-EFFICACY SCALE * Note. This post has been updated to provide an available measure of student self-efficacy. ———- Scale overview:  The  student self-efficacy scale i s a 10-item measure of self-efficacy. It was developed using data from university nursing students in the United States. Authors: Melodie Rowbotham and Gerdamarie Schmitz Response Type:  A four-choice rating scale as follows: 1 = not at all true 2 = hardly true 3 = moderately true 4 = exactly true   Self-efficacy is the perception that a person can act in a way to achieve a desired goal.  Scale items There are 10 items. Examples: I am confident in my ability to learn, even if I am having a bad day. If I try hard enough, I can obtain the academic goals I desire.   Psychometric properties The authors reported that their sample scores ranged from 25 to 40 with a scale mean of 34.23 ( SD  = 3.80. Internal consistency was high at alpha = .84. The authors reported the results of a principal compon

Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ)

  Scale name: Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ) Scale overview: The Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ) is a 29-item self-report measure of both mathematics self-efficacy and mathematics anxiety. Author: Diana Kathleen May Response Type: Items are rated on a 5-point Likert-type scale following a “no response” option: 1 = Never 2 = Seldom 3 = Sometimes 4 = Often 5 = usually Sample items 1. I feel confident enough to ask questions  in my mathematics class. 6. I worry that I will not be able to get a  good grade in my mathematics course.   Subscales and basic statistics for the MSEAQ       Self-Efficacy M = 44.11, SD = 10.78, alpha = .93       Anxiety M = 46.47, SD = 12.61, alpha = .93       Total Scale M = 90.58, SD = 22.78, alpha = .96 Reliability: See the Cronbach’s alpha levels reported above. Validity: There were significant positive correlations with similar measures. The results of a Fa