Standards for Interpreting Statistics Made Easy

By Ihor Cap

Cartoon by John Landers, Courtesy of Causeweb.org

One of the biggest problems faced by researchers and practitioners alike is the lack of helpful standards to make sense of all the research data. All the statistical data results I mean. The problem becomes more pressing if you are the person who must read that data, analyze it and even worse, present or discuss it with members of your audience. There is no time to waste because you needed it yesterday, right? If this sounds like you, then this article sums it up for you briefly.

More specifically, this article will expose you to a range of useful statistics and provide you with meaningful “tools” that will help you easily explain their worth to others. The meaning of those short classifying phrases is limited to interpreting PPM coefficients, test-retest stability coefficients, adjusted R-square values, index effect sizes, reliability or internal consistency coefficients, difficulty indices, item-discrimination indices or point biserial correlation coefficients. These apply to any research study.

Interpreting Pearson Product Moment Correlation or PPM Coefficients

Davis (1971 in Chappell,1984) labeled Pearson coefficient (zero order) correlations between .01 to .09 as “negligible”, .10 to .29 as “low”, .30 to .49 as “moderate”, .50 to .69 as “substantial” and .70 or higher as “very strong.” These short classifying phrases will help facilitate consistency in the interpretation of size (or strength) of all Pearsonian and adjusted R-Square values obtained in any study. These interpretations apply to simple correlation coefficients (or PPM correlation coefficients) as well as Pearsonian test-retest stability coefficients.

Interpreting the index Effect Size (ES)

The index Effect Size (ES), defined as “the mean difference between the treated and control subjects divided by the standard deviation of the control group,” (Smith, Glass & Miller, 1980) is often used to evaluate the magnitude of the experimental effect in standard deviation units. Schermer (1988) reviewed ES outcomes and devised a set of standards to facilitate consistency in the interpretation of these outcomes. Any researcher can adopt these standards. In quantitative terms, point size estimates of less than .2 are “small” effects, .5 as “medium” in size and higher than .5 as “large.”  Use these benchmarks to estimate the magnitude of the effect over the posttest or delayed posttest measure.

Interpreting Reliability Correlations or Internal Consistency Coefficients of Exams or Teacher-Made Tests

Fox (1969) labeled reliability correlations between 0 and .50 as “low”, .51 to .70 as “moderate”, .71 to .86 as “high”, and above .86 as “very high” for the purposes of educational research. Another researcher’s review of evaluation devices identified minimum reliability coefficient values of .85 for making effective decisions about individuals and .65 for groups (Ridley, 1976). Nothing below .50 for the latter would suffice (Jordan, 1953; Nunnally, 1967). Additionally, Diederich (1960), states that most teacher-made tests “…regarded as good, usable tests achieved reliabilities between .60 and .80.”  Lower test reliabilities may be acceptable for group research projects in education (Borg and Gall, 1989). Short form tests can expect slight drops in reliability in spite of retaining the best test items (Borg and Gall, 1989). If the reduction in length represents a negligible decrease in reliability, you will gain substantial savings in time-spent writing an exam. These short classifying phrases will facilitate consistency in the interpretation of size (or strength) of reliability coefficients for all instruments or exams used in any research project. Some well-known statistics that fall into this category include Cronbach’s Alpha, the Kuder-Richardson Formula 20 (KR-20) and the Kuder-Richardson Formula 21 (KR-21).

Interpreting the Quality or Power of each test item (or question) for the purposes of Item or Exam Analysis

Selection of  final composite test items (or questions) proceeds with the goal of obtaining a representative range of difficulties, and the highest possible item discrimination values balanced vis-à-vis the highest possible coverage over the Table of Specifications for content validity maintenance, thereby reducing researcher bias in the selection process (Richter, 1980).

Using the guidelines proposed by Kromhout (1987), test items passed by 80 percent of exam takers are extremely easy and items passed by less than 20 percent are extremely difficult for exam takers in a field-trial “test” study. In other words, removing difficulty indices above .80 and below .20 ensures that all exam takers receive a test with a moderate range of difficulty.

The item-discrimination index, which analyzes the power of each test (question) item, is the “Point Biserial Correlation Coefficient” (PBCC). Researchers consider this coefficient “… to be the single best measure of the effectiveness of a test item” (Lewis, 1989). Lewis (1989) proposes the following range of numbers and interpretations. A test item (or question) with a PBCC of .30 and above is a very good discriminator of the top 24% from the bottom 24% scoring groups. A test item with a PBCC of .20 to .29 is reasonably good, but subject to improvement. Test items with PBCCs of .09 to .19 are marginal, usually needing improvement, and those below .09 are poor, to be improved or discarded.  

Conclusions and Recommendations

This concludes your reading on “Standards for Interpreting Statistics Made Easy.” Researchers and practitioners are encouraged to use these standards and benchmarks in their future efforts related to analyzing, interpreting or explaining, and presenting their statistical data.  I hope that this read has made you a little less fearful of statistics and a little more confident in your newly acquired knowledge of the meaning and worth of these numerical performance benchmarks.

Author Information:

Ihor Cap, Ph.D. is an Education Research Specialist, Web Author and Marketing & Promotions Manager for EZREKLAMA.

References:

The complete reference to each of the cited sources is available in the following document cited below.

Cap, Ihor. (1995). The usefulness and effectiveness of a self-instructional print module on multicultural behaviour change in apprentices in Manitoba. Unpublished doctoral dissertation, Florida State University, Tallahassee. Available from University Microfilms Inc., P.O. Box 1764, Ann Arbor, MI 48106-1764 USA.  (377 pages)

 

Cartoon Picture by John Landers, Courtesy of Causeweb.org

This article first appeared August 24, 2009 in http://articlesandblogs.ezreklama.com.

VIEWS TO DATE

“Super Foods” for Health and Weight Control

By Ihor Cap

Most of us are busily engaged with all kinds of diets and forms of exercise these days. After all, most of us already know that eating right and being physically active are two important cornerstones of health and longevity.  Less of us know, however, that our food choices may be killing us.  Statistics show that a whopping 35 percent of all cancers are associated with what we eat.  The good news here is that it may be prevented. The key is choosing the right foods. We can make healthier choices, says Dr Bridget Farham, by selecting foods with certain compounds that help prevent or significantly reduce the risk of colon, rectum, oesophageal, and stomach related cancers.

Super Foods

While many experts will tell you that eating a balanced meal is vital to your whole essence, more research scientists are also coming to know that certain foods have better fighting power against a host of cancers and cardiovascular disease. Often referred to as “superfoods”, Maria Croce lists 15 such special cancer-fighting foods.  Each of these foods purports to counteract or neutralize the negative effects of cancer and other illnesses. However, it’s U.C Santa Barbara environmental toxicologist, Dr. J. Robert Hathrill and his book, Eat to Beat Cancer (Renaissance Books, New York, 1998) that is stimulating greatest interest among professionals and the public alike. Dr. Hathrill also produced a list of so-called super foods, plant-based albeit, but what makes his effort particularly appealing is that he organizes them into eight neatly prearranged categories to help you with your personal “anticancer” solutions. He brings together the most effective foods from around the world and places them in one “straight-forward” diet. He also discusses lifestyles and habits, environmental hazards and supplemental formulas, and provides you with many practical tips to reduce the prospects of specific ailments and illnesses associated with a Western diet.    

“Dr. Hatherill likens eating Super Eight Foods to wearing your full anticancer body armor; each part of the armor provides an exclusive form of defense that is not duplicated by other segments, and the whole is greater than the sum of its parts,” says VegSource who recommends his book and diet. VegSource is a web site source for vegetarian recipes, discussion forums, and articles and information from health experts and nutritionists who share an interest in health, nutrition, and the environment. The table below lists “The Eight Super Food Groups.” Each of the food groups and associated super foods are reproduced here in alphabetical order for your convenience and easy reference. It is not a course of study and the foods are not intended to be consumed in the sequence shown.

The Eight Super Food Groups

The Eight Super Food Groups from Eat to Beat Cancer by R. Robert Hatherill, Ph.D.

Cruciferous Group broccoli, bok-choy, Brussels sprouts, cabbage, cauliflower, Chinese cabbage, collards, garden cress kale, kohlrabi, mustard greens, radishes, rutabaga, turnips, watercress

Fruit Group apples, blackberries, blueberries, cantaloupe, grapes (red and Concord), grapefruit, honeydew melon, lemons, limes, oranges, pineapple, raspberries, strawberries, tangerines, watermelon

Grass Group corn, oats, rice, wheat

Legume Group beans (green and waxed), peas, soybeans

Nut and Seed Group almonds, flaxseed, pecans, pine nuts, pumpkin seeds, pistachios, sesame seeds, walnuts

Onion Group asparagus, chives, garlic, leeks, onions, scallions, shallots

Solanace Group beets, potatoes, sweet potatoes, tomatoes

Umbelliferous Group angelica root, anise, caraway, carrots, celeriac, celery, chervil, coriander, cumin, dill, lovage, parsley, parsnips

Other Important Foods Cucumber, ginger, lettuce, pepper (green and red), pumpkin, seaweed squash, spices, spinach, turmeric

All persons making use of the super foods contained within the eight categorical groupings are reminded to consult with Dr. Hathrill’s original work and your own Doctor, Nutritionist and/or Health Care Professional for all purposes of interpreting and applying the “anticancer” diet.” This same recommendation will apply to anyone pursuing any diet program especially if you are ill, pregnant, are diabetic or have problems related to your kidney.

Five a Day
The Five a Day article provides additional credible and trustworthy support for the above-mentioned super foods.  The MRC Human Nutrition Research unit last medically reviewed this article in July of 2008. Only five portions of fruits and vegetables of differing colors are recommended and the same health benefits can be derived from this mix be they “fresh, tinned (in natural juice), frozen, cooked, juiced or dried versions”, excluding potatoes, says the Five a Day article. They are also low in calories so long as you avoid the butter, dips and sauces. However, the phytonutrients contained in super foods are not enough in and of themselves. Variety is the secret because “each variety of fruit and vegetables contains its own combination of vitamins, minerals and fiber” the article concludes. Dietary fiber is an important contributor toward weight management. Our bodies digest fiber more slowly with an accompanying slow and steady glucose release that allows us to feel fuller for a longer period. In contrast, foods with a high Glycaemic Index (GI) will frequently leave you feeling hungry very soon after you have eaten.  Examples of high GI foods can be white bread and rolls, waffles, pretzels, cornflakes, rice krispies, instant potato, baguettes, brown rice pasta and parsnips.
South Beach Diet Plan
According to the South Beach Diet Plan, Low GI foods have an index of 55 or less. Medium GI foods have an index between 56 and 70, and High GI foods have indices over 70.  Carbohydrate foods and their effect on blood glucose levels form the basis of all GIs.  Low carbohydrate GI foods produce the least fluctuation in our blood sugar levels. Choosing Low GI foods ensures health and longevity. High GI foods produce the most fluctuation and increase your weight and risk of heart disease. Consult the South Beach Diet Plan Glycemic Index Food Chart  for a complete list of foods and their associated ratings to help you make healthier food choices and control your weight.  The South Beach Diet Plan insists it is not about eating less that is important but about eating well. It is about eating foods that do not renew your cravings as quickly and store a lot of residual fat.  It is about eating the right mix of carbohydrates, proteins and fats, and changing your lifestyle for the good of your cardiovascular system.

Author Information:

Ihor Cap, Ph.D. is an Education Research Specialist, Web Author and Marketing & Promotions Manager for EZREKLAMA.  

This article first appeared August 6, 2009 in http://articlesandblogs.ezreklama.com.

Promote your website, service or product by posting an article or blog

by Ihor Cap
Businesses and organizations are always looking for quick and inexpensive ways to promote their web sites, products or services. There is a way to do that easily and it need not cost you a dime.  How? You do it by publishing an article or blog in a web site directory. In fact, it is one of the most popular ways of advertising and marketing on the internet these days. Internet use is multiplying each and every year, and millions of surfers are hungry to read something of interest daily. Business owners and organizations are learning that more visitors can frequent their web page than their store window and from all corners of the globe. Moreover, web sites with translation buttons are making your article or blog understood worldwide. Best of all, it is free. Web site publishers are happy because they get free content for their site. Business owners and organizations are happy because they get free advertising. It is a win-win marketing situation for everyone.
It’s great because it does not require much of your time either. You may already have some brochures, pamphlets or press releases that you can easily modify for your article. Just pull out what you need from your promotional materials and adjust it to suit the needs of your web audience.  Be brief and to the point. Write about 300 to 600 words or no more than a page. Internet users do not tend to read for lengthy periods anyway. So, get to the point fast. Readers want information. They want to learn something. Do not try to sell them on anything or else they will tune out quickly. Besides, most publishers may not want you to “sell” on their site anyway.
Make your article or blog interesting. Relevancy and usefulness of products and services to your readers will usually make for interest. Persuade your readers to try something new. Offer an incentive, a free sample, or a discount. Tell them about an innovation, trend, and fashion or an up and coming product that you may know something about or only you can offer.  Explain to your reader the importance of a service you provide and why it might help them. Most of all, try to be helpful, and honest with your readers. Remember, every reader is a potential customer or web site visitor too.
Another way of making your content interesting is to add a picture or video with your article. These are great for illustrating your product, service or for providing a visual “how to” demonstration. Post a video on YouTube and then embed it with your article or blog. A picture will do just as well if you have no video. Like your article, keep your video short and sweet too.
Last, but not least, include your name or business name and URL address at the end of the article or blog. This is the customary way of leaving your “calling card” with web readers once they finish reading your article or blog. Here is where you “sell” your organization or the service you provide.  Encourage them to visit your web site for additional details or more of what you are offering. To summarize, posting an article or blog in a web site directory is a wonderful promotional tool and a quick way to generate interest in your web site, product or service.
Author Information:
Ihor Cap, Ph.D. is an Education Research Specialist, Web Author and Marketing & Promotions Manager at EZREKLAMA.
This article first appeared July 21, 2009 in http://articlesandblogs.ezreklama.com/