Not sure I understand the question. Do you mean "how do we double-check to see if the words on this page are correct?"

http://initialteachingalphabet.org/alphabet.html

(bed, cat dog…)

I am familiar with this chart, but what I am looking for is a dictionary to check the spelling of as many words as possible.

"What I am looking for is a dictionary to check the spelling of as many words as possible." is is very broad question. Do you mean the world's biggest? Most popular? Most languages? Sold most copies? Electronic? Reviewed? Up to date?

Can you provide a little more background information about yourself and this project? Is it personal, academic, or professional? Who is your audience? What are their goals? Information like this will help people provide you with more meaningful feedback.

Wikipedia's page on "Major English dictionaries" has many options. Be mindful that certain people the same word different ways of spelling the same word (eg, Americans = color, Canadians = colour).

I am not a linguist so I cannot offer much advice, but I fairly confidant that the people who designed this system double checked their sources. From their page, they appear to be an American company so they probably use an American English dictionary.

I still fear something is getting lost in translation (pun intended). Are you coming from an ESL perspective and looking at issues of spelling reform? Are you interested in the orthography they used?

You may want to research The Simplified Spelling Society. You have most likely read this article that Eye magazine published about the Initial Teaching Alphabet.

To rephrase and clarify your question, do you mean:

"What is the primary source that the Initial Teaching Alphabet Foundation used to determine the spelling of the words they selected when they originally developed the Initial Teaching Alphabet?"

Apologies if I have been unclear. What I am looking for is a dictionary where I can look up how to spell, for example, the word 'rules' using the ITA. Looking at the ITA chart that gives examples of how to pronounce each letter, I can see that there is a traditional 's', 'z' and a reversed 'z'. Now, if I am unsure of which letter to use to replace the 's' in the traditionally spelled word 'rules', it would be helpful to look this word up in a dictionary that shows how an American English word would be spelled using the letters and orthography of the ITA. Such a dictionary exists for the UNIFON alphabet and is extremely helpful.

As for my background, I am a Graphic Designer specializing in typography and book design, currently studying for an MA in Graphic Design. My original research question was 'Can I achieve greater correspondence between the spoken and written language by adapting an alphabet or creating a new writing system?', which led me to research alphabets such as the ITA and UNIFON. I am therefore, interested in both the orthography and the design of the letters.

Katrin wants essentially a Fall and Rise of Reginald Perrin GROT product – not in this case a Dutch–Dutch dictionary (“consisting of every word in the Dutch language alongside its equivalent in Dutch”), but an English-ITA dictionary, in which English words are rewritten in this failed pseudoalphabet.

@ Joe: Thanks for clearing the question up. I was way off on my interpretation. I did not understand that "…words set in the ITI…" meant "…words set using the glyphs from the ITI…"

@ katrin: I believe this is what you are looking for:

Downing, J. A. (1963). The Augmented Roman Alphabet for Learning to Read. The Reading Teacher, 16(5), 325–336.

On pages 326-7 they illustrate 32 glyphs (some characters, some ligatures) and a few words set using them. You may need database access to get this article. If you do not have immediate access, contact me and I can pass it on.

If you have access to JSTOR the stable link is:

http://www.jstor.org/stable/20197649

My mothers foundation from 1983 until 2010 was The Initial Teaching Alphabet Foundation - a person whom I befriended when my father died snuggled in and walked with it - so my voice remarks or naming it are forbidden. I also ran the foundation for 17 years. I am an expert on ita!

But you may reach the person at these email addresses -
V1perst10@yahoo.com or ita-foundation.org or land address is 100 Marcus Avenue, Suite 4, Hauppauge, New York

And check my FB page

@katrin s:
My original research question was 'Can I achieve greater correspondence between the spoken and written language by adapting an alphabet or creating a new writing system?', which led me to research alphabets such as the ITA and UNIFON.

IIRC, the ITA, because it was meant to teach children to read, rather than serve as a phonetic alphabet, was allowed to represent the same sound in more than one way, in order that in some cases there would not be too large a divergence between ITA spellings and conventional English spellings.

I could be mistaken, but if that is the case, that would reduce its applicability to your question. The answer to that question, though, of course is "Yes" - look at the Shaw Alphabet, or the suggestions of the Simplified Spelling Society - I recall a book by Mont Follick, in which the use of a new alphabet was avoided. The trick was using ' to indicate where two consecutive vowels did not form a dipthong.