T-test Male and Female Averages

Being able to numerically describe differences, or the amount of difference is the basis for many budgetary decisions. In this case we are using the  NCES average reading scale scores for the 2011 school year of 4th grade students from the previous post to see if there is a significant statistical difference between males and female scale scores. Looking at the straightforward scores, there are differences but are they statistically significant?




The 2-tail P value is greater than .05--no statistical difference.

To judge if the difference is numerically significant, T test scores are generated.  The hypothesis used: there is a difference; the null hypothesis: there is no difference. To investigate this, I went to the saved NCES chart of 4th grade scale scores, clicked on Data, then Data Analysis, and followed the options to select a variable 1 (male) and variable 2 (female) columns of scores. The two-tail P value is greater than .05, indicating there is no statistical significance difference between the scale reading scores of male and female students.

Initially, I questioned my numbers since they did not match other bloggers' numbers although I followed the same procedure and the conclusion was the same. Upon a closer look, I see I included the Dept. of Defense Education Agency 4th grade scale scores. In my opinion, these scores are part of the whole United States picture, even though they may not represent statehood, the students are United States citizens taught by US teachers using US approved curriculum. The addition of this 'state' appears to have adjusted the P values, but in the same direction they were going without them.  Without this addition, the P value one-tale is 1.60684 and two-tail is 3.21368 (as opposed to 2.51748 and 5.03496, with them). Either way, the P value is greater than .05 indicating no significant difference.








This procedure can be applied to another situation led by the question: How do end-of-year scores differ among gifted students placed in heterogeneously grouped classes and gifted students placed in classes of homogeneously grouped classes? The dependent variable-course scores; the independent variable-grouping in heterogeneous and homogeneous classes. The constants: curriculum, class size, teacher qualification.

Hypothesis 1 Being placed in a class with a wide spread of academic abilities alters the scores of the gifted thinkers. Scores are not as high as the scores from classes where gifted thinkers are challenged to their own levels. Hypothesis2 (null): There is no difference.

Once the course (school year) is completed and end-of-year scores are calculated, Excel Data Analysis can be used to do a P value of variable 1 (heterogeneous grouping) and variable 2 (homogeneous grouping) and determine if there is a statistically significant difference between the two sets of scores.

ISTE NETSt standard affected by this skill is #5, engaging in professional growth and leadership. By speaking to scores and differences based on numerical data, school boards, civic leaders, and budgetary faces can be convinced and possibility encouraged to see that gifted thinkers act and react to academic surroundings.

Just for fun, what would one-tail and two-tail gourds look like?

A one-tail gourd.

Two tails.....

...now, what would the P value be?  I'd say Pretty!

Dependent? Independent?

Statistics. Variables. OH my!

 

 

Excel - Descriptive Statistics

All critical information is there...

Using an Excel spreadsheet, numerical data can be analyzed to recognize differences and patterns. By looking at the National Center for Education Statistics, and going to state comparisons, a search can be made by grade, subject, student group, year(s) and type of data display desired. In this particular instance, national 4th grade reading scores for 2011 were downloaded into my Excel program for review.  I realized the scores I would have been interested in were not an option: gifted scores by state and gender. (States vary wildly with regard to mandating gifted education and funding and although the NAGC will give individual information, I have not located an Excel types chart with all the information in one place. Maybe that's my special project!)

However, I did like how the title, reference sources and websites traveled with the download to act as a one-stop-shopping sheet--an appealing aspect.

By using the sorting and data analysis functions, the scores could be arranged in ascending order. I produced a scatter plot describing the placement of Virginia's scores compared to the other states and overseas schools on military bases (which counts as a state). The plotted scores reflect the ascending order. Virginia places #9 among the states, closely aligned with Vermont by .40 -- almost the same score difference as Maryland and New Hampshire (.38). There are 8 states with higher scores (DoDEA is one of them) and 43 states with lower scores. Virginia is 5.96 points above the average.

Overall, a striking point of interest is the fact that both outliers are on the east coast: high score (MA 236.7738666) and low score (DC 200.6279879), with DC also having the biggest difference between male and female scores.

The ability to sift through numbers and interpret them is a valuable professional and leadership skill. Being able to do it using technology is a way to speak to data in an efficient and effective way. ISTE NETS-T standard 5 would be addressed with this skill: evaluate and reflect on current research on a regular basis. By using digital tools, student learning can be guided as trends emerge.

On second thought...

The Diigolet isn't loading properly so articles and images can be saved, but the annotations are sketchy. Luckily there's boatload of gourdheads coming to town this week for the Virginia Gourd Festival so life is good all around! Escape the political craziness and get crazy with gourds! Margaret "Sparky" Sparkman, the National Gourd Lady, sure would have!