CLICK GO:

2007 T Test:

• Go to the DATA ribbon
• Select the DATA ANALYSIS MENU (below)

• Select the data ranges and set the alpha (critical P) level:

Excel 2007 results sheets:

Writing a conclusion:

We can see the analysis from 2 parameters:

option 1 : P (T<=t) two-tail

We reject H0 if “P (T<=t) two-tail” < critical P level (commonly 0.05)
Option 2: t Stat

We reject H0 if t Stat is not in range of -(t Critical two-tail) and +(t Critical two-tail)

on the example above,

tStat is= – 4.54 . it is out of range between t critical two-tail (- 2.1 up to 2.1) so we reject the H0 …so …There is a significant deferent

or

P (T<=t) two-tail = 0.0003 and this value is < 0.05 so we reject H0

*******************************************

The results of the dependent t-test can be seen in the resultant table. The value of t (t Stat) is -4.53744, which we can round off to -4.54.

The probability of this result being due to chance can be read from the table as 0.000291 (two-tail) which means that this result is significant at the .0003 level.

We will set our alpha level as .05, so we will say that p < .05 rather than that p = .0003.

We could also look up the t critical value or cut-off value for t from the table by looking at t Critical one-tail which is 2.110 without using the spreadsheet.

We now have all the information we need to complete the six step statistical inference process:

1. State the null hypothesis and the alternative hypothesis based on your research question.
   Null hypothesis: There is no significant difference between the height of the two samples of snail shells.
   Alternative hypothesis: There is a significant difference between the height of the two samples of snail shell.
2. Set the critical P level (also called the alpha level )
   P=0.05
3. Calculate the value of the appropriate statistic. Also indicate the degrees of freedom for the statistical test if necessary.
   t = -4.53
   df = 17 (unpaired , unequal sample variance)
4. Write the decision rule for rejecting the null hypothesis.
   Reject null hypothesis since t is <= -2.110
5. Write a summary statement based on the decision.
   Reject null hypothesis , p < .05, two-tailed
6. Write a statement of results in standard English.
   There is a significant difference between the height of snail shells in the two samples.

Office Icon (left top corner) –> Excel options –> Add-Ins : highlight “analysis ToolPak” and click GO button

then we will have ‘Dana Analysis’ icon on Analysis group on DATA tab

CORRELATION COEFFICIENT

The correlation coefficient between two series, say x and y, equals

Covariance(x,y) / [Sqrt(Variance(x)) * Sqrt(Variance(y))]

where

• Covariance(x,y) is the sample covariance between x and y:  (1/(n-1)) × Σ _i (x_i – xbar)(y_i – ybar)
• Variance(x) is the sample variance of x: (1/(n-1)) × Σ _i (x_i – xbar)²
• Variance(x) is the sample variance of y: (1/(n-1)) × Σ _i (y_i – ybar)²

CALCULATION USING THE DATA ANALYSIS ADD-IN

This requires the Data Analysis Add-in: see Excel 2007: Access and Activating the Data Analysis Add-in

The data used are in carsdata.xls
We consider only two series, but we could do the same for more than two series.

• In the Data Group select the Data Analysis Add-in
• Select Correlation
• Fill out the Correlation dialog box as below

Hit enter yields

The correlation coefficient is 0.894427.

This can be extended to several series.
For example if there are data in columns A, B, C, D and E then the array chosen is A1:E6 and produces a 5 x 5 table of correlations.

CALCULATION USING THE CORREL FUNCTION

This does not require the Data Analysis Add-in

• Click on the cell you want result to appear on.
• On the Formula Tab select the Function Library group and More Functions and Statistical
• Select Correlation and fill out the dialog box as below

Alternatively directly type  = CORREL(A1:A6,B1:B6)  which yields  0.894427.

Note that Excel dropped the first row (or labesl).
= CORREL(A2:A6,B2:B6) yields the same result.

COVARIANCE

This is obtained in a similar way to correlation.

• We can use Data Analysis Add-in and Covariance
• We can use function CORREL

IFor example, = COVAR(A1:A6,B1:B6)  yields  0.8.

LittleBrother is watching you

If you happen to be reading this article online from your computer at work, your boss may be reading over your shoulder-electronically. New technologies allow employers to check whether employees are wasting time at recreational Web sites or sending unprofessional e-mails. But when do an employer’s legitimate business interests become an unacceptable invasion of worker privacy?

By Miriam Schulman

Last year, a software package came on the market that allows employers to monitor their workers’ Internet use. It employs a database of 45,000 Web sites that are categorized as “productive,” “unproductive,” or “neutral,” and rates employees based on their browsing. It identifies the most frequent users and the most popular sites. It’s called LittleBrother.

Though the title is tongue-in-cheek, LittleBrother does represent the tremendous capabilities technology has provided for employers to keep track of what their work force is up to. There are also programs to search e-mails and programs to block objectionable Web sites. Beyond installing monitoring software, your boss can simply go into your hard drive, check your cache to see where you’ve been on the Net, and read your e-mail.

Did you delete that message you sent about his incompetence? Not good enough. The e-mail trash bin probably still exists on the server, and there are plenty of computer consultants who can retrieve the incriminating message.

All told, such monitoring is a widespread-and-growing-phenomenon. Looking just at e-mail, a 1996 survey by the Society for Human Resource Management found that 36 percent of responding companies searched employee messages regularly and 70 percent said employers should reserve the right to do so.

The Law

Legally, employees have little recourse. The most relevant federal law, the 1986 Electronic Communications Privacy Act, prohibits unauthorized interception of various electronic communications, including e-mail. However, the law exempts service providers from its provisions, which is commonly interpreted to include employers who provide e-mail and Net access, according to David Sobel, legal counsel for the Electronic Privacy Information Center in Washington, D.C. A federal bill that would have required employers at least to notify workers that they were being monitored failed to come to a vote from 1993 to 1995.

The situation in the courts is similar. “There aren’t many cases, and they tend to go against the employee,” according to Santa Clara University Professor of Law Dorothy Glancy. “Often, court opinions take the point of view that when the employees are using employers’ property—the employers’ computers and networks—the employees’ expectation of privacy is minimal.” When courts take this view, Glancy continues, “if employees want to have private communications, they can enjoy them on their own time and equipment.”

In a presentation on employee monitoring, Mark S. Dichter and Michael S. Burkhardt of the law firm Morgan, Lewis & Bockius explain that courts have tried to balance “an employee’s reasonable expectation of privacy against the employer’s business justification for monitoring.”

For example, in Smyth v. Pillsbury Co., Michael Smyth argued that his privacy was violated and he was wrongfully discharged from his job after his employers read several e-mails he had exchanged with his supervisor. In the electronic messages, among other offensive references, he threatened to “kill the backstabbing bastards” in sales management.

The court ruled that Smyth had “no reasonable expectation of privacy” on his employer’s system, despite the fact that Pillsbury had repeatedly assured employees that their e-mail was confidential. In addition, the court held that the company’s interest in preventing “inappropriate and unprofessional” conduct outweighed Smyth’s privacy rights.

Privacy as a Moral Matter

But the fact that employee monitoring is legal does not automatically make it right. From an ethical point of view, an employee surely does not give up all of his or her privacy when entering the workplace. To determine how far employee and employer moral rights should extend, it’s useful to start with a brief exploration of how privacy becomes a moral matter.

Michael J. Meyer, SCU professor of philosophy, explains it this way: “Employees are autonomous moral agents. Among other things, that means they have independent moral status defined by some set of rights, not the least of which is the right not to be used by others only as a means to increase overall welfare or profits.”

Applying this to the workplace, Meyer says, “As thinking actors, human beings are more than cogs in an organization—things to be pushed around so as to maximize profits. They are entitled to respect, which requires some attention to privacy. If a boss were to monitor every conversation or move, most of us would think of such an environment as more like a prison than a humane workplace.” But, like all rights, privacy is not absolute. Sometimes, as in the case of law enforcement, invasions of privacy may be warranted. In “Privacy, Morality, and the Law,” William Parent, also a philosophy professor at SCU, sets out six criteria for determining whether an invasion of privacy is justifiable:

1. For what purpose is the undocumented personal knowledge sought?
2. Is this purpose a legitimate and important one?
3. Is the knowledge sought through invasion of privacy relevant to its justifying purpose?
4. Is invasion of privacy the only or the least offensive means of obtaining the knowledge?
5. What restrictions or procedural restraints have been placed on the privacy-invading techniques?
6. How will the personal knowledge be protected once it has been acquired?

These questions can offer guidance as we consider both sides of the controversy.

The Case for Workplace Monitoring

If an employer uses a software package that sweeps through office computers and eliminates games workers have installed, few people will feel such an action is an invasion of privacy. Our comfort with this kind of intrusion suggests that most of us don’t fault an employer who insists that the equipment he or she provides be used for work, at least during working hours.

Why, then, should we balk when an employer tries to ensure that his equipment is not being used to surf non-job-related Web sites? Hours spent online browsing the recipe files of Epicurious are no less a breach of the work contract than games playing.

“The underlying principle is value for money,” says Joseph R. Garber, a columnist for Forbes magazine. “If you don’t deliver value for money, in some sense, you’re lying.”

Garber gives this illustration: If we hired someone to paint our house, and they didn’t do the northern wall, we would feel moral outrage. Similarly, if we pay workers to give a good day’s work and they are, instead, surfing X-rated Web sites, we are also morally outraged.

Such “cyberlollygagging” is no small problem. A study by Nielsen Media Research found that employees at major corporations such as IBM, Apple, and AT&T logged onto the online edition of Penthouse thousands of times a month.

Beyond worry about lost productivity, employers have legitimate concerns about the use of e-mail in thefts of proprietary information, which, according to the “Handbook on White Collar Crime,” account for more than $2 billion in losses a year. The transfer of such information can be monitored by programs that search employee e-mails for suspect word strings or by employers simply going into the employee’s hard drive and reading the messages.

In a case last year, a former employee of Cadence Systems was charged with stealing proprietary information and intending to bring it to the rival software maker Avant! According to prosecutors, before leaving Cadence, he e-mailed a file containing 5 million bytes to a personal e-mail account. Such large messages suggested that he might be sending source code for the company’s products and prompted Cadence to contact the police.

Electronic communications can pose other dangers for employers besides breached security and lost productivity. More and more, employers are being held legally liable for the atmosphere in the workplace. Although the case was ultimately dismissed, employers worry about litigation like the $70-million suit brought by Morgan Stanley employees, who claimed that racist jokes on the company’s electronic mail system created a hostile work environment.

Sexual harassment cases also often hinge on allegations of a hostile work environment, which might be evidenced by employees downloading or displaying pornographic material from the Web or sending off-color e-mails. “The days of guys putting naked bunnies up on their computer screens are gone because that’s actionable stuff,” Garber comments.

To prevent such abuses, Garber argues, employers need to be allowed to monitor: “We can’t make corporations responsible for stopping unacceptable forms of behavior and then deny them the tools needed to keep an eye out for that behavior.”

The Case Against Workplace Monitoring

Consider this scenario: It’s lunch hour. An employee writes a note to her boyfriend. She puts it in an envelope, affixes her own stamp, and drops it in the basket where outgoing mail is collected. Does the fact that the pencil and paper she used belong to her employer give her boss the right to open and read this letter?

Although most people would answer no, that’s just the argument employers are making to defend monitoring e-mail, according to the Electronic Privacy Information Center’s Sobel: Employers claim that because they own the computer, they have the right to read the e-mail it produces. The situation is complicated by the fact that work and personal life are not as clearly delineated as they once were, due, in part, to the very technologies that are being monitored. Employees may telecommute, doing much of their business through e-mail and the Net. Often, they work a good deal more than 40 hours a week. If they take a moment to send a message to Aunt Margaret in Saskatoon, do they not have a right to expect their e-mail will be confidential?

“Most people don’t work 8 to 5,” says Anthony Pozos, senior vice president for human resources and corporate services at Amdahl Corp. “We pay people to do a job; we don’t really pay by time increment. Employees probably do use our e-mail or Web access for personal matters; it’s analogous to using the telephone. People do sometimes need to do personal things on the job, but as long as it doesn’t interfere with work, that should be okay.”

Another ethical consideration in the debate is fairness. Usually, it’s not corporate higher-ups who are subject to monitoring, but line workers. That’s particularly true when it comes to key-stroke monitoring, a form of electronic surveillance that measures the speed of data entry. According to an article in Public Personnel Management, “The majority of employees being electronically monitored are women in low-paying clerical positions.”

Then there’s Parent’s question about whether the invasion of privacy (represented by monitoring) is the only or the least offensive means of obtaining the information employers seek. In a survey conducted by PC World, slightly more than half of the executives interviewed were opposed to monitoring employees’ Internet use. Scott Paddock, manager of PC Brokers, told the magazine, “First, I trust my employees; that’s why they work for me. If there were to be any problems with an employee, those problems would present themselves without the need for me to get involved in cloak-and-dagger shenanigans. And second, if I spent time monitoring their Web usage, I would be just as guilty of wasting time as my behavior implies they are.”

Trust is often mentioned by opponents of monitoring as a major ethical issue. As Rita C. Manning writes in the Journal of Business Ethics, “When we look at the workplaces in which surveillance is common, we see communities in trouble. What is missing in these communities is trust.”

If, Manning continues, employers create trust, employee behavior “will conform to certain norms, not as a result of being watched, but as a result of the care and respect which are part of the communal fabric.”

Some Possibilities for Common Ground

It is possible to moot many of these ethical issues by arguing that monitoring all comes down to a question of contract. That is the view of David Friedman, an economist and professor at SCU’s School of Law.

“There isn’t an agreement that is morally right for everybody. The important thing is what the parties agree to,” he says. “If the employer gives a promise of privacy, then that should be respected.” If, on the other hand, the employer reserves the right to read e-mail or monitor Web browsing, the worker can either accept those terms or look elsewhere for employment, Friedman continues.

Friedman’s argument doesn’t address the problems of lower-income workers who may not have a choice about whether to accept a job or, if they do, may be choosing between entry-level positions where monitoring is a feature of the work environment.

But he does point to an area where some common ground may exist between opponents and proponents of monitoring. Most parties to the debate agree that companies should have clear policies on electronic surveillance and that these should be effectively communicated to employees.

A recent study by International Data Corp. suggests that such clarity does not currently prevail. A survey of employees at 110 businesses showed that 45 percent thought their company had no policy on e-mail at all. Most of those who did know the company policy had either learned it by word of mouth or were directly involved in writing it.

Spelling out company policy “is our bottom line,” says Sobel. “We would like to see an outright prohibition on e-mail monitoring in the workplace, but, at the very least, there needs to be notice to employees if that’s the policy.”

Pozos believes that involving employees in the creation of a monitoring policy is also a way to find common ground. By bringing employees and managers together to develop principles and guidelines for electronic mail, Amdahl was able to create a policy that was acceptable to both sides, Pozos says.

In any case, employers who reserve the right to monitor should attend to the considerations Parent proposes, ensuring at least that the monitoring serves a legitimate purpose and follows clear procedures to protect a worker’s personal life from unnecessary prying, either by LittleBrother or by Big Brother.

Further Reading

Dichter, Mark S., and Burkhardt, Michael S. “Electronic Interaction in the Workplace: Monitoring, Retrieving and Storing Employee Communications in the Internet Age.”
www.mlb.com/speech1.htm

Garber, Joseph. “The Right to Goof Off.” Forbes (Oct. 20, 1997) p. 297.

Greenlaw, Paul S., and Prudeanu, Cornelia. “The Impact of Federal Legislation to Limit Electronic Monitoring.” Public Personnel Management26, 2 (June 22, 1997) p. 227.

Manning, Rita C. “Liberal and Communitarian Defenses of Workplace Privacy.” Journal of Business Ethics 6, 8 (June 1997) p. 817.

Parent, W.A. “Privacy, Morality, and the Law.” Philosophy & Public Affairs12, 4 (Fall 1983) p. 269.

Related Web Sites

Center for Democracy and Technology
www.cdt.org

Electronic Frontier Foundation
www.eff.org

Electronic Privacy Information Center
www.epic.org

Privacy Rights Clearinghouse
www.privacyrights.org

ACLU Freedom Network: Cyberliberties
www.aclu.org/issues/cyber/hmcl.html

Yahoo Privacy Resources
www.yahoo.com/Law/Privacy/

Privacy Protection Principles for Electronic Mail
www.ipc.on.ca/web_site.eng/matters/practice/email.htm

then watch this basic TWIKI tutorial: http://www.youtube.com/watch?v=nUapWzlwpDk&feature=related

or in this site: http://www.twiki.net/twikitutorials.html

How to use TWIKI for a company: http://www.youtube.com/watch?v=ZRQgKlX-bOA&feature=related

FORMULAS tab –> “Defined Names” Group –> NAME MANAGER

In Excel, the If function returns one value if a specified condition evaluates to TRUE, or another value if it evaluates to FALSE.

The syntax for the If function is:

If( condition, value_if_true, value_if_false )

condition is the value that you want to test.

value_if_true is the value that is returned if condition evaluates to TRUE.

value_if_false is the value that is return if condition evaluates to FALSE.

Example: Let’s pretend I have this data and on column D I wanna Excel automatically type “Good Sales” if Sales>$10,000.00 and “Bad Sales” otherwise

Answer: To do that I type IF Formula in column D

******************************************************

Nesting IF Function
source: http://personal-computer-tutor.com

Let’s use some new data. Open a blank workbook in Excel and enter this data:

Let’s pretend this is data which shows your salespeople’s district, annual sales, and number of years employed by your company.

Now, let’s suppose you want a formula in column E that will assign a job level based on two different criteria:

* Salespeople who have been employed for more than 5 years AND have annual sales of more than $10,000 should be assigned a job level code of 2, and
all others should have a job level code of 1.

To include two criteria, when both criteria must be met, you must nest an AND function within your IF statement. Put this formula in cell E2:

=IF((AND(D2>5,C2>10000)),2,1)

=IF((OR(D2>5,C2>10000)),2,1)

=IF((AND(D2>5,C2>10000)),3,(IF((OR(D2>5,C2>10000)),2,1)))

=IF((B2=”East”),4,IF((B2=”West”),3,IF((B2=”North”),2,IF((B2=”South”),1,”"))))

Only when it can be assumed that all variables that are correlated with any of the predictor variables and the criterion are included in the analysis can one begin to consider making causal inferences. It is doubtful that this can ever can be assumed validly except in the case of controlled experiments.

One measure of the importance of a variable in prediction is called the “usefulness” of the variable. Usefulness is defined as the drop in the R² that would result if the variable were not included in the regression analysis. For example, consider the problem of predicting college GPA. The multiple R² when College GPA is predicted by High School GPA, SAT, and Letters of recommendation is 0.3997. In a regression analysis conducted predicting College GPA from just High School GPA and SAT, R² = 0.3985. Therefore the usefulness of Letters of Recommendation is only: 0.3997 – 0.3985 = 0.0012.

On the other hand, leaving out SAT and predicting College GPA from High School GPA and Letters of Recommendation yields an R² = 0.3319. Therefore, the usefulness of SAT is 0.3997 – 0.3319 = 0.068.

Selalu diingat bahwa Usefulness sebuah variable lebih tepat mewakili nilai penting variable tersebut dibandingkan Pearson Correlation coeefisient. Karena bisa jadi sebuah Predictor memiliki nilai koefisien Pearson Correlation (misal 0.35), tetapi ketika variable-variable predictor lainnya dimasukkan maka nilai Usefulness nya ternyata 0. Hal ini menunjukkan bahwa memang benar variable predictor tadi berhubungan dengan variable dependent nya tetapi ternyata nilai hubungannya(correlation) tadi bisajadi karena adanya variable perantara lainnya.

It is important to bear in mind that the usefulness of a variable refers specifically to the usefulness of a variable when the other variables are included in the regression equation. For instance, although the Letters of Recommendation add practically nothing to the ability to predict College GPA once High School GPA and SAT are known, they are somewhat predictive of College GPA when taken alone: The Pearson correlation between Letters of Recommendation and College GPA is 0.35.

In sum, the usefulness of a variable refers how much it adds to the predictability of the criterion over and above the other predictor variables in the equation. If two predictor variables are highly correlated, then neither will contribute much to the prediction above and beyond the other.

1. Tanya:
kenapa uji kenormalan data perlu dilakukan dalam analisis data menggunakan metode Parametrik?

Jawab:
Uji kenormalan data, sebelum menggunakan statistik uji parametrik, perlu dilakukan. Hal ini disebabkan karena statistik-statistik uji parametrik diturunkan dari sebaran normal. Tentu saja, data yang akan dianalisis juga harus menyebar normal agar data yang dianalisis relevan dengan alatnya (statistik uji parametrik). Namun, apabila kita menggunakan statistik uji nonparametrik, kita TIDAK PERLU mempertimbangkan mengenai kenormalan data sama sekali.

2. Tanya:
Kalo jumlah sampel<= 30, pake uji t ya? dan sebelumnya pake uji kenormalan ga?

Jawab:
Dasar penggunaan uji-t bukan dilihat dari banyaknya sampel.
Uji-t digunakan untuk melakukan uji hipotesis terhadap rata-rata dimana peneliti atau analis tidak memiliki informasi sama sekali mengenai ragam (variance) dari populasi (ingat!!!, bukan ragam SAMPEL, tapi ragam POPULASI). Kemudian, uji-t mengasumsikan bahwa data memiliki sebaran normal.

Jadi, kalo kita  memiliki informasi mengenai nilai dari ragam populasi datanya, maka metode yang tepat adalah uji-z. kalo ragam populasi gak diketahui, maka pake uji-t. Tentu saja, sebelum melakukan analisis dengan uji-t, mas John harus melakukan uji kenormalan data (misal pakai statistik uji Kolmogorov-Smirnov, dll). Jika data tidak menyebar normal, maka metode yang tepat adalah statistika nonparametrik, dalam kasus ini misalnya uji median.

3. Nanya:
Apa bedanya uji satu pihak /one tail dengan 2 pihak /two tail?

Jawab:

Uji satu pihak (uji 1-arah/one tail) digunakan untuk melakukan uji hipotesis ketika peneliti memiliki asumsi tambahan mengenai arah/kecenderungan dari suatu karakteristik.
Namun, apabila peneliti tidak mempertimbangkan mengenai arah/kecenderungan dari karakteristik, maka uji dua pihak (uji 2-arah) sebaiknya digunakan.

Ilustrasi ini mungkin bisa menunjukkan kapan uji 1-arah dan 2-arah digunakan.
Misal, ingin diketahui rata-rata IQ mahasiswa univ. X. Untuk itu dilakukan penelitian dengan mengambil beberapa sampel mahasiswa univ.X. Nah, apabila peneliti memiliki asumsi bahwa rata-rata IQ mahasiswa univ. X lebih dari 140, maka uji hipotesis yang digunakan adalah uji 1-pihak. Namun, apabila asumsi ini tidak dimiliki, dengan kata lain, peneliti tidak tahu apakah rata-rata IQ mahasiswa univ.X lebih dari atau kurang dari 140, maka akan tepat jika menggunakan uji 2-pihak.
Ciri khas dari uji 1-pihak atau 2-pihak adalah tanda pertidaksamaan yang digunakan dalam penulisan HIPOTESIS 1.
Dari kasus di atas, maka

-uji 1-pihak memiliki hipotesis:

H0: mu = 140
H1: mu > 140

Hal ini berarti, rata-rata IQ mahasiswa univ.X lebih besar dari 140

-uji 2-pihak memiliki hipotesis:

H0: mu = 140
H1: mu != 140

Hal ini berarti, rata-rata IQ mahasiswa univ.X tidak sama dengan 140, entah itu lebih besar atau lebih kecil dari 140.

Yang perlu diperhatikan adalah, asumsi mengenai arah/kecenderungan suatu karakteristik tidak dipengaruhi oleh data sampel. Maksudnya, informasi atau asumsi mengenai arah/kecenderungan karakteristik sudah dimiliki oleh peneliti SEBELUM data diambil.

keterangan: mu = dibaca myu, merupakan huruf Yunani sebagai lambang matematis bagi rata-rata
!= = tanda pertidaksamaan yang berarti tidak sama dengan.

(Tentu saja, Anda harus menulis dengan lambang yang baku di paper Anda. Oleh karena di sini tidak disediakan lambang matematis, maka inilah cara yang saya gunakan.)

Sejauh pengalaman saya, uji 2-arah (uji 2-pihak) lebih sering digunakan dalam penelitian.

Nah…biasanya kita nggak mungkin mengambil data dari semua populasi, sehingga kita hanya mengambil sample dari masing-masing populasi.

Bagaimana kita membandingkannya??

Biasanya kita membandingkan nilai dua kelompok data dengan menggunakan membandingkan Mean dari masing-masing kelompok Sample.

Pertanyaannya: jika kita telah mengetahui Mean dari dua kelompok sample Berbeda, apakah kita bisa menarik kesimpulan bahwa Mean dari ke dua Populasinya juga berbeda??

Contoh kasus:

Saya mau minta pendapat dari 17 mahasiswi (cewek) dan 17 mahasiswa (cowok) saya tentang Penelitian dengan menggunakan hewan sebagai object nya apakah Jahat/Kejam atau Tidak. Pertanyaan berupa Likert Scale 1-7 dari “Sangat Tidak Jahat” sampai “Sangat Jahat Sekali”

Ternyata hasil yang saya peroleh data:

Banyak sample     Mean        Variance

Mahasiswi (cewek)……..17…………………..5,35 …………….2,74

Mahasiswi (cowok)……..17…………………..3,88 …………….2,99

Disini kita lihat, ternyata berdasar nilai Mean, Mahasiswi berpendapat lebih Jahat daripada Mahasiswa..yakni dengan selisih nilai Mean 1,47 lebih tinggi.

Benar……jika kita mengatakan Nilai Mean kedua kelompok sample itu Berbeda, dan Sample Mahasiswi berpendapat “lebih jahat” daripada sample Mahasiswa.

Tetapi nilai ini tidak penting, jauh lebih penting kesimpulan apakah berarti Mean Populasi Mahasiswi “Lebih Jahat” dari Mean Populasi Mahasiswa?

Untuk menarik kesimpulan Perbedaan pada level POPULASI, ada 3 asumsi yang harus dipenuhi:

1. Ke dua populasi memiliki nilai Variance yang sama (homogeneity of variance)

2. Nilai data kedua populasi sama-sama terdistribusi Normal

3. Masing-masing kelompok sample Independent terhadap nilai data kelompok lain. Maksudnya satu kelompok sample menghasilkan satu kelompok data. Kelompok data yang lain diambilkan dari kelompok sample yang lain.

Null Hypothesis nya (dugaan awal) adalah “Selisih antara kedua Mean Populasi=0″ atau “Kedua Populasi TIDAK BERBEDA“

dari kalimat nasehat saya ini, benernya saya udah bikin asumsi adanya hubungan (korelasi/correlation/relationship/association) antara

Frequency latihan sepakbola –> Kemampuan sepakbola

Benarkah??

Gimana sih caranya menganalisis ada/tidaknya hubungan 2 variables menurut statistics?

Cara paling sederhana untuk menganalisis ada/tidaknya hubungan antara 2 variable adalah dengan melihat ada/tidaknya hubungan antara variance kedua variable itu (atau disebut “covariance“).  Maksudnya?

Variance itu maksudnya variety nilai antara ke dua variable tersebut. Jika variable 1 berubah nilainya, kita lihat apakah variable 2 juga berubah, dan kita lihat apakah perubahan yang terjadi setiap waktu atau setiap case/sample konsisten arahnya (+ atau negatif).

Ingat, variance atau dilambangkan s kuadrat, rumusnya kan:

Gimana ngitung Hubungan antar variance atau “covariance”:

rumus Covariance ini disebut juga cross-product deviation
dengan rumus covariance ini jika misalnya variance variable 1 (x) dan variable 2 (y) berbeda arahnya (yg satu lebih besar dari Mean yg satu lebih kecil) maka nilai covariance nya juga akan menghasilkan nilai negatif (-) karena perkalian + dengan -. Sehingga nilai covariance juga menunjukkan arah hubungan/correlation dua variable tersebut (searah atau berlawanan arah).

Catatan!!!: rumus Covariance diatas belumlah Covariance yg ter-standard (standardized covariance), maksudnya nilai covariance akan bisa berubah-ubah tergantung dari measurement unit (satuan pengukuran) dari tiap-tiap variable (contoh: kalo variable dihitung pake meter kemudian ingin kita ubah nilai tiap2 item variable menjadi cm maka tiap item kita kalikan 100, hasilnya nilai covariance nya pun juga akan berubah significant juga).

Nah…agar nilai covariance dapat independent dr apapun satuan pengukurannya maka covariance perlu di standard-kan (=standardized covariance).

Standardized Covariance kita peroleh dengan membagi Covariance dua variable dengan Standard Deviation dua variable tersebut:

r = cov (x,y) / S (x,y)

rumus ngitung Standard Deviation untuk Sample (S) dan untuk polulasi (delta) bisa diingat lagi di http://tonyteaching.wordpress.com/2010/09/16/yuk-mendeskripsikan-data-kita/

Standardized covariance ini disebut = “Correlation coefficient” = disebut juga “Pearson correlation coefficient“

sehingga nilai standardized covariance atau correlation coeeficient berkisar antara -1 (berhubungan kuat dengan nilai hubungan terbalik) hingga +1 (berhubungan kuat dengan nilai hubungan searah).

Klasifikasi besar correlation

Menurut Cohen (1988, 1992) di buku Andi Field (2009, pp. 57):

r= 0.10 –> “Small effect” karena the effect explains 1% of the total variance (r kuadrat)

r= 0.30 –> “Medium effect” karena the effect explains 9% of the total variance

r= 0.50 –> “Large effect” karena the effect explains 25% of the total variance

Confidence Interval untuk Correlation Coefficient

Nilai correlation coefficient pun (r) selain dinilai berdasarkan besar nilai r mendekati 1/-1 juga dapat dinilai dari probabilitas nilai corellationnya tidak sama dengan 0 (probabilitas different from ‘no relationship’).

Biasanya kita tertarik mencari

95% confidence interval = significance at p < 0.05 atau dilambangkan *

99% confidence interval = significance at p < 0.01 atau **

99.9% confidence interval = significance at p < 0.001 atau ***

Ingat: Correlation bukan berarti Sebab (Causality)!!!

Saat kita menganalisis correlation atau r, nilai hubungan atau korelasi BUKAN BERARTI ‘sebab-akibat’

Dua variable yang memiliki corelation berarti keduanya pasti berhubungan tetapi tidak musti yang satu sebab yang lain,
hubungan bisa saja:

A –> X –> – Y –> B  (jadi disini hubungan A dengan B bukan sebab akibat langsung, bisa jadi ada ‘third-variable’ atau ‘forth-variable’)

Ingat: Correlation juga tidak menunjukkan Arah causality!!!

Jadi jika kita punya r kuat antara A dengan X tidak bisa kita katakan ‘A menyebabkan X’ saja..karena bisa jadi ‘X menyebabkan A’ juga
Jadi lebih tepat kita katakan ‘X memiliki hubungan positif dengan A’ itu aja!