Stat Review packet 4 Statistical Inference

what are the 2 common types of questions in psychology that are addressed by Inferential Statistics?

1) Case I Research 2) Case II Research

What is the formula for CI of 99%?

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In order to be able to make inferences/generalize your results to the population, it is important to____?

have a sample that is REPRESENTATIVE of the population. (where the sample has the same variability as the population)

What are Confidence Intervals?

Just how SE's help us understand how close the statistic is to the parameter (small SE = ur statistic is close to the parameter), CONFIDENCE INTERVALS help us understand it even more. Confidence intervals are usually a high number, 90, 95, or 99 percent. Before we learned how to get a mean (__). But you can also say "I'm pretty sure, 95% sure that the mean falls b/w __ and __" confidence intervals-can have on many different statistics, but most commonly computed on the mean. For a particular statistic (e.g. the mean), the size of a CI depends on three things: 1) the level of confidence selected (usually 95%) 2) how variable the scores are in the sample 3) the size of the sample

What are interval estimations?

sampling errors, standard errors (SE), and confidence intervals.

How does the selection of different CI's effect ur guess about the population mean?

A confidence interval will be smaller when the level of confidence is lower, the scores vary less (i.e. are more homogeneous), and the sample is large. *If its 95% CI, then the # will be smaller ex: 45-55 but if its 99% CI, the # will be larger ex: 40-70

Give an example of how a researcher would make an inference about a population if he's interested in knowing whether a new tx works for ppl who are afraid of snakes.

He would 1) select a SAMPLE from the population of ppl who are afraid of snakes, try the tx on that sample (ex: half in control group) 2) study/observe the results of the tx 3) and then try to GENERALIZE these results to the POPULATION of ppl with snake phobias. That is, he would try to make an INFERENCE about the population based on his observations of a sample.

What is Hypothesis Testing?

Hypothesis testing is a method for answering the research questions: 1. Does the sample belong to a particular population? (Case I) 2. Do the two samples/populations differ? (Case II)

A confidence interval tells you how confident u are that the mean falls b/w certain numbers. There is also another way researchers guess the population parameter. What is it?

POINT ESTIMATION- is another form of estimation and here again, an educated guess is made from the sample data to the population parameter. But here, its easier for the researcher cuz all he does is gets the statistics from the sample data and then says that the unknown value of the population parameter is the same as the data-based-number. ex: " Because the sample based statistic turned out equal to__, my best guess is that the value of the parameter is also equal to that particular value" (buck p. 124) *BUT point estimation is likely to produce statements that are incorrect. (interval estimation [ex: CI] is better to use than point estimation)

Before we talked about how to summarize data (using frequency distributions/graphs) and how to talk about the strength of a relationship b/w 2 variables. But at other times, researchers want to do more than just talk about the data, they want to make conclusions about a larger group by taking a sample of that group. They want to generalize their results...In this case, when your data is based on SAMPLE data but ur trying to make a statement about the POPULATION, then this is called_______

Statistical Inferences/Inferential Statistics. (when you take a sample and you try to generalize to the larger population, your educated guess is the statistical inference. a researcher uses info from a known value of a sample statistic to make an educated guess of the unknown value of the population parameter. If for ex; the focus is on the mean, then info about the known value of M is used to make an educated guess about the value of mue

What is sampling error? explain and then give the exact definition.

When you take a sample from a population, u try to get the value of the sample and wish it'll be identical to the population value. But its unlikely that the sample mean will be identical with the population mean (mue). It is much more likely that the population mue is different from the sample. SO sampling error refers to the magnitude of the difference b/w the sample and the population. SAMPLING ERROR definition: *The difference between the STATISTIC computed from the SAMPLE data and the POPULATION PARAMETER (which is usually unknown). ex: difference b/w r and "row" (sample vs population). These are usually not equal (rarely do you get a sampling error of 0 b/c no sample is EXACTLY like the population)

Statistical Inference refers to ____?

a method of making inferences on the bases of limited information (data)

Any statistic that is used to estimate a population parameter is called what?

an ESTIMATOR.

What is the symbol for standard deviation for the population? *go to buck p. 95 and write all symbols

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Attach packet 8 here and study!

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Why do we use statistical inference?

1) bc its too costly/time consuming to get data from the ENTIRE population 2) even if you did get data from EVERYONE, its NOW and future ppl can be different so you can't generalize.

In research, we have 3 ideal steps. We____?

1) randomly select a SAMPLE from a population of interest 2) study the SAMPLE (ex: measure anxiety/IQ/how ppl respond to a tx) and 3)generalize the results from the sample to the population. Its the POPULATION that we're interested in, not merely the sample. *the last step # 3 is when we draw an INFERENCE about a population based on what we observed/measured from the sample. Note: this is important b/c we want to know about the POPULATION but we can't study everyone in the population so we take a little sample from the population and study the sample. But we're not interested about the SAMPLE conclusions, we want to make conclusions about the POPULATION & this is how we make inferences. If we were just making conclusions about the sample, we wouldn't need to do statistics (ex: getting average age of ppl in one class).

How else can you do Case II research?

A slightly different example involves 2 groups which are created rather than simply observed (as with the income example). A group of people with snake phobia is sampled, and each person is randomly assigned to a therapy group or a control group. The therapy group is given some therapy and the control group some other (placebo) treatment. Afterwards, the people in both groups are tested to determine their level of snake phobia. Before the therapy, the 2 groups represented populations with the same mean. After therapy, if the means of the two groups differ greatly, the researcher concludes that the groups now represent samples from populations with different means. This is equivalent to saying that the therapy had an effect, or was effective. ex: saying the mean of the therapy group is now different form the mean of the control group (2 groups, 2 means = Case II).

Explain Case II research:

Case II research is much more common. Here you have 2 groups/2 different samples that differ in some way. ex: male psychologists vs. female psychologists = 2 groups. Case II research asks: Do two groups differ in some way? Example: Do male psychologists make more money than female psychologists among CSPP alumni? More specifically, do two sets of observations (data) represent samples from identical populations (the same population) or different populations? EXAMPLE: 1) a HYPOTHESIS is made about whether there is a difference. ex: Male CSPP alumni and Female CSPP alumni have equal incomes. 2) Two sets of observations are made, i.e., 2 groups are sampled. ex: male and female CSPP alumni are sampled and each person's income is noted. 3) The mean of each group is calculated. *IF the two groups have very unequal means, the researcher concludes that the population means differ. ex: A mean is calculated for the men and a mean is calculated for the women. If the mean incomes of males and females in the sample differ, the researcher concludes that the population of male and female alumni have different incomes, i.e., their incomes are NOT equal. (reject the null hypothesis) {Note: in case I, we only calculate 1 mean and compared it to the norm that we already knew. Here, were calculating 2 means and comparing it to each other}

Explain what Case I research:

In Case I research - you only have 1 sample and you only compute 1 mean, and ur comparing the mean to a mean that already exists. (you just have 1 sample thats why its called case 1) *Case I research asks, "does a particular sample of observations belong to a hypothesized population of observations? This is for ex: when we want to know if the norm for a test apply to African Am. kids We'd get the norm and then collect data from African Am kids to see if THEIR mean corresponds to the mean of the norm (compare it). This is how ppl find out when the norms aren't appropriate for a certain population. Here, to begin with, you have a norm on a test. Then you collect data from the sample of the population that ur interested in (ex: CSPP students/African Am's) and then u test them and you get a mean. And then you COMPARE and see if the mean in the norms are appropriate for ALL that group (all CSPP students) This is case I. EXAMPLE: 1) A HYPOTHESIS is made about a population. This hypothesis involves a PARAMETER, usually the mean ("mue"). ex: CSPP students have a mean creativity score of 100 on a particular test 2) A random sample of people are selected and data is gathered on each of them. ex: select a random sample of CSPP students and give each a creativity test. 3) an INFERENCE is made (conclusions drawn) about whether the people in the sample belong to the hypothesized population or to some other population. ex: conclude either that the average creativity score of CSPP students is 100 OR that u were wrong and it is not 100.

In order to distinguish population parameters from sample statistics, parameters are represented by Greek letters and statistics by regular (Latin) letters. For example: ( *see packet 9, pg 2)

Mean: for SAMPLE = Mean for POPULATION = ("mue") Variance for SAMPLE = Variance for POPULATION = (sigma squared)

Since a sample is generally much smaller than the populaton, estimates can be inaccurate. For example, the mean traditionalism of a sample of 100 college women may not be a good estimator of the average traditionalism in the population of college women. How does statistics help us with this?

Statistics gives us a way to determine the likelihood (or probability) that a particular inference is inaccurate (e.g. how likely it is that our estimate of the average traditionalism of college women is inaccurate). ex: imagine the difference u'd get if ur sample was form a religious college vs. a liberal college. That would influence what you got. Have to always pay attention to the sample. Where do the ppl come from? How did they get there? These all influences the results

What is a 95% confidence interval? And what is the formula used for 95% CI?

The 95% confidence interval is that interval for which the probability is .95 that the POPULATION mean falls within the interval. This interval is given by: *see packet 8 .

What is the Standard Error? What is Standard Error of the Mean?

The Standard Error (SE) is a # that tells you how much sampling error is likely to occur (how much the statistic varies from the parameter) IF the SE is small, then we should expect the statistic (sample) to approximate closely to the value of the Parameter (population). If the SE is large, this means theres a big discrepancy b/w the statistic (sample) and parameter (population). Another way to look at it is: if the SEM is small, we expect the means of other samples to be close to the mean of a particular sample taken; in this case, the sample mean is a good estimate of the population mean. before you did standard deviation of SCORES. But if you had a bunch of MEANS & not scores, then if you graph it, the standard deviation of this is called "the Standard Error of the Mean" when you read an article and it tells you the sampling error (SE), then the author should be commended cuz they're helping us remember that they're only making educated guesses as to parameters.

When can conclusions from the sample data be generalized to the population?

When the sample is representative of the population, then conclusions from sample data can be generalized to the population--that is, the conclusions are valid. If the sample is not representative, conclusions may or may not be valid, i.e. applicable to the population.

What is the relationship between Confidence Intervals and Hypothesis testing?

You REJECT the null hypothesis if the observed z is < -1.96 or > 1.96 alpha= .05 The confidence interval (1-alpha), here (1-.05) = .95 When the confidence interval around the sample mean __ does NOT include the mean in the null hypothesis, the null hypothesis would be rejected. Note: You WANT to Reject the null hypothesis ex: "yes there IS a relationship b/w CBT and lowered depression"

What are estimators? Give an example of how a formula is used to estimate?

____ is an estimate of the population mean; ____ is an estimate of the population variance. Also called estimators. ex: (see packet 9, p 2)

How can you best get a sample thats representative of the population?

by RANDOM SAMPLING aka Random Selection. In a random sample, each person in the population has an EQUAL CHANCE of being included in the sample.

Statistical Inference is ____ and involves _____?

it's an educated guess about the population. It involves 1) ESTIMATION 2) HYPOTHESIS TESTING

When analyzing data, there will always be two numerical values:

one of these is in the SAMPLE = the STATISTIC, and the there is in the POPULATION = PARAMETER. (the parameter of course can never be computed b/c u can only collect data from only a portion of the population) *so what we do is take the statistics that we got from our data and use that to ESTIMATE the parameters of the population. For ex: the sample mean ( a statistic ) is used to estimate the mean of the population (a parameter "mue") (statistic thats used to estimate parameter is called an estimator) *This process involves making INFERENCES from the sample data to the population.

What does inferential statistic ask?

what can you conclude about the population on the basis of sample data (given that you know that estimates of population parameters based on sample statistics may be inaccurate)