Test one guidelines (z test/ t test)

How does the z-test differ from the one-sample t-test?

Z-test: compares a sample of scores with a populations's. WHEN you know the populations variance One-sample t-test: Comparing a sample score with a populations. WHEN you DONT know the populations variance

What is the general idea for all t-tests?

"difference in values" ----------------------- "natural variability"

Type I error

Falsely rejecting the null False positive "crying wolf" Telling a man he is pregnant Our error rate for type 1 error towards the null is set at .05

Type II error

Falsely retaining the null Failing to announce the wolf Telling a women that is pregnant, that she is not

x

The value we will test (used in finding z-score)

Region of rejection

the area of a sampling distribution that lies beyond the test statistic's critical value; when a score falls within this region, H0 is rejected

What is the calculation for the z-test

( x̄/µ) -------- σx̅

***Refresh on

***how to use the z-table and t-table

Paired samples t-test calculations

(difference in means of the two samples) x̄ D - 0 ------- s(d) ------- √ n

What are the 3 steps in hypothesis testing?

1. we determine what the population (distribution) would look like if the null hypothesis were true 2. we see if our sample data are likely to have come from this distribution 3. if it is unlikely that our data came from the null hypothesis distribution, we reject the idea that the null hypothesis is the best way to describe our sample

Sampling distribution of the mean

A population is actually a distribution of sample means

Paired sample t-test logic and when is it used?

A t-test is used when you do not know the population variance. A paired sample t-test is used when you have two related levels or conditions of a SINGLE IV score differently on a continuous IV. 2 types of related: 1. repeated measures 2. match sample

Central limit theorem

As a sample of means increases in N, it will approach a normal distribution curve

Null hypothesis

H0 There is no effect (no difference) The one that, statistically, you are testing Goal: reject the null hypothesis We either support the null hypothesis or we reject the null hypothesis

Alternative hypothesis

H1: your research hypothesis There is an effect The one that you believe is true Goal: reject the null

Differences scores and when are they used

In the numerator: to compare mean difference scores to zero In the denominator: use variability in difference scores Used when we are comparing two groups with the same IV. Comparing difference of two related groups of the same IV

Degrees of freedom

N-1.

How do we estimate population variance in a independent sample t-test

Now that we have 2 sample variances and sample size, we need to pool them! Find pooled variance estimate: Two ways to do this, depending on if you know the SS (sums of squares) SS1 + SS2 Sp²= ----------- DF1+DF2 OR When we know the SD or variance. S² stands for variance (n1-1) S1² + (n2-1) S2² Sp²= ------------------------ n1+n2-2

Obtained t-value vs. critical t-value

Obtained is from the formula and where your mean score falls on the distribution. The critical t-value is found using the DF and the chart to find what number indicates the top 5% of that distribution (rejection area).

What is a matched sample measure

One of the ways levels or conditions can be related for a paired sample t-test Two different groups, measured on the same DV. Groups are either connected naturally, explicitly, connected or matched in specific pairs.

What is a repeated sample measure

One of the ways levels or conditions can be related for a paired sample t-test Within subject's designs. Meaning several measurements from the same participants. Only 2 groups but 1 IV

S

Our sample standard deviation

What is the one-sample t -test, and when is it used?

Tests for the null hypothesis that a SAMPLE mean does not differ from the POPULATION mean This is used when we do NOT know population variance so we must estimate it based on sample size and variance

What is the logic of the z-test and when is it used?

The logic is calculating how a SAMPLE of scores compare with a POPULATION. *this is used one when we know the populations variance* We can use this type of test ONLY when we know the populations variance to compare a single score to a population

Common misunderstandings and controversies in hypothesis testing

The logic is intuitive Even research scientists cant understand what they are actually doing when using hypothesis testing Dichotomous options are potentially constraining "marginally significant" Type 1 error rates are inflated with multiple analyses on same data sets

Independent-samples t-test calculations

The long ass complication one with an Sp²

Critical value

The point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis

P-value

The probability of obtaining a test statistic at least as extreme as the one that was observed, given that the null hypothesis is true. We find levels of significance at .05 (the likelihood that the effect we found, or a bigger effect, could have occurred by chance is less than 5%) If the p-value is less than .05 (alpha), there will be a significant effect

Alpha level

The probability of rejecting the null hypothesis when the null hypothesis is true

What is the logic of hypothesis testing

The process of determining whether data supports your prediction. It is statistically impossible to demonstrate that our hypothesis is supported, instead we demonstrate that it is unlikely that our hypothesis is false Inferential tests involve hypothesis testing and the most essential statistic is the p-value

Population variance estimate s²

The sample variance will most likely underestimate the population variance, which results in "inflated" values if we simply substitute sample variance into the direct equation for Z. So, we use the t-distribution: (x-x̄)² ------ = s² N-2

The t-distribution and how it differs from the z-distribution

The t-distribution is not a standard normal distribution like the z- distribution, because the t-distribution is a family of distribution (the distribution changes based on sample size) Higher the N, higher the DF, the less there is of variability and extreme critical values. Meaning, we will need less extreme t-values to have significant effect

One tailed test

This is a directional test because we a predicting the direction of the effect (predicting that mean X is higher than mean Y) µ0 < µ1 OR µ0 > µ1

Two tailed test

This is a non-directional test because there is no prediction about the direction of the effect (we are predicting that mean X and mean Y differ, but not specifying which is higher) H0: µ0 = µ1 H1: µ0 ≠ µ1

Levels of an independent variable

Two independent groups with one between-subject IV with two levels

Independent-samples t-test logic and when is it used:

Used to compare two independent groups (one between-subjects VI with two levels)

How does variance and standard deviation relate

Variance is standard deviation squared The square root of variance is standard deviation

Pooled error term

We are adding the sample variance for both condition 1 and condition 2

How does the z-test differ from the z-score?

Z-score: comparing a single score to a population WITH knowing the pop's variance Z-test: comparing a sample of scores with a population's WITH knowing the pop's variance

The one-sample t-test is used when.. a. You are comparing a sample to a population estimate b. You know the standard deviation of the population c. When you have one independent variable d. Two of the above e. All of the above

a.

Tina tells her parents that her sister took her shoes, but it later turns out that she had misplaced them herself. Tina has committed: a. A type 1 error b. A type 2 error c. Measurement error d. Random error

a.

The Z-test is a _______________________ test that is used to determine whether a __________ differs from a population estimate a. Parametric; score b. Parametric; sample c. Non-parametric; score d. Non-parametric; sample

b.

The paired-samples test tests for the difference between ________ groups. a. Two unrelated b. Two or more unrelated c. Two related d. Two or more unrelated

c.

In the independent-sample t-test, "independent" means that a. The iv is not dependent on the DV b. The DV is not dependent on the IV c. Same participants participate in both levels of the IV d. Difference participants participate in the two levels of the IV

d.

Which of the following is the most accurate description of the goal of hypothesis testing? a. The goal is to be able to say that it is unlikely that our sample distribution is well-represented by the null-hypotheses distribution b. The goal is to be able to say that is it likely that our sample distribution is well-represented by the null hypothesis distribution c. The goal is to reject the null hypothesis and retain the alternative hypothesis d. The goal is to retain the null hypothesis and to reject the alternative hypothesis e. A and C f. A and D g. B and C h. B and D

e.

Between- vs. within-subjects designs

o A between subject variable is a variable that is either given to one condition or the other but not both o A within subject variable is two levels of a variable that gets exposed to the same group of participants. Participants see both levels

σ

population standard deviation

σ²

population variance

µ

population mean

x̄

sample mean

N

sample size

s²

sample variance

SD

standard deviation

σx̅

standard error of the mean

Calculation for a one-sample t-test

x̄-µ ----- s = t ----- √ n

What is the calculation for (standard error of the mean) σx̅

σ --- (√ n) Needed in order to do a Z-test