# Normal or Gaussian Distribution

## Characteristics of Normal Distribution

– Tails should meet the axis at infinity

– Bell-shaped distribution

– Mean = mode = median

– The area under the curve is 1 standard deviation away from the mean and makes up 68% of the entire distribution under the curve (This means that if you randomly select a point under the curve, there is a 68% chance it will fall one standard deviation from the mean)

– The area under the curve 1.96 SD (round to two) away from the mean makes up 95% of the entire distribution under the curve (This means that if you randomly select a point under the curve, there is a 95% chance it will fall 2 standard deviations from the mean)

– The sample mean = mean of the population

– The standard deviation of the mean distribution or standard error = (SD of the population)/(square root of the number of scores)

– The standard error indicates the degree to which sample means deviate from the mean

– The sample mean distribution converges to normal distribution as the size of the sample increases

– The bell-shaped curve can also be reflected in the lay-out of a histrogram

Here the SD is 15 units

## Questions Dealing with Standard Deviation

Question: Assume the standard deviation is 10 and the mean score is 100. If you randomly select any point 1 standard deviation from the mean, what would be your range?

Answer: The range would be between 90 and 110. As one standard deviation is 10 units left or right. You could also say that you have a 68% chance of randomly picking a score between 90 and 110 on the this graph.

Question: Assume the standard deviation is 10 and the mean score is 100. If you randomly select any point 2 standard deviations from the mean, what would your range be?

Answer: The range would be between 80 and 120. As one standard deviation is 10 units left or right, 2 standard deviations would be 20 units left or right. You could also say that you have a 95% of randomly picking a score between 80 and 120 on this graph.

N.B: 95% is the commonly accepted probability, which is the alpha level or confidence level in psychological studies for rejecting the null hypothesis is p<0.05.

## The z-Score

It is possible to convert all normal distributions to the standard normal distribution.

For a standard normal distribution the mean has to equal 0 and the SD has to equal 1.

You can find the z-score by subtracting the mean from each data point, and then dividing the this zero-meaned data by the standard deviation.

If your final data point is +1, this point is one standard deviation above the mean. If your final data point is -3, this point is 3 standard deviations below the mean. The z-score is particularly useful for comparing data across different situations.

## Error Bar Charts

Error bar charts are away of representing the confidence interval. Error bars display your mean means as a point on a chart and a vertical line through the mean point that represents the confidence interval. The longer the line, the longer the confidence interval. Error bar charts can also be used to see if two population means differ from each other by comparing confidence interval. If the confidence intervals do not overlap we can be 95% confident that both population means fall within the intervals indicated and therefore do not overlap.

Bibliography

ZHENG, Y. (2013). Referencing and citation – Harvard style, from PSY104 Methods and Reasoning for Psychologists. University of Sheffield, Richard Roberts Building on 11th February. Available from: Blackboard.
[Accessed 4/02/13].

# The Statistical t-Test

The statistical t-test is used to compare two conditions, specifically the means of two conditions. A t-test can be applied to both a between participants and within participants design. This test can only be done on normally distributed data, and as such is a parametric test. The purpose of the t-test is to decide whether or not the difference between the means of the two conditions is statistically significant. If the difference is statistically significant we are able to except our experimental hypothesis and also give some directionality to our hypothesis. If the difference between the means of the two conditions is not statistically significant we must reject our experimental hypothesis and accept the null hypothesis. The t-score is technically more than just the difference between the means. Just like normal data distribution, the t-score also has a 95% confidence interval, which means for the difference between the means to be statistically significant, the alpha level needs to be less than 0.05. The alpha level was decided on 0.05 to try and reduce the amount of type I and type II errors. Type I errors is when we reject the null hypothesis but should not have, and type II errors is when we reject the experimental hypothesis but we should not have. If the sample size is large and the null hypothesis is true, the distribution of the t-scores is also normal. The smaller the sample size becomes, the more tail-heavy the distribution becomes.

The way this is interpreted is if two groups come from the same population,  then 95% of the time, the t-score (reflecting the difference in the means) will be within the 95% area under the graph of the data.

## Degrees of Freedom

Degrees of freedom for within-participants design is the same as the number of participants.

Degrees of freedom for between-participants design is the (number of participants in group 1 -1) + (number of Ps in group 2 -1)

SPSS will do the math for you!

## Basically…

When you start with your mean scores, assume that the null hypothesis is true and that there is no significant difference between the means.

Then set your significance level at p<0.05 or the alpha level, which is the same thing. SPSS should do this automatically.

Then using SPSS calculate the t-score.

If the t-score is within the 95% interval: accept the null hypothesis and reject the experimental hypothesis.

If the t-score is outside the 95% interval: reject the null hypothesis and accept the experimental hypothesis. You have now established that there is a significant difference between the two means.

This is an example of the type of output that will be given by SPSS. From this output you can answer the following questions:

Question 1: Is the experimental design within or between participants?

Answer: The experimental design is within. You can tell this from the heading where it says paired difference.

Question 2: What is the t-score?

Question 3: What are the degrees of freedom?

Answer: The degrees of freedom (df) is 77.

Question 4: Is it two-tailed or one-tailed test?

Answer: It is two tailed as shown in the last box. Sig. (2-tailed).

Question 5: Is the result significant at an alpha level of 0.05? Why?

Answer: The result is significant at the alpha level because p<0.001, which obviously is less than 0.05.

## Reporting the Results

This is an example of how you would report the following data for the results section of a lab report:

The mean and standard deviation of participants’ reaction time under conditions 1 and 2 are given in Table (not in this post). The data were analysed using a two-tailed within-participants t-test and an alpha level of 0.05.There is a statistically significant difference between the ideal IQ and the estimated IQ, with the estimated IQ significantly lower than IQ for an ideal job, t(77) = -9.60, p <0.001.

# Designing a Research Experiment

## Steps for Experimental Design

1. Figure out what you want to explore and formulate a research question based on a previous theory.

2. Formulate a hypothesis

4. Decide which type of experiment is appropriate

5. Carry out statistical analysis and discussion

## The Hypothesis

When you are designing an experiment in psychology you will have an experimental hypothesis and a null hypothesis. Both of these will predict how the variables relate to another.

The null hypothesis predicts that there will be no relationship between the variables.

The experimental hypothesis predicts that where will be a relationship between the variables; however, there are two kinds of experimental hypotheses. A non-directional hypothesis will only say that there will be a relationship between the variables. For example, caffeine will have an effect on motor skills.  A directional hypothesis will state what kind of relationship will exist between the variables. For example, caffeine will have a positive effect on motor skills OR caffeine will have a negative effect on motor skills. If we can accept the experimental hypothesis, we can reject the null hypothesis and vice versa.

## Variables

In an experiment you must have an independent variable and a dependent variable. The independent variable is the manipulated variable or in the case of categorical variable, one with limited levels. For example nationality (Levels: English and Chinese).  The dependent variable is what the independent variable will have a causal effect on.

There are also confounding variables. However, unlike the independent and dependent variable, we want to avoid confounding variables in our experiments as much as possible. Confounding variables are variables that could influence the dependent variable. They have a systematic effect on the conditions. To reduce the effect of confounding variables you need to ensure the the independent variable is the only difference between experimental conditions. This includes random assignment, random sampling, controlling for age, gender and skills, etc.

## Deciding on the Right Experiment

In psychological experiments your two options are within participants design (or related samples) and between participants design (or unrelated samples).

Within participants designs compare the performance of the person or participant across all the conditions. This is done through repeated measures or a related design. This type of design is usually preferable. The advantages are that you need fewer participants, you have much better control of confounding variables because you are comparing the person against themselves. Of course, there are also disadvantages of a within participant design. The first one is called the carry-over effect, which means that once you have learnt a skill it’s hard to unlearn it or forget it. This means that if a person makes progress in a different condition it could just be down to practice. The second disadvantage is the order effect, which is when practice, fatigue or just plain boredom affects the performance of the participant. Luckily, most order effects can be avoided by counter balancing. This is when you randomly assign participants to the conditions, so that one person’s first task might be the second person’s fourth task. Controlling for confounding variables helps increase the experiments internal validity (the extend to which we can relate changes in the IV to the DV). External validity relates to how well the findings can be generalised to the population at large. External validity relies on random assignment, random sampling and ensuring that factors such as setting do not differ from experimental settings to the real world.

Between participants designs compare the performance of participants each in different conditions. One participant is only exposed to one of the conditions. Between participant design is the best alternative for within participant design. It should be used when you are trying to make comparisons in performance across different groups like gender, age groups, culture, etc. The main advantage is not having to deal with order effects or the carry-over effect; however, you do need more participants that are far more similar to each other to avoid confounding variables. This must be done before the experiment and is known as matching participants.

Sometimes there is also a third type of experiment called a one-sample design. This is when a sample mean is compared against a known population.

Bibliography

ZHENG, Y. (2013). Referencing and citation – Harvard style, from PSY104 Methods and Reasoning for Psychologists. University of Sheffield, Richard Roberts Building on 18th February. Available from: Blackboard.
[Accessed 4/02/13].

# Methods in Systems Neuroscience: Histological Stains and Tract Tracing

## Histological Stains

Cells and major fibre tracts make up the basic structure of the brain and are observed using histological procedures. The most common histological procedures involve stains such as the Nissl and Weil stains. This particular cell stain stains the Nissl substance (granular bodies) found in neuronal cytoplasms. The Nissl bodies are composed of rough endoplasmic reticulum and free polyribosomes and as such are the site of protein synthesis. For a Nissl stain, neurones are held in a parofromaldehyde or formalin fixed tissue. The selective stain uses aniline dye, which colours the somas and dendrites of neurones blue, or more specifically their ribosomal RNA. The Weil fibre stains is regressive, requiring differentiation. Weil fibre stains use a hematoxylin based stain, which dyes myelin and red blood cells dark red. Weil is unique in that is can be used on a frozen section of tissue.

## Tract Tracing

Anterograde tract tracing is used to identify projections than run from cell bodies to axon terminals. Various tracer molecules are used including but not limited to the green fluorescent protein, lipophilic dyes and radioactively tagged amino acids. Genetic tracers are also used including viruses and proteins. The most common genetic tracers are the Herpes complex virus type 1 (HSV) and the Rhabdoviruses. Lipophilic dyes are commonly used in electrophysiology as anterograde tracer; however, they are not selectively unidirectional nor are they actively transported across the synaptic cleft. An example of an anterograde projection is the transmission of visual information from the superior colliculus to the substantial nigra.

Retrograde tract tracers are used to identify projections from axonal terminals to somas. The most common retrograde tracers are viral stains such as the modified rabies virus or pseudorabies virus (PRV) or Batha stain. The PRV infection spreads upstream through a pathway of linked neurones. An example of retrograde projections is the transmission of nociceptive information from the parabrachial nucleus to dopaminergic neurones in the midbrain.

Also, bidirectional tracers, as the name suggests, can work both in an anterograde and retrograde fashion. Common bidirectional tracers include WGA-HRP, biotinylated dextran and cholera toxin subunit b. A major pitfall of bidirectional tracers or dyes is that they can move retrograde then anterograde along branches axon collateral falsely indicating an anterograde tracing. In other words, one might falsely observe that A projects to C (see diagramme above). It is important to correctly identify the direction of projections as it helps identify the morphology of a cell. Cells with different morphologies, unsurprisingly, have different processing capacities. An example of a branched projection is the tectonigral projection.

Finally, simultaneously anterograde and retrograde tracers do exist; however, not as common as one or the other. The use of tracers can be accompanied by TH immunochemistry to help identify the locations of certain neurones.

Bibliography:

Coizet, V., et al. (2010). “The parabrachial nucleus is a critical link in the transmission of short-latency nociceptive information to midbrain dopaminergic neurons.” Neuroscience 168(1): 263-272.

Comoli, E., et al. (2003). “A direct projection from superior colliculus to substantia nigra for detecting salient visual events.” Nat Neurosci 6(9): 974-980.

Fung, K. (n.d.). Stains in Neuropathology. Retrieved January 15, 2015, from http://moon.ouhsc.edu/kfung/JTY1/NeuroHelp/ZNEWBS12.htm

QBI Histology and Microscopy. (n.d.). Retrieved January 15, 2015, from http://web.qbi.uq.edu.au/microscopy/cresyl-violet-staining-nissl-staining/

Redgrave, P. (Director) (2014, November 11). Methods in Systems Neuroscience. BMS224 Brain and Behaviour 1 . Lecture conducted from University of Sheffield , Sheffield.

# Methods Used for Studying Infants’ Perception

Part of getting onto a good masters or Ph.D programme means having real-life experience. As only a second year undergraduate that can sometimes seem like an age away, but time really does fly by. In order to get some experience in research I transcribed videos for a developmental researcher at my department. Even though my job was pretty menial in the whole scale of things, writing down all the speech and movements of infants really made me appreciate something substantial; infants are very hard to understand and observe. Their intentions, their desires and even just their knowledge can be difficult to interpret. As such, psychologists use a set of methods to study infant perception, intentions, desires and capabilities.

This post will deal with studying infant perception.

Preference Technique

Basic set-up

1. A researcher presents two stimuli to an infant simultaneously

2. The researcher monitors the infant’s eye movement. Researchers use various techniques for this, one being the ASL Model 504.

3. If the infant looks more at one stimulus than the other, it is inferred that the infant prefers that stimulus over the other.

If accurate, measures of the eye movements can be made, this technique is quite simple and effective. The infants preference can be inferred because of habituation, a fancy word for boredom.

Habituation

Habituation and dishabituation are another method used to study infant perception and preference. After looking at a stimulus for a certain amount of time, we become bored of it. Just like after awhile we stop feeling the clothes on our body. Our brain gets bored with the touch sensation, and so eventually it stops informing us of it. On this basis, psychologists infer that babies will stop looking at a stimulus if they gets bored of it. If a stimulus is then presented with a new stimulus, it is likely he or she will prefer looking at the new stimulus that the infant has not seen before. If the infant does prefer the new stimulus, we can infer that the infant is capable of discriminating between the two stimuli. Discrimination between two stimuli allows researchers to detect the stage of perceptual development of infant has reached.

Conditioning

Classical and operational conditioning are terms you should be familiar with have you ever taken an introductory psychology course. Conditioning with infants consists of the same learning system. Fortunately, infant studies usually just involve rewarding the infant with pleasant sounds or images, usually of or from their mother.

Basic set-up

1. Infant is given a dummy or pacifier

2. Researcher waits for the infant to begin sucking on it at their usual rate

3. If the infant begins sucking at a faster rate than usual they are rewarded with the sound of their mothers voice

4. The infant will soon learn that as long as her or she continues sucking at the increased rate, they will hear their mother’s voice

5. After awhile, habituation sets in as the baby loses interest in the sound and their sucking rate decreases

6. The researcher then proceeds to introduce a new sound

7. If the infant is capable of discriminating the new sounds, they will begin to suck more again to her this new sound

All of these various tests of perception, as mentioned above are used to measure the development of infants.

# Dispersion and Central Tendency

I think people underestimate the amount of statistics that is necessary for psychological research. Luckily, as long as you understand the theory behind the statistics, most of the math is done by a computer. For my undergraduate course we use a programme called SPSS, which you can buy of amazon but most universities supply for a reduced price for their students. This post will be an introduction to the basics of statistical theory used in psychological research.

## Levels of Measurement

Nominal measurement is the lowest level of measurement, and includes categorical data and measures of frequencies.

Ordinal measurement involves rating scales to measure participant responses.

Interval measurement involves equal intervals; for example, measuring temperature. Interval measurement has no absolute zero worth.

Ratio measurement involves intervals with an absolute zero worth.

N.B: parametric tests can only be used with interval or ratio measurement unless you convert the data into numerical values.

## Types of Data Seen in Psychological Research

Continuous numerical data is data that can take any value within a certain range. The issue with continuous numerical data is that it is heavily dependent on the accuracy of measuring instrument.

For example: height, weight, reaction time

Discrete numerical data is data that can only take a specific value within a certain range. Questions that involve how many of something or the presence or absence of data is usually dealing with discrete numerical data.

For example: Numerical scores on a questionnaire: how many times have you been oversees?

Categorical data does not deal with a specific numerical value, but rather what group variables can be placed into. The issue with categorical data is that it can be too extreme. The people under one label can be very different from each other. Plus, it is very difficult to make appropriate intervals for categorical data.

For example: gender, nationality, etc.Categorical data can also come from continuos or discrete variables

## Types of Statistics

Descriptive statistics summarise the properties of a sample of data usually through measures of central tendency and dispersion. Measures of central tendency include: mean, median and mode. Dispersion refers to the spread of data, providing information about the mean accuracy. Different measures of dispersion include: range, variance, and standard deviation.

Inferential statistics use the properties found from the descriptive statistics to make estimations of of the properties of the population.

## Central Tendency

The mean is the average score. The mode is the most frequently occurring score, and the median is the middle score (when points are organised from lowest to highest value). The mean is the preferred measure of central tendency because it takes into account all the data of the population. The problem with using the mean, however, is that is easily influenced by extreme scores.

## Dispersion

Dispersion measured the spread of data and as mentioned above, gives the mean accuracy.

The most common approach for calculating the deviance is by calculating the variance. The variance is the: (sum of the squared deviances)/(the number of observations – 1). The unit is always the square of the measurement unit. The variances indicates how much the scores differ from one another.

N.B: The squared deviances is found by calculating the difference between each observation and the mean, and then squaring this value.

Standard deviation is the square root of the variance, and is much easier to deal with because it does not have squared units like the variance.

Bibliography:

ZHENG, Y. (2013). Referencing and citation – Harvard style, from PSY104 Methods and Reasoning for Psychologists. University of Sheffield, Richard Roberts Building on 4th February. Available from: Blackboard.
[Accessed 4/02/13].